Download How do we distinguish substances?

UNIT 1
How do we
distinguish
substances?
Our world is characterized by its diversity at all levels, from
the wide variety of living organisms to the multitude of
materials that make everything that surrounds us. Understanding the diversity of the material world has been
particularly important for our survival on the planet.
The ability to detect, identify, separate, and quantify
different types of substances has allowed humans to
take advantage of the many natural resources that
Earth has to offer. These same abilities are also likely to
help us save the planet from the environmental consequences of our decisions and actions.
The central goal of this unit is thus to help you understand and apply basic ideas and ways of thinking
that can be used to distinguish the different substances
present in a variety of systems of interest. Although the
ideas and models that we will discuss are useful in many
relevant contexts, to illustrate their power we will analyze
many examples related to our own planet’s atmosphere, trying
to answer questions such as:
What is it made of?
How do we separate its components?
How do we identify them?
How do we explain their properties?
How do we model their behavior?
2
Chemical Thinking
UNIT 1 MODULES
M1. Searching for Differences
Identifying differences that allow us to
separate components.
M2. Modeling Matter
Using the particulate model of matter to
explain differences.
M3. Comparing Masses
Characterizing differences in particle
mass and number.
M4. Determining Composition
Characterizing differences in particle
composition.
3
4
MODULE 1
Searching for
Differences
Most things in our surroundings are, from the chemical point of view, complex
systems composed of many substances in different states of matter. Take, for example, something as common as the air we breathe. It contains at least a dozen
of different substances, from oxygen gas to microscopic water droplets to solid
sodium chloride particles. This chemical complexity can be seen as a blessing and
a curse. On the one hand, the diversity of substances and phases in
our world has allowed the emergence of life in our planet and
the development of the rich natural resources that sustain it.
On the other hand, the large number of substances that
can be found in a single breath makes more difficult the
detection, identification, and isolation of the things that
can threaten that same life.
The mixed nature of our own bodies and of most of
the systems with which we interact on a daily basis poses
Earth’s
a constant challenge to many professionals. How do we deAtmosphere
tect the presence of cholesterol in a complex mixture such as our
NASA
blood? How do we identify the pollutants that may be present in our drinking
water? How do we know what substances can be found in the soil of our farms or
in the minerals that we extract from the ground? The answers to these questions
require some “chemical thinking.” For example, consider this challenge:
THE CHALLENGE
Extracting Oxygen
Imagine that you were interested in extracting pure oxygen from the atmosphere for commercial purposes. You may want to sell it to hospitals for use
in the treatment of pneumonia, emphysema, and other respiratory diseases.
•
How would you extract oxygen from air?
•
What properties of this substance would help you separate it from other
air components?
Make a list of potential strategies that you would follow to solve this problem.
Then, share and discuss your ideas with one of your classmates.
This module will help you develop the type of chemical reasoning that is used
to answer questions similar to those posed in the challenge. In particular, the central goal of the module is to help you recognize distinctive properties of chemical substances that can be used to identify and separate them.
Chemical Thinking
U1
5
How do we distinguish substances?
Differentiating Characteristics
Choosing PropertiesLET’S THINK
Air is a mixture of many substances, including nitrogen, oxygen, carbon dioxide, argon, and water. Which of the following properties would be good
“differentiating characteristics” to separate each component?
TemperatureMassViscosity
Boiling PointDensityVolume
PressureSolubility
Concentration
Share your ideas with one or more classmates. Make sure to:
•
Identify the basic features that you think a good differentiating characteristic should have.
•
Discuss why some properties in this list are not good differentiating
characteristics.
Total Ozone
Low
High
CLICK TO PLAY
In modern times, it is common for people to be interested in finding out the
chemical composition of a variety of things in their surroundings. Everybody now
expects food labels to list the contents of what we eat. Many cities around the
world monitor the presence of well known atmospheric pollutants on a regular basis. Artificial satellites detect and quantify the amount
of important substances in our atmosphere, such as
ozone and carbon dioxide, every day (see Figure 1.1).
If you think about it, the fact that we can now detect
or identify all of the substances present in a given
system is an incredible achievement of human kind.
Most of the systems we deal with, natural or artificial,
are mixtures of many different substances. Many of
these mixtures are homogeneous: combinations of
substances that have uniform composition and properties, such as clean air and drinking water, and may
look like single substances. Other mixtures are heterogeneous and they are composed of visibly different substances that can be in
the same or in different phases (e.g., solid, liquid, or gas), as is the case of many
minerals in our planet and our own body. In many cases, the composition and
properties of these systems remain constant for long periods of time, but in many
others it changes on a continuous basis. Given the diversity of the materials in our
world, how is then possible to figure out their chemical composition?
The chemical analysis of the substances present in any given system is based on
a simple assumption made by chemists about the nature of the world. It is assumed
that each substance, no matter how simple or complex, has at least one differentiating
characteristic that makes it unique. If we find this differentiating property and are
able to measure it, we are then in a good position to detect, identify, separate, and
quantify the amount of that substance in a variety of places.
Figure 1.1 NASA has developed
and launched instruments that
allow constant monitoring of the
amount of ozone in the stratosphere. Click on the movie to see
how ozone amounts vary during
the year over Antarctica.
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MODULE 1
Searching for Differences
Good differentiating characteristics should have values that do not depend on
the amount of substance that we have (intensive properties). These are properties such as melting point, density, and conductivity. Properties with values that
depend on the amount of substance (extensive properties), such as mass and
volume, are not useful as differentiating characteristics because they can take either
many values for the same substance or similar values for different ones. However,
being an intensive property is not good enough for purposes of identification.
Temperature and pressure are intensive properties of a system, but they cannot be
used as differentiating characteristics for any substance because they are properties
of the entire system, and not of its individual components. We need to look for
properties with unique values for each substance that do not vary with the size of
the sample and that can be selectively measured.
For example, in the case of the air in the atmosphere, the
boiling points of the different components are very useful difTable 1.1 Air Main Components
ferentiating characteristics to separate them. The boiling point
Boiling Temperatures ( 1 atm) indicates the temperature at which the liquid phase of a subSubstance
stance becomes a gas at a given pressure and, in general, takes
o
C
K
values that vary from substance to substance. The boiling temWater
100
373.15
perature also corresponds to the temperature at which the gas
Oxygen
-182.9
90.20
turns into a liquid. Thus, if we were to gradually cool down an
Argon
-189.3
87.36
air sample at see level, we would see the different air components condensing at the temperatures shown in Table 1.1 where
Nitrogen
-195.8
77.36
we show their normal boiling points (their boiling temperatures at atmospheric pressure at see level). Using this information we could identify the substance that is condensing and separate it from the mixture.
USEFUL TOOLS
The differentiating characteristics of chemical substances are conventionally measured
at constant atmospheric temperature and
pressure. However, these quantities can be
expressed in a variety of units that is important to recognize and be able to manipulate
(check Appendix A for more details).
Units of Temperature. In the International
System of Units (SI), temperature is measured using the Kelvin scale. This is an absolute temperature scale in which the zero
of the scale (0 K) corresponds to the lowest temperature that can be theoretically
achieved. Increments in temperature are
measured in degrees Kelvin (K).
Another commonly used temperature
scale used in science and engineering is
the Celsius scale. In this system, the zero of
the scale is defined as the freezing point of
water (0 oC) and 100 oC corresponds to the
boiling temperature of the same substance.
A temperature measurement in degrees
Celsius can be transformed into degrees
Kelvin using the following relationship:
[K] = [oC] + 273.15
Thus, for example, the boiling point of water (= 100 oC) corresponds to
[K] = 100 oC + 273.15 = 373.15 K
Units of Pressure. In the SI, pressure is measured using units called Pascals (Pa). One
pascal is equivalent to a pressure of one
newton per square meter (1 N/m2). In science and engineering it is also common to
use the standard atmosphere (atm) as unit
of pressure, where 1 atm is approximately
equal to the average atmospheric pressure
at see level in our planet. Another common
unit is “millimeters of mercury” (mm Hg or
torr). Conversions between these different
units can be achieved using the following
conversion factors:
1 atm = 101, 325 Pa = 760 mm Hg
Chemical Thinking
U1
How do we distinguish substances?
Phase Transitions
The transformation from one phase to another in a pure substance at constant
pressure occurs at a well defined temperature that in many cases can be used as its
differentiating characteristic. During this phase transition, or phase change, the
chemical nature of the substance does not vary and the transition temperature can
be measured with great accuracy and precision using digital devices. Understanding phase behavior is crucial to devise successful strategies for the identification
and extraction of many substances of interest, from oxygen in the atmosphere to
caffeine in coffee beans to medicines in plants.
Changing PhasesLET’S THINK
It is almost certain that you have seen ice melting and liquid water boiling.
Imagine that you had a sample of solid water at -20 oC at atmospheric pressure
and you heated it up supplying energy at a constant rate until the temperature reached 120 oC. If during the experiment you were to measure the temperature of the sample as a function of time, as well as the amount of energy
absorbed by the system during the heating process, what would you expect to
see if you were to plot the data using the following types of graphs?
CLICK AND DRAG TO DRAW
T(oC)
100
0
CLICK TO PLAY
E
t
0
100
T(oC)
Based on your prior knowledge and experience:
•
Make a prediction of how temperature will change as a function of time.
Keep in mind that solid water turns into a liquid at 0 oC and that the
liquid becomes a gas at 100 oC.
•
Make a prediction about how the total amount of energy absorbed will
evolve as the temperature of the system increases. Consider whether
more, or less, energy will be required to change the sample from solid to
liquid than from liquid to gas.
•
Compare your predictions with those of another classmate. Discuss how
your predictions would change if you were cooling down a gas sample or
you were working with a different substance.
Keep in mind that, by convention, energy absorbed by a system is represented
using positive values while energy released is expressed with negative numbers.
How does the temperature of
the system change as
water ice melts?
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8
MODULE 1
Searching for Differences
T(oC)
Vapor cools
and condenses
Tb
Liquid cools
and solidifies
Tm
Solid cools
t
Figure 1.2 Cooling curve for a
generic substance that undergoes two phase transitions, from
gas to liquid at Tb and from liquid
to solid at Tm.
Tb
Tm
T(oC)
G
L
E
S
Figure 1.3 Amount of energy released as a function of temperature during cooling of a generic
substance that undergoes two
phase transitions, from gas to liquid at Tb and from liquid to solid
at Tm.
Phase transitions between two different states of matter share many similarities
independently of the chemical nature of the system of interest. For example, during a change of state at constant pressure the temperature of the system remains
constant until one of the phases has been fully transformed into the other. Thus,
the transition points clearly delimit the range of temperatures within which each
phase is stable at any given pressure. In the case of water, the liquid phase is stable
between 0 oC and 100 oC at 1 atm of pressure. Within these two points, adding
energy to the system will result in increasing temperatures; removing energy from
the system will cause the temperature to decrease. However, at the phase transition, the energy added or removed induces a change of state without altering the
actual temperature of the system as shown in Figure 1.2.
Common
Phase
Some changes of state require the addition
Changes
of energy, as it is the case of the transitions from
solid to liquid (melting), liquid to gas (boiling),
and from solid to gas (sublimation). The reverse
processes (solidification, condensation, and deposition, respectively) release energy into the environment and this energy needs to be removed if
we want the phase transition to occur. As shown in
Figure 1.3, these energy changes occur at constant
temperature and the amount of energy absorbed
or released varies from substance to substance. In
fact, the energy per of unit mass transferred during
a phase transition is also a differentiating characteristic of the material. In general, the larger the
change in density induced by the phase transition, the larger the energy transfer.
During a phase transition many of the physical properties of the substance
change, in some cases quite dramatically as illustrated by the drastic decrease in
density in the transition from liquid to gas. However, a phase transition is a prototypical example of a physical change in which the transformation does not alter
the chemical nature of the substance involved. In some cases, adding or removing
energy from the system could cause the substance to chemically decompose or to
react with other substances in the environment before the phase change occurs. In
these cases, it is not possible to use phase behavior as a differentiating characteristic
for the substance of interest.
USEFUL TOOLS
Adding energy to a system or removing
energy from it are common strategies to
change its properties. Being able to measure or indirectly determine the amount of
energy that is transferred is critical to control the change. In science and engineering,
energy is commonly measured using the
following units (check Appendix A for more
details).
Units of Energy. In the International System
of Units (SI), energy is measured in joules
(J). One joule (1 J) is equivalent to the energy invested in applying a force of one newton (1 N) through a distance of one meter
(1 m).
Another commonly used unit of energy is
the calorie (cal). One calorie (1 cal) is approximately equal to the amount of energy
needed to increase the temperature of one
gram (1 g) of water by 1 oC. Energy measured in calories can be transformed into
joules using the following conversion factor:
1 cal = 4.184 J
Chemical Thinking
U1
How do we distinguish substances?
9
Phase Diagrams
For any given substance, the temperatures at which any of its phases undergoes a
transition depend on the value of the external pressure. This
means that the range of temperatures in which each phase
is stable changes with pressure. For example, liquid water is
stable between 0 oC and 100 oC at 1 atm of pressure but if
the pressure is increased to 50 atm, melting will now occur
at -0.37 oC while the liquid will boil at 262.5 oC. In this
case, increasing the pressure widens the range of temperatures in which liquid water is stable. By carefully measuring the temperatures at which a phase transition occurs at
different pressures one can build a graphical representation
that depicts the zones of stability for each phase and their
corresponding boundaries (the temperatures and pressures at which a transition
to another phase will occur). These graphical representations of phase change and
stability are called phase diagrams (see Figure 1.4) and each substance will have a
characteristic phase diagram.
Figure 1.4 Phase diagram for
a generic substance. The letters
indicate the phase that is stable
at that particular temperature (T)
and pressure (P): Gas (G), liquid
(L), or solid(L). The solid lines indicate the T and P values at which
a phase transition will occur.
Water’s CaseLET’S THINK
The following tables include experimental information about the temperatures at which water undergoes a phase transition at different pressures.
Liquid-Solid
Solid-Gas
T
(K)
P
(mm Hg)
T
(K)
P
(mm Hg)
T
(K)
P
(mm Hg)
273.16
4.58
273.16
4.58
248.15
0.475
324.77
100
273.16
100
253.15
0.774
339.65
200
273.15
200
258.15
1.24
356.15
400
273.15
400
263.15
1.95
366.68
600
273.15
600
268.15
3.01
374.58
800
273.15
800
273.16
4.58
•
Use this information to build the phase diagram for water in the range
from -20 oC to 120 oC and from 0 to 800 mm
Hg.
•
Indicate on the diagram the areas in which the
solid, liquid, and gas phases are stable.
•
Estimate the boiling point of water in Tucson,
Arizona where the atmospheric pressure is
close to 700 mm Hg.
•
Discuss with one of your classmates whether
any of the phase transition in the diagram may be induced by changing
the pressure at constant temperature.
CLICK TO USE
Liquid-Gas
10
MODULE 1
Figure 1.5 Pressure-temperature phase diagram for a generic
substance showing the location
of the different phase transitions, the triple point, and the
critical point.
Searching for Differences
In a pressure-temperature phase diagram like that shown in Figure 1.5, the
transition lines not only define the specific temperature and pressure at which a
phase change will occur but they also specify the conditions under which the two
phases can simultaneously exist as stable phases. It is common to say that the two
phases coexist or are in equilibrium with each other under such conditions. This implies that at the temperature
and pressure that corresponds to the point in which two
phase transition lines intersect, three different phases can
coexist with each other. This particular state is called a
triple point. For water, for example, the solid-liquid-gas
triple point occurs at 0.01 oC and 4.58 mm Hg. The
temperature and pressure at the triple point have specific
values that differ from substance to substance and thus
can be used as a differentiating characteristic.
The phase transition between the solid and the liquid phase, or between the solid and the gas phase of a
pure substance always leads to an abrupt density change
as the phase change occurs. However, the transition between the liquid and gas phases exhibits a different behavior. In this case, as the
temperature and pressure increases, the two coexisting phases on the liquid-vapor
transition line become more alike and the density difference between them decreases. At certain temperature and pressure, called the critical point (see Fig.
1.5), both phases become identical and the possibility of observing an actual phase
change disappears beyond this point. At temperatures and pressures higher than
the critical point, the gas and liquid phases are indistinguishable from each other
and the substance is said to exist as a supercritical fluid.
LET’S THINK
Comparing Phase Behavior
Consider the pressure-temperature phase diagrams for water and carbon dioxide:
Water
Carbon Dioxide
•
Identify the stable phase of each substance at 1 atm and 40 oC.
•
Lists the phase changes that this stable phase may undergo by increasing or decreasing
a) the temperature and b) the pressure. Estimate the temperatures and pressures at which
these phase changes will take place.
•
Analyze what particular features of each of the phase diagram are responsible for such different phase behaviors.
Chemical Thinking
U1
The liquid-gas transition line in a pressure-temperature phase diagram is also
called the vapor pressure curve. At any given temperature, a liquid enclosed in
a sealed container evaporates to a certain extent producing vapor
that exerts pressure on its surroundings. The higher the temperature, the higher the rate of evaporation and the larger the pressure
exerted by the vapor (or vapor pressure). Boiling occurs when the
vapor pressure of a liquid becomes equal to the external pressure
acting on the fluid as the gas can then freely escape. Thus, the
liquid-gas transition line traces the value of the vapor pressure of
the liquid at different temperatures. Liquids that are more volatile
(evaporate more easily) will have higher vapor pressures than less
volatile fluids at any given temperature (see Figure 1.6). Volatile
liquids will then have lower boiling points as their vapor pressure
will become equal to the external pressure at lower temperatures.
The comparison of vapor pressure curves for different substances
is very useful in the process of separating mixtures in gaseous or
liquid state as it helps predict the order in which different substances will separate.
Separations
A
B
Figure 1.6
C
Vapor pressure
curves for A) Methanol B) Ethanol, and C) Water. A is more
volatile than B; B is more volatile
than C.
Now that we have a better understanding of the general phase behavior of pure
substances, we can use our knowledge to analyze and discuss how important separation techniques used to chemically analyze a system work. Not all separation
techniques rely on phase properties or phase behavior to separate substances, but
some of the most commonly used strategies do. Among them we find: Filtration,
crystallization, and distillation.
Filtration: This technique is based on the mechanical separation of substances in the solid state from substances in a fluid phase (liquid
or gas) by using a physical barrier which only the fluid can pass.
The separation of the two types of phases is never complete as
some solid will pass through the filter and some fluid will be attached to the solid material. The efficiency of the separation will
largely depend on the filter’s thickness and pore size. Air filters
are commonly used to improve air quality in house, building,
and car ventilations systems.
Car Air Filter
Insulin Crystals
11
How do we distinguish substances?
Crystallization: In this strategy, the formation of a solid phase is induced
by changing the temperature or the concentration of the components in a fluid (liquid or gas) mixture, or by adding other
substances. For the crystallization to occur, the mixture should
be supersaturated with the substance we want to separate. This
means, the concentration of the substance needs to be higher
than the concentration at equilibrium (saturated mixture).
Crystallization can be used to separate substances, like in the
extraction of common salt from sea water, or to purify materials, like in the production of silicon for electronic devices.
12
MODULE 1
Figure 1.7 Main components of
a fractional distillation apparatus.
Searching for Differences
Distillation: This technique is used to separate substances in a fluid mixture taking advantage of differences in the boiling points of the various components. Traditionally, the method involves a phase change from liquid to gas and subsequent
reconversion of the separated substances to the liquid phase. In a simple
distillation, the liquid mixture is heated up in a flask. When the boiling point of the most volatile component is approached, the mixture
will boil and the temperature will remain relatively constant until most
of the volatile substance becomes a vapor. The vapor produced can be
directed to a condenser where it will cool down and transform back
into a liquid that can be collected. By continuously heating the liquid
mixture, the same process can be repeated until all of the components
are separated.
Separation by distillation is never perfect and it is common to redistill the different portions or fractions of liquid that are collected. To
improve the separation, particularly for substances with similar boiling
points, one may use fractional distillation (see Figure 1.7). In this case,
the evaporating fluid is passed through a vertical column with trays or
plates placed at different heights. The temperature decreases gradually
from the bottom to the top of the column and substances condense
on different plates depending on their boiling points: the most volatile substances
require lower temperatures to condense and will be found towards the top; the
least volatile substances will condense on the bottom plates.
LET’S THINK
Distilled Spirits
Hard liquors or spirits, such as brandy, whisky, and tequila, are commonly
produced by fermentation of carbohydrate-rich natural products. In the process, a mixture containing water (C), ethanol (B), methanol (A), and many
other components is generated. Methanol needs to be removed because of its
toxic properties; water is extracted to produce beverages with various concentrations of ethanol. Given the information provided, together with your
understanding of phase behavior and separation techniques:
•
•
What would you expect
to happen as you heat up
the alcoholic mixture? In
which order will the three
main substances separate?
At which temperatures
will each fraction distill?
Based on the vapor pressure curves, would you
see any advantage in
changing the pressure at
which the distillation is
performed? Why?
A
B
C
Chemical Thinking
FACING THE CHALLENGE
U1
How do we distinguish substances?
condense. The liquefied air is then heated up and
distilled in one or two different distillation columns, depending on the desired products.
Separating Air
More than half of the oxygen extracted from
air by cryogenic distillation is used to produce
The concepts, ideas, and ways of thinking intro- steel. The rest is consumed
duced in this module can be applied to the chemi- for medical applications,
cal analysis of a variety of systems, from the atmo- water treatment, and to
sphere in our planet to the oil spilled the Gulf of power rocket fuels. On the
Mexico in 2010. For example, let us go back to other hand, the argon that
our original challenge: the separation of substances is produced in the process
present in the air we breathe.
is used to fill incandescent
The separation of air components can be use- lights, create inert atmoful for a variety of reasons. We may want, for ex- spheres to avoid undesirample, to know the proportion in which different able chemical reactions,
Solid Argon Melting
substances are present in the air. Or we may be in- and in cryosurgery (appliterested in eliminating atmospheric pollutants. We cation of extreme cold to eliminate diseased tissue)
could also be interested in “mining” air; this means to destroy cancer cells.
to extract from it substances that have commercial
Nitrogen also has important industrial applivalue. In fact, air is the main source of nitrogen, cations, such as in the creation of safe atmospheres
oxygen, and inert gases such as argon used for in fuel systems in military aircraft or on top of
industrial or medical purposes. These three sub- liquid explosives. The gas it is also used to create
stances are the main components of our planet’s modified atmospheres to preserve packaged food.
atmosphere:
One of the main uses of the nitrogen extracted
form air is in the synthesis of ammonia, one of
Air Components
the most highly-produced substances in the world
o
because of its central role in the production of ferSubstance % Volume
Tb ( C)
tilizers.
Nitrogen
78.084
-195.79
Liquid nitrogen is also widely used in cryogenOxygen
20.957
-182.95
ics, the study and production of very low temperaArgon
0.934
-185.85
tures (lower than -150 oC) and the investigation of
the properties of materials under such conditions.
These air components are actually separated Some substances acquire surprising properties at
using a technique called cryogenic air distilla- very low temperatures, such as losing all electrition. How? Well, the first step is to filter the air to cal resistivity and becoming superconducting maeliminate solid particles and
terials. Superconductors
then compress it to presare currently used to prosures between 5 to 10 atm.
duce magnets that generThe mixture is then passed
ate strong magnetic fields,
through another filtering
such as those required for
system that allows the reMagnetic Resonance Immoval of water and carbon
aging (MRI). This nondioxide. The processed air is
invasive medical imaging
then cooled down to temtechnique is currently
peratures as low as -200 oC
used to visualize internal
(73 K), conditions under
structures and functions
Air
Distillation
Column
which all main components
in our body.
13
14
MODULE 1
Searching for Differences
Let’s Apply
ASSESS WHAT YOU KNOW
Investigating Other Planets
The analysis of the atmosphere of other planets in our Solar System is of central importance for
understanding not only how our planet originated but for exploring the possibility of life beyond
Earth. The following table summarizes relevant information for the atmosphere of Venus, Earth,
and Mars:
Distance from Sun in
Astronomical Units (AU)
Average Surface
Temperature
Extreme Temperatures
Air Density at
ground level
Atmospheric pressure
at ground level
Atmosphere
composition
(Main components)
As you can see, the atmospheric conditions in
these three planets are very
different. This implies that
the same substances may
exist in different states of
matter from one planet
to another. The phase behavior of a substance in a
given planet can be predicted using their respective phase diagrams. In
particular, in these pages
we present the phase diagram of water and carbon
dioxide. Notice, that pressure in these diagrams is
represented using a logarithmic scale.
Venus
Earth
Mars
0.723
1.00
1.50
460 oC (day)
460 oC (night)
20 oC (day)
10 oC(night)
-5 oC (day)
-85 oC(night)
500 oC (highest )
400 oC (lowest)
58 oC (highest)
-88 oC (lowest)
27 oC (highest)
-143 oC (lowest)
65 kg/m3
1.2 kg/m3
~0.020 kg/m3
92 atm
1.0 atm
0.0059 atm
96.5% Carbon Dioxide
3.5% Nitrogen
0.002% Water
78% Nitrogen
21% Oxygen
~1% Water
0.035% Carbon Dioxide
95.3% Carbon Dioxide
2.7% Nitrogen
0.13% Oxygen
0.03% Water
CARBON
DIOXIDE
Chemical Thinking
U1
How do we distinguish substances?
15
WATER
Earth
NASA
Mars
NASA
Answer the following questions based
on the information provided and
your own knowledge of the phase
behavior of chemical substances. You
may also need to do some basic research
to find relevant phase behavior data for
other substances present in these planets.
•
What is the state of matter of water
and carbon dioxide at day and night in
each of these three planets? Justify your answer by indicating on
the phase diagrams the state of matter of the different substances in each of the planets.
•
Would it be possible to find solid carbon dioxide (dry ice) in
any of these three planets? Justify your answer.
•
Would it be possible to find liquid nitrogen in any of these
planets? Justify your answer.
•
The United States and Soviet Union have sent many spacecraft
to Venus. Some flew by the planet, some orbited it, and some
descended through the atmosphere. Imagine that you were able
to get a sample of Venus’ atmosphere, how would you propose
to separate its main components? In which order would you be
able to separate them? Write a detailed description of what you
propose to do and what you would expect to happen at each
step of the separation process.
• Would it be possible to find a planet in which both water and
carbon dioxide exist in liquid form? If yes, what average temperature and pressure could this planet have?
Venus
NASA
ASSESS WHAT YOU KNOW
Your Predictions
16
MODULE 1
Searching for Differences
Let’s Apply
ASSESS WHAT YOU KNOW
Refining Petroleum
Crude oil or petroleum is a mixture of hundred of substances, most of them made of hydrogen
and carbon (hydrocarbons). The mixture is a thick black liquid in which different substances that
are solid, liquid, and gases at room temperature are present. In an oil
refinery, crude oil is separated into “fractions” (mixtures that consist
of compounds with similar boiling points) by fractional distillation.
During the distillation process, crude oil is injected into a boiler
and heated. The vapor passes into a distillation column with a temperature gradient, coolest at the top, hottest at the bottom. There are
plates or trays across the column with holes through which the rising vapor passes. Different substances condense in trays at different
temperatures according to their boiling points.
Imagine that you have to separate the components of different
samples of crude oil extracted from the ground. What strategies
would you follow? Let’s explore how well you can apply the concepts, ideas, and ways of thinking introduced in this module.
Problem Mixture 1
A rich fuel mixture containing the following hydrocarbons has been extracted
from underground:
A
A. Propane
B. Butane
C. Neo-Pentane
D. 2-Heptene
The mixture is at an initial temperature of
5 oC. Based on the data provided:
•
Identify a differentiating characteristic that you could use to separate
each of the components.
•
Design a procedure to separate each
component. Describe what steps
you would follow and what you would expect to see happening
as you implement your strategy.
B
C
D
Chemical Thinking
U1
How do we distinguish substances?
17
Problem Mixture 2
The second mixture you have to separate contains all of the following components listed in
order of increasing melting (Tm) and boiling temperatures (Tb) at atmospheric pressure:
Tm(oC)
Tb (oC)
Substance
Tm(oC)
Tb (oC)
Methane
-182
-164
Pentadecane
10
271
Propane
-188
-42
Hexadecane
18
287
Butane
-138
-0.5
Heptadecane
21
302
Hexane
-95
69
Nonadecane
33
330
Heptane
-91
98
Tricosane
49
380
Octane
-57
126
Tetracosane
52
391
Nonane
-53
151
Pentacosane
54
402
Dodecane
-10
216
Tetracontane
81
524
Your task is to design a fractional distillation column that will allow you to separate the following five fractions:
1. Liquid fuels less volatile than water that can be used to
power vehicles at all temperatures between the lowest
(5 oC) and the highest (38 oC) average temperatures in
Tucson, Arizona (the fuel should remain liquid in that
range of temperatures).
2. Gaseous fuels that can be used for cooking and heating
houses in Tucson.
3. Liquids with a higher volatility than water that can be
used as solvents in industries and labs.
4. Dense oils that can be used as lubricants in cars and
Gasoline and diesel are most often
machinery (these substances may be solid or liquid deproduced by fractional distillation
pending on the temperature in Tucson).
5. Solid paraffin waxes that can be used to make candles in Tucson.
15 oC
You should assume that the temperatures at the top and bottom of your
column are 15 oC and 360 oC, respectively.
•
What is the minimum number of distillation plates or trays, beyond the top and bottom exhausts, that you will need to complete
the separation?
•
At what temperatures should each of these trays be placed to
ensure that the fractions you want get separated?
•
What substances will be mixed in each of the fractions that you
will extract from the column?
360 oC
ASSESS WHAT YOU KNOW
Substance
18
MODULE 2
Modeling
Matter
The assumption that every single substance in our surroundings has a at least one
differentiating characteristic that makes it unique is at the base of all of the chemical techniques used to analyze our world. But, what causes these differences? Why
is it that a substance like water boils at 100 oC while oxygen does
Why are
it at -183 oC? Why is carbon dioxide a gas at room temperadiamond and
graphite so
ture while pure carbon is a solid under the same conditions?
different if
both are made
To try to explain these differences, humans through history
of carbon?
have developed “models” of matter. Models are simplified
representations of objects or processes built to better describe, explain, predict, and even control their properties
and behavior. Some of these models may be concrete, as
the model of a bridge used by an engineer to understand how the system
will respond to stress. Some models are abstract, composed of entities
that may be treated as tangible objects (e.g., force, energy) but actually represent
concepts or ideas that help us make sense of properties and events.
Modeling substances and processes is at the core of chemical thinking. It is
through modeling that chemists have been able not only to analyze and explain
the diversity of the material word, but to design strategies to create new materials.
Many of the models used in chemistry are abstract and refer to entities that cannot
be seen by the naked eyed. That sometimes makes chemical thinking challenging.
However, the explanatory and predictive power of those models is extraordinary.
THE CHALLENGE
Clouds
The formation of clouds in the atmosphere is of critical importance to sustain
life on Earth. Clouds are necessary for precipitation to occur and help regulate
the energy absorbed and reflected by the planet.
•
At this stage, how do you think clouds form?
•
Based on what you know, how would you “model”
the process of cloud formation in the atmosphere?
Share and discuss your ideas with one of your classmates.
This module will help you develop the type of chemical reasoning that is used
to answer questions similar to those posed in the challenge. In particular, the
central goal of the module is to help you understand and apply the particulate
model of matter to explain differences in the phase behavior and related physical properties of diverse substances in our world.
Chemical Thinking
U1
How do we distinguish substances?
19
Particulate Model of Matter
The tasks of analyzing and synthesizing substances has been greatly simplified by
the development of models about their internal composition and structure. Since
ancient times, humans have proposed different models to explain and predict the
properties of matter. Aristotelians, for example, thought of all substances as composed by four elemental principles: water, fire, air, and earth (Figure 1.8).
It was thought that these “elements” gave a substance its characteristic
properties depending on the proportion in which they were present. Other greek philosophers, like Leucippus and Democritus thought of matter
as made up of small indivisible particles called “atoms” moving around in empty
space. In this model, differences in substance properties were attributed to the
existence of atoms with an infinite number of different shapes and sizes that could
move and arrange in diverse ways. Although our theories and models of matter
have evolved considerably over the years, some core assumptions about the composition and structure of the substances in our world are similar to those of the
ancient Greeks. For example, we still consider the existence of atoms as essential
components of matter although we model them in different ways.
Plato’s Model
Figure 1.8 The four Aristotelian
elements and their associated essential properties.
LET’S THINK
Plato, the Greek philosopher, proposed an interesting geometric model of matter. In this model,
each of the particles of the Aristotelian elements: fire, water, air, and earth was assigned a threedimensional shape. Fire consisted of tetrahedra, earth of cubes, air of octahedra, and water of
icosahedra. Each of these “Platonic” shapes can be built using basic right triangles as shown on the
image.
Fire
Earth
Air
Water
Plato proposed that different elements could transform into one another through dissociation and
rearrangement of the elemental triangles. So, the transformation of liquid water into vapor was
modeled in this way:
Water
20 x 6 Triangles
2 Air
=
+
1 Fire
2 (8 x 6) + 4 x 6 Triangles
•
In which ways is Plato’s explanation for the transformation of liquid water into vapor is
similar or different to our current ideas about this phenomenon?
•
Which of the following transformations would be possible according to this model?
a) 1 Air --> 2 Fire; b) 1 Water --> 3 Fire + 1 Air; c) 4 Fires --> 1 Water. Justify your reasoning.
•
Based on your analysis, to what extent can Plato’s model be considered a useful intellectual
tool to explain and predict the transformations of matter?
20
MODULE 2
Modeling Matter
During the 18h and 19th centuries, chemists and physicists accumulated
enough experimental evidence to support a model of matter that proposes that
all substances are composed of small particles in constant movement. This particulate model of matter has become one of the most powerful ideas of modern
science, as it can be used to explain and predict the physical properties of many
materials. This model is built upon the following fundamental assumptions:
http://www.powersof10.com/
CLICK TO
ZOOM IN
Assumption 1. Any macroscopic sample of a substance is composed of an extremely large number of very small identical particles.
In a first approximation, these “particles” may be thought of as very small
rigid objects. However, as discussed later, we will need to assume that these
particles have internal structure if we want to better explain the physical
and chemical properties of matter. The size of the particles is assumed to
be pretty small, of the order of one billionth of a meter, or one nanometer
(1 nm = 1 x 10-9 m), although the actual value will vary from substance to
substance. Thus, a macroscopic sample of any substance can be expected
to be composed of trillions of billions of the same type of particles. For
example, one milliliter (1 mL) of liquid water contains approximately 3.35
x 1022 water particles. This number is similar to the estimated number of
stars in the entire Universe! Imagining the world at this small scale can be
difficult, but chemists have devised ways to simplify the challenge.
USEFUL TOOLS
The study of the properties of chemical
substances often requires the measurement
of quantities that can be very large or very
small. In order to simplify the representation
and manipulation of these amounts it is common to use scientific notation and multiple or
submultiples of standard measurement units
(check Appendix A for more details).
Scientific Notation: In this notation numbers
are represented as the product of a real number A and a power of ten:
A x 10n
where the coefficient A is a number greater
than or equal to 1 and less than 10, and the
exponent n is an integer. Numbers greater than
one have positive exponents; numbers smaller
than one have negative exponents. For example, the number 54000 is expressed in the following way:
54000 = 5.4 x 10000 = 5.4 x 104
The number 0.00054 is written as:
0.00054 = 5.4 x 0.0001 = 5.4 x 10-4
Numbers larger than one can be written in scientific notation by increasing the exponent by
one for each place the decimal point is moved
to the left. For numbers smaller than one, the
exponent is decreased by one for each place
the decimal point is moved to the right.
Multiples/Submultiples: In the International
System on Units (SI) prefixes are added to produce a multiple or a submultiple of the original
unit. All multiples and submultiples represent a
power of ten. The following table summarizes
some of the most common prefixes used to express units in chemistry:
Larger
Smaller
Name
hecto-
kilo-
mega-
giga-
Symbol
h
K
M
G
Factor
10
10
10
109
Name
centi-
milli-
micro-
nano-
Symbol
c
m
m
n
Factor
10
10
10
2
-2
3
-3
6
-6
10-9
For example, the size of a water particle,
0.00000000028 m, can be expressed as
0.28 nm (nanometer) using the nano prefix.
Chemical Thinking
U1
How do we distinguish substances?
The particles of matter are expected to be so small that they cannot be seen
by the naked eye or even using an optical microscope. That is why it is common
to make references to the “submicroscopic world” when describing matter at the
particulate level or scale. Experimental results indicate that these particles also
have very small masses. For example, a single particle of the oxygen we breathe has
a mass close to 5.3 x 10-23 g. This is a billion billion times less massive than a tiny
speck of dust!
21
CLICK TO PLAY
Assumption 2. Particles of matter are constantly moving in random directions
through empty space.
In order to explain the different properties of matter, the particulate model
also assumes that the particles that make up a substance are in constant random
motion through void space (see Figure 1.9). It is this motion which allows us to
explain, for example, why gases and liquids exert pressure on the walls of their
containers. The pressure can be seen as the result of the force per unit area exerted
by particles of the fluid that collide with the particles of the container. But what
determines the speed at which the particles are moving? Let us explore your initial
ideas on this topic before moving on.
Particle’s speedLET’S THINK
Imagine that you had a sample of pure liquid water, water vapor, and water ice
at this substance’s triple point (273.16 K, 4.58 mm Hg). If you could measure
the speed of the water particles at the submicroscopic level:
•
In which state of matter would you expect particles to be moving at the
lowest speed? In which phase would they be moving at the lowest speed?
•
Would you expect all of the particles in a given phase to be moving at
the same speed?
•
How would you expect the speed of the particles in the different phases
to change when the temperature of the system is increased or decreased?
Share and discuss your ideas with one of your classmates. Don’t forget to
clearly justify your predictions.
One of the most common difficulties in applying the particulate model of
matter to describe, explain, or predict the properties and behavior of a substance is
that we tend to project the macroscopic properties that we observe or measure to
the submicroscopic level. Thus, for example, people may think that particles in a
solid are moving at lower speeds than particles in a fluid because solids seem more
static, or that particles in a solid only move when the actual object is moving. We
need to be careful with this type of thinking because the properties that we measure in a macroscopic sample are often quite different from the properties of the
individual particles that comprise the system.
In the case of particle motion, the particulate model of matter assumes that
the speed of the particles depends on two main variables: the temperature of the
Figure 1.9 Representation of a
gas using the particulate model
of matter. The sides of this square
should be assumed to be only a
few nanometers long.
22
MODULE 2
Modeling Matter
system (T) and the mass of the individual particles (m). In particular, temperature
is seen as a measure of the average kinetic energy per particle (< Ek >) given bv
Fraction of Particles
T1
T2
T3
(1.1) < Ek > = 1/2 m < v >2
T1< T2< T3
0
250
500
v (m/s)
1000
1250
Figure 1.10 Distribution of par-
Fraction of Particles
0.1
0.2
0.3
0.4
ticle speeds for the same substance at different temperatures.
m1
m1> m2> m3> m4
m2
where < v > represents the average particle speed. The larger the temperature, the
larger the average kinetic energy per particle in the system and the faster the particles will move. Particles of the same substance in two different coexisting phases
at a certain temperature will have the same average kinetic, and thus the same average particle speed independently of the state of matter of the material.
Now, within a given system at a constant temperature one should expect individual particles to move at different speeds. Some particles will move fast, some
of them will move slow; many of them will have speeds close to the average value.
This is illustrated in Figure 1.10 where we show the typical shape of the distribution of speeds for a generic gaseous substance at three different temperatures. As
shown in this figure, as the temperature increases the fraction of particles with low
speeds decreases while the fraction with high speeds increases. Substances made up
of particles of different masses will have different speed distributions at any given
temperature (see Figure 1.11), but their average kinetic energy will be the same.
Based on equation (1.1) we can then predict that lighter particles will have higher
average speeds than heavier particles at any given temperature.
m3
m4
v (m/s)
Figure 1.11 Distribution of parti-
cle speeds for different substances at the same temperature.
Assumption 3. Particles interact with each other and the nature and strength
of these interactions depends on distance.
In order to explain the existence of phase transitions between different states of
matter it is necessary to assume that particles exert attractive forces at relative long
distances but repel each other when they come into close proximity (Figure 1.12).
Without these interactions all substances would always exist in a single phase.
LET’S THINK
•
Use this simulation to analyze the effect of changing temperature on the speed and spatial distribution of particles
in a simple substance. Study the behavior of the system in
the presence and in the absence of interactions between
particles. Share and discuss your findings with one of your
classmates.
CLICK TO PLAY
The core assumptions of the particulate model of matter,
together with basic physics principles to predict the dynamic
effects of the interaction between particles, can be used to build
computer simulations to analyze the predictions of the model
under different conditions:
Phase Changes
Note: Repulsion between particles at short distances is modeled by assuming that particles behave
like hard billiard balls.
Chemical Thinking
U1
How do we distinguish substances?
Distance
Interaction Force (N)
According to the particulate model of matter, the solid
phase forms as a result of the attractive interactions between
particles that keep them together at low temperatures, when
the average kinetic energy of the particles is relatively low.
Attractive and repulsive interactions constrain the movement
of particles and they cannot freely translate from one place to
another. As the temperature increases, the average speed of
the particles increases and they gain some freedom to move
around each other, which explains the fluidity of the liquid
phase. At some point at higher temperatures, when the liquid
transforms into a gas, most particles acquire enough kinetic
Repulsion
energy to move across the entire system barely influenced by
their interactions. The stronger the attractive interactions between particles the more energy will be needed to separate
them and induce a phase transition from solid to liquid or from liquid to gas.
Within this model, differences in melting and boiling points are then attributed
to differences in the strength of the interactions between particles at the submicroscopic level. This is a very important claim because it highlights the importance of
understanding the specific composition and structure of the particles of matter in
order to explain the diverse properties of the substances in our world.
The particulate model of matter can be used to build explanations and make
predictions of the properties and behavior of a variety of systems and phenomena.
To illustrate it, in following sections we will apply the model to the analysis and
understanding of a) the properties of gases and b) the nature of phase transitions.
23
Attraction
Distance (m)
Figure 1.12 Simulated in-
teraction force between two
particles of argon as a function of distance between any
two particles. By convention,
repulsive forces are given
positive values and attractive forces negative values.
Modeling Gases
Substances that exist in the gas phase at room temperature play a central role in
our lives. We breathe in air which contains gaseous substances such as oxygen and
nitrogen, and we breathe out air richer in other gases such as carbon dioxide. This
latter gas is also one of the main products of the combustion of the fossil fuels
that we use to generate electricity and power our cars. The rapid increase of the
concentration of carbon dioxide in the atmosphere in the last two hundred years is
thought to be the main cause for global warming. Thus understanding gas properties and behavior is of central relevance in modern times.
Historically, the study of the properties of gases was of central importance in
the development of modern chemistry. Natural philosophers and scientists such
as Robert Boyle, Antoine Lavoisier, Joseph Priestley, and John Dalton, who many
consider the founding fathers of modern chemistry devoted much of their time to
this endeavor. It was through the study of the properties of the different gaseous
substances found in the atmosphere, or those generated in chemical reactions, that
chemists were able to build many of the fundamental models and theories that
guide chemical thinking nowadays.
Although the gas phase is perhaps the simplest in structure at the particulate
level, many people struggle to understand its properties because most gases cannot be seen or felt. So, it is not uncommon for people to think that gases have
no weight or that the particles of matter become smaller or lose mass when a
substance turns into a gas. Modeling and analyzing the gas phase at the submicroscopic scale may help us dispel some of those misconceptions.
In which ways is
types of particulate
representations of
solids, liquids, and
gases are limited or
inaccurate?
MODULE 2
Modeling Matter
Most substances exist in the gas state at high temperatures and low pressures.
Under those conditions we can imagine the particles that make up the system to
be far apart from each other and rarely crossing paths. So, in a first approximation,
the particulate model of a gas could be simplified by assuming that particles do not
interact with each other at all; the only interactions that they experience are with
the walls of their container. This is a reasonable hypothesis if the average distance
between particles is much larger than their own size. What can this simple model
predict about the properties and behavior of gases? Let’s explore it.
LET’S THINK
Ideal Gases
The simulation included in this activity is based on a particulate model of matter that neglects
all interactions between particles and treats their interactions with the walls of the container as
perfectly elastic collisions (no kinetic energy is lost during the collision). Use this simulation to
analyze the effect on the pressure (P) exerted by the particles on the walls of the container by:
a) Changing the temperature (T) at constant volume (V) and number of particles (N);
b) Changing V at constant T and N;
c) Changing N at constant T and V.
•
Use your data to sketch three graphs that show how P changes with increasing T, V, or N
when the other variables are held constant.
P
P
P
T
•
CLICK TO PLAY
The simulation will allow you to collect the value
of the average pressure in the system as a function
of different variables. Use the load button to collect
data making sure that the pressure is stabilized before registering its value. Small pressure fluctuations
can always be expected in systems with few particles
as is the case for this simulation.
CLICK AND DRAG TO DRAW
24
V
N
Share your results and ideas with one of your classmates. Discuss what types of mathematical equations could best describe the relationships between P and T, P and V, and P and N
predicted by this model of gases.
Our simplified particulate model of gaseous substances predicts that the pressure (P) of the gas will be directly proportional to both the absolute temperature
(T, measured in kelvin) and the number of particles (N) in the system, and inversely proportional to the volume (V). This behavior is actually observed in many
Chemical Thinking
U1
How do we distinguish substances?
gases at high temperatures and low pressures; when this happens it is said that the
substance behaves as an “ideal gas.” The quantitative relationship between pressure, temperature, volume, and number of particles in the ideal gas model can be
expressed in mathematical terms as:
P = kB ( N T / V )
(1.2)
where the proportionality constant kB = 1.380 x 10-23 J/K is known as Boltzmann
constant. One of the most interesting features of this relationship, also called the
ideal gas law or ideal gas equation of state, is that none of the quantities in equation (1.2) depends on the chemical composition of the actual system. The ideal
gas model predicts that all substances, independently of their chemical structure
and composition, will behave identically under those conditions of temperature
and pressure where the interactions between their particles can be neglected. This
prediction of universal behavior has been confirmed experimentally and it is one of
the greatest accomplishments of the model.
Up and Down
LET’S THINK
The properties of gases change when you move up and down in Earth’s atmosphere or underwater.
This table shows temperature and pressure data gathered at various altitudes in the atmosphere and
various depths in the ocean:
Altitude
(km)
0
1
2
3
4
5
Atmosphere
Temperature
(K)
293
287
280
273
267
261
Pressure
(atm)
1.0
0.883
0.779
0.687
0.607
0.536
Hydrosphere (middle latitudes)
Depth
Temperature
Pressure
(km)
(K)
(atm)
0
293
1.0
0.1
290
11
0.2
279
21
0.3
278
31
0.4
277.4
41
0.5
276.9
51
Imagine that you model your lungs as a 5 L sealed balloon filled with an ideal gas at sea level:
•
How will the volume of your lungs change as you climb up to the top of a mountain at 5 km
above the sea level? Estimate the volume of your lungs at the top of the mountain.
•
How will the volume of your lungs change as you dive down into the ocean to
100 m below sea level? Estimate the volume of your lungs at the bottom of your
diving.
•
Why would you need pressurized tanks for scuba diving? Why would it be necessary to exhale and rise slowly when ascending from the ocean depths?
•
How do the problems that you might have in scuba diving compare with those
of a pilot climbing to a higher altitude in an pressurized plane?
•
Build a particulate representation of the air inside your lungs (the balloon) as you move from
5 km above sea level to 100 m below the ocean surface. How would the following properties
change as you descend a) Average speed of the particles; b) Mass of a single particle; b) Volume of a single particle; d) Location of the particles inside the balloon.
25
26
MODULE 2
Modeling Matter
The ideal gas model works well for describing and predicting the behavior of
gases at high temperatures and low pressures. However, one can expect problems
to arise when the effects of particle interactions cannot be neglected. As we discussed before, in the absence of particle interactions a gas would never turn into a
liquid or a solid. Thus, the closer we get to the conditions under which a gaseous
substance will undergo a phase change, the worse the predictions of the ideal gas
model will be. In order to find a relationship that better describes and predicts the
behavior of “real” gases we need to understand how particle interactions affect the
behavior of the system.
LET’S THINK
Real Gases
The simulation in this activity allows you to turn on or off particle interactions in the particulate
model of a simple substance, as well as to change the strength of the attractive forces. Use the simulation to investigate the effect of particle interactions on the pressure of a gas.
Analyze how the average pressure changes as you turn on the repulsive interactions but not
the attractive interactions (Repulsions between particles are modeled by assuming that the
particles behave like hard billiard balls). Investigate whether the magnitude of the effect depends on the temperature, volume, and number
of particles in the system.
•
Analyze how the average pressure changes as you
increase the strength of the attractive interactions keeping repulsive interactions on. Investigate whether the magnitude of the effect depends on the temperature, volume, and number
of particles in the system.
CLICK TO PLAY
•
Discuss your results with one of your classmates and suggest possible explanations for what you
observe in each case. Propose ways in which the ideal gas law could be modified to better describe
the effects of particle interactions on the behavior of the system?
Particle interactions affect gas properties because they alter particle movement. For example, given that particles repel each other at close distances, there
is less effective space for particles to move. Their movements are more constrained; it is as if the particles where in a container with a smaller effective volume
Veff = V - Nb, where b represents the volume occupied by a single particle and
N x b is then the volume that all of the particles take. So, if the volume occupied
by all of the particles is not so small compared to the volume of the container, one
can expect more frequent particle collisions with the walls of the container due
to the reduced available space. This in turn should result in higher pressures than
those predicted by the ideal gas model.
Attractive interactions will also constrain particle movement as forces will
change particles’ velocity, both speed and direction. Particles will accelerate towards each other but their speeds will decrease as they separate. On average one
can expect particles to spend more time close together and to interact less frequently with the walls of the container; this will lower the pressure. This effect will
Chemical Thinking
U1
How do we distinguish substances?
be more noticeable the larger the number of particles and the smaller the volume
of the container. It will also depend on the strength of the attractive interactions
between particles in the system.
The analysis of the effect of particle interactions on the properties of a gas can
be used as a guide to modify the ideal gas law as expressed in equation (1.2) to better describe and predict the behavior of real gases. One of such modified equations
was proposed by Johannes Diderik van der Waals in 1873 and is now known as
the van der Waals equation of state for real gases:
(1.3)
27
CLICK TO
INCREASE T
P = [ N kB T / (V - N b) ] - a N2 / V2
In this relationship, the constants a and b are related to the overall strength of the
attractive interactions and to particle size, respectively. Equation (1.3) has a similar structure to the ideal gas law, but it takes into consideration the reduction in
effective free volume due to particle repulsions as well as the effect on pressure of
the attractive interactions. The constants a and b take different values for different
substances which implies that the response of real gases to changes in temperature
and pressure depends on the chemical nature of the system. Although the van der
Waals equation does not accurately describe the behavior of many real fluids, it is
able to predict the existence of a gas to liquid phase transition at low temperatures
and its disappearance at the critical point (Figure 1.13). Scientists and chemical
engineers have developed a variety of equation of states that describe and predict
the properties of many different fluids with great accuracy and precision.
Experiments and ModelsLET’S THINK
The actual value of the van der Waals constants a and b for real substances
can be derived from experimental values of temperature, pressure, and density
measured at their critical point. This illustrates how we can combine experimental data with the predictions of a theoretical model of the same system to
derive important information about properties of substances at the submicroscopic scale. Take, for example, the magnitudes of a and b for three important
components of our atmosphere listed in the following table:
•
What do these data tell you
about the comparative sizes
of the particles of these three
substances?
•
What do these data tell you
about the comparative strengths of the attractive interactions between
the particles of these three substances?
•
Based on these data, what could you predict about the relative boiling
temperatures of these three substances at a given pressure?
•
Looking at the actual boiling temperatures for each of the substances
in the table, which factor, particle size or strength of attractive interactions, seems to have a stronger influence on the temperature at which
the liquid-gas phase transition occurs?
Substance
Oxygen
Water
Carbon Dioxide
a
1.378
5.536
3.640
b
0.03183
0.03049
0.04267
Figure 1.13 Particulate
models of matter that include particle interactions,
such as van der Waals model, predict the existence of
a liquid-gas critical point
such as the one shown here
for carbon dioxide.
28
MODULE 2
Modeling Matter
Modeling Phase Transitions
Figure 1.14 Some people
think that the bubbles in
boiling water are made of
oxygen and hydrogen particles, instead of water particles. What do you think?
We have seen how the particulate model of matter can be used to describe, explain,
and predict the properties of substances in the gas phase. The same model can be
applied to analyze the properties and behavior of materials in the liquid and the
solid phases, as well as to study the transition between different states of matter as
we will discuss it in the following paragraphs.
A phase change is a very interesting event given that two or more phases with
rather different properties can coexist during the transition. Understanding this
phenomenon has not been easy. For many years natural philosophers and scientists
thought that the chemical nature of substances actually changed during a change
of state. The observable properties of liquid water and water vapor, for example,
are so different that is not surprising that people had problems thinking of them
as the same substance (Figure 1.14). However, chemical analysis revealed that no
chemical change occurred during a phase change and the particulate model of
matter helped make sense of the results.
One of the most fundamental ideas to understand when using the particulate
model of matter is the concept of emergence. The particulate model relies on the
assumption that the macroscopic properties of a substance that are observable
or measurable in our laboratories may not be the same as the properties of the
individual particles that compose the system. The idea is that many macroscopic
properties “emerge” from the spatial distribution, movement, and interactions between the myriad of particles present in a macroscopic sample of the material. So,
for example, according to the particulate model of matter a solid is more rigid than
a fluid because the close proximity and low kinetic energy of the particles in the
solid phase make it difficult for them to move around and separate. An alternative
explanation would be to think that particles in the solid state are hard and become
softer as we increase the temperature. However, experiments indicate that hardness is not a property of each individual particle but rather a property that emerges
from the interactions between the many particles in a system.
LET’S THINK Emergent Properties
Consider the following intensive properties of a substance:
Density
Viscosity
Boiling Temperature
Malleability
Color
•
Which of these properties are emergent properties of the substance and
which of them are properties of the individual particles that compose
the system?
•
How would you expect the value of each of these properties to differ for
samples of the substance that have 10, 102, 1012, and 1023 particles?
•
Which other emergent properties of a substance can you identify?
Share and discuss your ideas with a classmate. Don’t forget to clearly justify
your reasoning.
Chemical Thinking
U1
How do we distinguish substances?
The temperatures at which phase transitions occur are in fact emergent properties of substances. According to the particulate model of matter, individual
particles do not melt or boil with changing temperature or pressure; they
do not become smaller or larger, or softer or harder, during a phase change.
The nature of the interaction forces between particles, this is, their overall
strength and how these forces vary with distance, does not change with
temperature and pressure either. The only thing that changes during the
phase transition is how particles are distributed in space and the amount
of energy that they have. Because the temperature at which a substance
boils is an emergent property of a system with many particles, we cannot
expect a nanoscopic droplet of water comprised of 20 particles to boil at
the same temperature as a macroscopic droplet of the same substance with
1022 particles (Figure 1.15). In fact, it is likely that the nanoscopic droplet
would gradually evaporate and never actually boil because each of its particles is
not subject to the attractive force of many others. The particulate model of matter
can still be applied to explain and predict the behavior of systems made up of a few
particles, but their properties will be different from those of macroscopic samples.
We have seen that to induce a phase transition in a macroscopic sample of a
material we need to provide or extract energy from the system. However, once the
transition point is reached, the temperature remains constant until the transformation is complete. Why does this happen? How can the temperature stay constant
when energy is being added to or removed from the system? Let us analyze this
phenomenon using the particulate model of matter.
In a dynamic system of interacting particles energy can be present in two main
forms, kinetic energy (Ek) due to particle motion (Equation (1.1)) and potential
energy (Ep) due to particle interactions. This latter energy is conceived as stored energy due to the relative position of the interacting particles. The potential energy for
a pair of particles at a certain distance can be defined as the kinetic energy that they
could gain if they were to move freely under the sole action of their interacting force.
Let us illustrate this idea in the case of an attractive force. In this situation, the farther away the particles the more kinetic energy they can gain as they move towards
each other under the action of the attractive force. Thus, if the interaction force is
attractive the potential energy increases with particle separation (see Figure 1.16)
and decreases as the particles get closer to each other. A pair of particles that moves
under the influence of their attractive force will gain kinetic energy as particles approach each other and will lose
potential energy
in the process.
Attractive Force
Potential
Energy
Decreases
29
Figure 1.15 Images of
silica nanoaggregates using
different electron microscopy techniques. Nanostructures made of a few
particles have different
properties than the bulk
material.
Figure 1.16 The potential energy (Ep) of a pair of
particles that attract each
other decreases as the
distance (r) between them
decreases. By convention,
the maximum potential
energy is set to be zero for
this case (at infinite r).
30
MODULE 2
Modeling Matter
In situations when particles repel each other, the shorter the distance between
them the more kinetic energy they can gain under the action of the force pushing them away. Thus, for repulsive forces the potential energy is greater at shorter
distances and it decreases as particles separate. As particles move away under the
action of their repulsive force, they will lose potential energy but gain kinetic energy. By convention, the zero of potential energy is set to be zero when the particles
are at an infinite distance from each other, no matter whether the interaction force
between them is attractive or repulsive.
LET’S THINK
Potential Energy Plot
•
Identify on the graph the range of distances
where the particles attract each other and
the range of distances where they repel each
other (Hint: Analyze how Ep is changing with
increasing distance). Is there a finite distance
where the force between them is zero?
•
Describe what would happen to the potential
energy and to the kinetic energy of two argon
particles initially separated by a large distance
if they were to move freely under the influence
of their interaction force.
Potential Energy (J)
The following graph shows the calculated potential energy for the interaction of two argon particles
as a function of distance.
Distance
Distance (m)
Share and discuss your ideas with a classmate. Don’t forget to clearly justify your reasoning.
E
Liquid
For substances in the solid or liquid phase, attractive and repulsive interactions
between particles tend to keep them at distances where the average force is close
to zero and the potential energy is at a minimum. Thus, particles of substances in
these states of matter have much lower potential energy than the same particles in
the gas phase, where the potential energy due to particle interaction is almost zero.
Thus, in order to induce a phase transition from liquid to gas energy needs to be
provided to separate the particles and increase their potential energy to the values
that it has in the gas phase (Figure 1.17). During a liquid to gas phase transition
the temperature remains constant because the energy provided is transformed into
potential energy and not into kinetic energy of the particles (remember
that temperature is a measure of the average kinetic energy per parGas
ticle). In the reverse process, the change from gas to liquid, energy is
released as the particles lose potential energy as they get closer together.
In a similar fashion, energy will be needed to separate particles in the
melting of a solid, and energy will be released in the solidification of a
liquid. The energy released or absorbed during a phase transition due to
changes in the potential energy of the system is often called latent heat.
Kinetic Energy
Potential Energy
Figure 1.17 During the phase transition from liquid to gas, the total kinetic energy of
the particles in the system remains constant while the total potential energy increases,
going from a negative value to almost zero as particles are far apart in the gas phase.
Chemical Thinking
U1
Modeling
How do we distinguish substances?
LET’S THINK
A critical skill in chemical thinking is the ability to use the particulate model of matter to describe, explain, and predict the properties and behavior of systems in our surroundings.
Let us explore how well you can do it.
Evaporation
Even when the temperature of a small pond of water never
reaches 100 oC, the water evaporates and the pond disappears.
•
How could you explain this phenomenon using the particulate model of matter?
Sweating
Our body uses “sweating” as a cooling mechanism.
•
How does this work?
•
How would you explain it based on the particulate model
of matter?
Cooking
Recipes for cooking with boiling water need to be modified
based on the altitude of the place where you cook.
•
Why is that? How would you explain it based on the
particulate model of matter?
Fizzing
A soda can fizzes when we open it.
•
Why does it happen?
•
How would you explain it based on the particulate model
of matter?
31
32
MODULE 2
Modeling Matter
Atomic Model of Substances
Helium Atom
Hydrogen
Molecule
Water
Molecule
Figure 1.18 Particles of helium are made of single atoms; particles of hydrogen
are made up of molecules
with two identical atoms;
particles of water are made
up of molecules with three
atoms, two hydrogen atoms
and one oxygen atom.
In the particulate model of matter, many differences between substances are attributed to the presence of interaction forces of different types and strengths between
their particles. This naturally brings up the question: Why are the interaction forces different? To answer this questions we need to zoom into the submicroscopic
world to better understand the structure of matter. This is the task that will guide
most our analysis through the first three units of this book. However, we will summarize some of the core ideas in the following paragraphs.
It is a fundamental assumption in modern chemical thinking that substances
in our world have different properties because they are made of particles with different compositions and structures. In particular, in the atomic model of substances
it is proposed that the particles that compose the substances in our surroundings
have internal structure. They are made up of smaller units called atoms which are
held together by strong attractive forces called chemical bonds. There are some
substances composed of particles that are single atoms; argon and helium are two
examples. However, most natural and synthetic substances have a more complex
submicroscopic structure. For example, many of them are made up of particles
where two or more atoms of the same or different types are bonded together. These
composite particles are called molecules (Figure 1.18). All of the molecules of a
given substance are assumed to be identical to each other but different from the
molecules of a different substance. Differences between molecules result from differences in either the types of atoms present in them or the way they are arranged
in space or both. A molecule’s composition and structure determines how the
molecule will interact with other particles of similar or different type.
LET’S THINK
Particles in the Atmosphere
The image in this activity shows a particulate representation of a nanoscopic section of the air in
our atmosphere.
•
How many different substances are included in this representation?
•
Which substances in air are made up of
particles that are single atoms and which
are made up of molecules?
•
Air is a mixture of substances. How is a
mixture different from a single substance
at the particulate level?
Share and discuss your ideas with a classmate.
Don’t forget to clearly justify your reasoning.
Note: The following color code is commonly used to represent atoms of different types:
Argon
Hydrogen
Carbon
Nitrogen
Oxygen
Chemical Thinking
U1
33
How do we distinguish substances?
The atomic model of substances just described allows us to make sense of
many observations and experimental results about the properties of substances and
their mixtures. For example, if we assume that air is a gaseous mixture of several
substances each of them characterized by a particular type of particle, then
that explains why the different components can be separated by simply
cooling down the mixture. The strength of the interaction between different
types of particles can be expected to be different and thus they will condense at different temperatures. Now, how do we know that molecules of carbon dioxide are
made up of two oxygen atoms and one carbon atom, or that nitrogen molecules
have two atoms of the same type? The answer to these questions will take us
some time to build through the following units. However, we can present
some experimental evidence that supports this model.
For some time now chemists have identified two major types of substances. There are some substances that cannot be separated into simpler
substances by any physical or chemical procedures. This means, there
is no known experimental technique that allows us to take a sample
of these substances and split it into different stable substances. We call
these types of substances chemical elements (Figure 1.19). They include,
for example, the oxygen, nitrogen, and argon that we separate from air in the
atmosphere. However, there are substances that we can split into simpler stable
substances by inducing a chemical reaction. We call these types of substances
chemical compounds; water and carbon dioxide are two typical substances in
this group. Water can be broken apart into the chemical elements hydrogen and
oxygen, while carbon dioxide can be split into carbon, another chemical element,
and oxygen. Whenever a chemical compound undergoes this decomposition, the proportion in which the chemical elements that make
up the substance are recovered is always the same. For example, during the decomposition of water into its chemical elements, twice the
volume of hydrogen gas than oxygen gas is always produced.
The atomic model of substances allows us to explain the differences in the
behavior of chemical elements and compounds in the following way. Chemical elements cannot be split into simpler stable substances because they are made up of
particles, atoms or molecules, that contain one single type of atom. Chemical
compounds can be split into chemical elements because their particles contain two or more different types of atoms that can rearrange to produce
the elemental substances. Given that the particles of a chemical
compound are identical to each other, they produce the same
ratio of chemical elements when they are broken apart.
Gold
Copper
Sodium
Mercury
Silicon
Figure 1.19 Samples of different chemical
Sulfur
Bromine
elements, together with a particulate representation at the nanoscale. The particles
of all of these substances are made up of
single atoms or molecules with the same
types of atoms.
34
MODULE 2
Modeling Matter
LET’S THINK
Elements, Compounds, Mixtures
Analyze the following particulate representation of nanoscopic samples of elements, compounds,
and mixtures
•
Classify each of the images as
a representation of an element,
a compound, or a mixture of
substances.
•
In the case of mixtures, identify
what types of substances, elements or compounds, are present in them.
•
Identify the state of matter in
which each of the substances or
mixtures is represented to be.
Share and discuss your ideas with a classmate. Don’t forget to clearly justify your reasoning.
Figure 1.20 Periodic
CLICK AND ROLL OVER TO DISPLAY NAMES
Table of the Elemental
Atoms displaying the
symbols
commonly
used to represent
each type of atom.
From the perspective of the atomic model, chemical elements are the most
simple stable substances that we know. They are composed of identical particles
made up of free or bonded atoms of the same type. The isolation and identification
of the various chemical elements in Nature has allowed chemists to identify all of
the different types of atoms that made up the particles of all substances, natural
and synthetic, in our world. Up to this day, over a hundred of different types of
atoms have been identified. The list of these atoms is presented in the following
“Periodic Table of the Elemental Atoms” (Figure 1.20). Each type of atom in this
table is assigned a symbol that, as we will see later, greatly simplifies its representation. Atoms in a given column in the Periodic Table are said to be in the same
“group,” while atoms in the same row belong to the same “period.”
Chemical Thinking
U1
How do we distinguish substances?
Each of the atoms listed in this table has the same name as the chemical element whose particles are made up by that type of atom. However, it is important
to recognize that the properties of the atoms included in the Periodic Table are
not necessarily the same as the properties of neither the particles that make up the
chemical elements nor the actual chemical substance. For example, the oxygen
that we found in the atmosphere is made up of molecules composed of two atoms
of oxygen each. The structure and properties of these molecules are different from
those of a single oxygen atom. Similarly, a sample of copper is made up of many
copper atoms bonded together in a metallic network; this sample conducts electricity. A single atom of copper does not.
Chemical elements are traditionally subdivided into three main groups: Metals, metalloids or semimetals, and nonmetals, based on similarities in physical and
chemical properties. Metals are usually solids at room temperature that conduct
heat and electricity remarkably well; most nonmetals, in the other hand, are gases
under the same conditions and are poor conductors of heat and electricity. Metalloids share some properties of metals and nonmetals. The symbols of the atoms
that make up the particles of these different types of chemical elements are commonly displayed with different colors on the Periodic Table (Figure 1.20).
Chemists have developed a variety of ways to represent and try to visualize the
composition, structure, and properties of both the actual chemical substances in
our surroundings as well as the models used to describe, explain and predict their
behavior (see Figure 1.21). At the macroscopic level we can use actual images of
the substances or descriptions of their measured properties. At the submicroscopic
level, we can create drawings or create dynamic animations and simulations to try
to capture the core components of the particulate models that we use. Additionally, chemists have developed a rather sophisticated symbolic language to represent
the composition and structure of chemical substances. A chemical formula, for
example, is a symbol that conveys information about the atomic composition of
a given substance. Thus, the chemical formula for the chemical element oxygen
is O2(g), where the subindex is used to indicate that every single molecule of this
substance is made of two oxygen (O) atoms and the label within parenthesis indicates the state of matter (g, gas; l, liquid, s, solid) of a macroscopic sample.
Macroscopic
Atomic
Element
Argon
Gas
Liquid
Nitrogen
Molecular
Element
Solid
Red
Phosphorus
Submicroscopic
Iodine,
Chemical Element
REPRESENTATIONS
Iodine Solid, I2(s).
Iodine Molecule, I2
Figure 1.21 Different ways
of representing chemical
elements. The labels (g),
(l), (s), indicate the state of
matter of the substance.
Symbolic
Ar
N2
P4
35
Ar(g)
N2(l)
P4(s)
36
MODULE 2
Modeling Matter
Caffeine
Molecule
C8H10N4O2
Cholesterol
Molecule
C27H46O
Color Code
C
H
Macroscopic
Solid
Carbon
Dioxide
N
O
Figure 1.22 Different
ways of representing
molecular compounds.
Most substances in Nature are not chemical elements, but chemical compounds. As mentioned before, within the atomic model chemical compounds are
substances whose particles are made up of bonded atoms of two or more different
types. Chemists classify chemical compounds into two major groups: Ionic and
molecular (or covalent) compounds, based on their physical and chemical properties. Ionic compounds tend to be solids with high meting points that conduct
electricity when dissolved in water or in the liquid state (molten). Molecular compounds are variable in their state of matter and, in general, are not good electrical
conductors in any phase. Differences in properties can also be explained based on
the composition and structure of these substances at the submicroscopic level.
Molecular compounds result from the chemical combination of atoms of nonmetal elements (see Figure 1.20). When these atoms combine they tend to form
molecules, this is, independent particles composed of two or more bonded atoms
of different types. For example, water is a molecular compound in which each of
its molecules contains two hydrogen atoms and one oxygen atom. The chemical
formula of liquid water is thus H2O(l). Numerical subindexes after an atomic
symbol are used in chemical formulas to indicate the actual number of atoms of
that type in the particles of the compound (see Figure 1.22). From the perspective
of the atomic model, the wide number and diversity of molecular compounds in
our world is due to the possibility of having many different types of molecules that
differ in composition, size, and structure.
Ammonia
Gas
Submicroscopic
Symbolic
CO2
NH3
CO2(s)
NH3(g)
Ionic compounds are the result of the combination of metal atoms with nonmetal atoms. Their particular properties can be explained by assuming that their
submicroscopic structure is rather different from that of molecular compounds.
In particular, ionic compounds are not seen as composed of individual molecules
but of electrically charged particles arranged in a crystalline network (Figure 1.23).
These charged particles are called ions and they can be atoms or molecules with a
net electrical charge. An ionic network is made up of positively charged ions (cations) and negatively charged ions (anions) held to each other by electrostatic forces. The ratio of anions to cations in any sample of this type of substances is such
that the material has no net electrical charge. These different ions gain mobility
when the solid compound is molten or dissolved in water and that explains why
ionic compounds conduct electricity under such conditions. Typical examples of
ionic compound include sodium chloride, the major component in common salt,
and calcium carbonate, the main component in limestone.
Chemical Thinking
Color Code
Cl
H
N
Na
U1
Macroscopic
How do we distinguish substances?
Submicroscopic
Symbolic
Na+
Solid
Sodium
Chloride
NaCl(s)
Cl-
Solid
Ammonium
Chloride
NH4+
NH4Cl(s)
Given that ionic compounds are not made up of molecules, their chemical
formula conveys different information than that of a molecular compound. The
chemical formula of an ionic compound, or its formula unit, simply establishes
the lowest ratio of cations to anions in the system. For example, the formula unit
of sodium chloride is NaCl, which indicates that the ionic network of this chemical compound is composed of sodium cations (Na+) and chloride anions (Cl-) in a
ratio of one to one (1:1). The formula unit of calcium fluoride is CaF2, which tells
us that calcium cations (Ca2+) and fluoride anions (F-) are present in a 1:2 ratio.
Figure 1.23 Different
ways of representing
ionic compounds.
Submicro and SymbolicLET’S THINK
The ability to translate from submicroscopic (particulate) representations of
matter to symbolic language and vice versa is a critical skill in chemical thinking. The following images show submicroscopic representations of several pollutants in our atmosphere in different states of matter.
•
Write the chemical formulas of each of theses substances.
C
H
Cl
O
•
KCl(s)
Cl2(l)
Share and discuss your ideas with one of your classmates.
CLICK TO USE
Create submicroscopic representations of the
following substances. You may use the interactive tool on this page to make your drawings.
CH4(g)
NO(g)
37
38
MODULE 2
Modeling Matter
Methane
CH4
Molecule
Throughout this book we will use a variety of visual representations of chemical elements and compounds at the submicroscopic level using drawings and symbols of different types. These diverse representation are intended to emphasize
different characteristics or properties of the represented atoms, molecules, or ionic
networks. For example, the so-called space-filling representations are typically
used to emphasize the relative size of the atoms that compose a system. On the
other hand, ball-and-stick representations highlight the connectivity between different atoms in a molecule or ionic network.
In both cases, the representations allows us
to develop a better sense of the three dimensional geometry of the objects of interest.
In general, modern computational technology has helped us generate many types of
static and dynamic images to better visualize the modeled submicroscopic world.
Space-Filling
Representation
USEFUL TOOLS
Chemists have not only created useful ways of
representing chemical substances at the macroscopic, submicroscopic, and symbolic levels, but
they have also developed a systematic language
to name each chemical element and compound
in our world. Understanding this “chemical nomenclature” greatly simplifies chemical thinking
and communication. Let us explore how to name
molecular and ionic compounds made up of two
different types of atoms, or binary compounds
(check Appendix B for more information):
Ionic Compounds: The name of binary ionic
compounds results from the combination of the
names of the positive ions (cations) and negative
ions (anions) present in the system.
The cations have the same name as the atom
from which they derive. These are atoms of
metallic elements that acquired a positive
charge. For example, Na+ is the sodium ion while
Al3+ is the aluminum ion. Some atoms can form
more than one type of positive ion and a Roman
numeral in parenthesis is used to distinguish one
cation from another. For example, Cu+ is named
the copper(I) ion, while Cu2+ is the copper(II) ion.
The name of the anions is built by adding the
suffix -ide to the root of the name of the atom
from which the ion is derived. These are atoms
of nonmetallic elements. Thus, Cl- is the chloride
ion while O2- is the oxide ion.
Ball-and-Stick Representation
CLICK AND DRAG TO ROTATE
The name of a binary ionic compound includes
the name of the cation followed by the name of
the anion. For example, NaCl is named sodium
chloride while Al2O3 is called aluminum oxide.
Notice that the number of each type of ion
present in the formula unit is not included in the
name of the compound.
Molecular Compounds: The name of a binary
molecular compound is also derived from the
atoms that made up their molecules. In this
case, the name of the atom farthest to the left in
the Periodic Table (Figure 1.20) goes first. If both
types of atoms are in the same group, the atom
farthest down in the table is named first. So, for
example the name of the compound CO2 begins
with “carbon”, and that of SO2 with “sulfur.”
The name of the second component of the
molecular compound is built by adding the suffix
-ide to the root the atom’s name. Greek numeral
prefixes are used to indicate the number of atoms of each type (mono- for one; di- for two; trithree). However, this numeral is not added if the
molecule only has one atom of the element that
is named first. The following examples illustrate
the application of these rules:
CO
CS2
N2O
PCl3
Carbon monoxide
Carbon disulfide
Dinitrogen monoxide
Phosphorus trichloride
Chemical Thinking
FACING THE CHALLENGE
From Clouds to Proteins
How can everything that we have discussed in this
module be used to understand the formation of
clouds in our planet? Clouds are large atmospheric
objects made up of small liquid droplets or tiny
crystals of water (H2O) and other minor components. Clouds form as hot air raises in the atmosphere and rapidly expands due to
reduced atmospheric pressures at
higher altitudes. In order for the
gas to expand, molecules in the ascending air need to push particles
in their surroundings and transfer
part of their kinetic energy. The
average kinetic energy of the molecules in the raising air decreases,
and thus the system cools down. At
this lower temperatures, the attractive forces between water molecules
cause them to aggregate into clusters or nuclei that may grow into larger droplets by
the addition of more water molecules.
In order for nuclei to grow, the rate at which
water molecules escape from the cluster should be
smaller than the rate at which other water molecules deposit onto it. For this to happen, clusters have to reach a critical size in which there are
enough molecules in the system to hold it together
through attractive interactions between particles.
The formation of nuclei, or nucleation process, is
facilitated by the presence of other substances that
attract water molecules and act like seeds on which
the water nuclei can form. Typical nucleation seeds
include dust and sodium chloride, NaCl, crystals.
Liquid droplets tend to form at low altitudes, but
ice crystals are prevalent at higher elevations.
Humans have developed strategies to “seed
clouds,” this is to artificially induce the formation
of nuclei in regions where the concentration of water molecules is not enough for them to aggregate
spontaneously. Cloud seeding often requires the
dispersion in the atmosphere of solid substances
with a crystalline structure similar to ice, such as
silver chloride (AgCl), which induces the nucle-
U1
How do we distinguish substances?
ation of water crystals. Solid carbon dioxide, CO2
(dry ice), can also be used as this material reduces
the temperature to such low values that ice crystals
form spontaneously from the vapor phase.
Most clouds in our planet form in the lowest
region of the atmosphere, called the troposphere.
Higher layers of the atmosphere tend to be too
dry for the nucleation process to occur. However, some clouds that form in the winter polar
stratosphere, between 15,000 to 25,000 m above
sea level, play a crucial role in our
planet. Nucleation in these clouds
occurs at temperatures close to -80
o
C. The clusters that form at these
temperatures are mixtures of water
with chemical compounds such as
nitric acid (HNO3) and sulfuric acid
(H2SO4). These droplets and crystals
trap pollutants and accelerate chemical processes that consume ozone
molecules (O3) in the stratosphere.
The phenomenon of ozone depletion
in our planet is thus strongly associated to the formation of these types of clouds.
Nucleation is not only important in the formation of clouds. Most phase transitions in our
surroundings are initiated via the nucleation of
nanoscopic droplets, bubbles, or crystals. Inducing and controlling the formation of these nuclei is
one of the ways we have to influence the properties
of the new phase that emerges from the process.
The development of new materials via nanotechnology relies on a great extent on the ability to stop
the nucleation process when clusters of atoms or
molecules rich the proper size. In biochemistry,
the nucleation of protein crystals is a necessary
step to determine the structure of enzymes and
other important molecular components of our
cells. However, producing good crystals
for analysis can be
extremely challenging. In all these cases,
understanding phase
transitions at the
particulate level is an
invaluable asset.
Protein Crystal
39
40
MODULE 2
Modeling Matter
Let’s Apply
ASSESS WHAT YOU KNOW
A Soda Can
Soft drinks are very popular across the world. The average American drinks
more than 50 gallons (close to 150 L) of soda a year. These beverages are mixtures of a variety of substances and are canned at high pressures (over 2 atm).
Let us explore to what extent you can apply the concepts and ideas discussed
in this module to analyze the properties of these popular drinks.
Phase and Components
The image shown to the right is a particulate representation of a nanoscopic portion of the surface of a soft
drink inside a can at high pressure.
•
How many different phase are present in this
system? Which phases are these?
•
How many substances are present in each phase?
•
How many of the substances in this system are
chemical elements?
•
What is the chemical formula of each of the
chemical elements in the system?
•
How many of the substances in this system are
chemical compounds?
•
What is the chemical formula of each of the
chemical compounds in the system?
•
How many molecular compounds are represented in the image? How many ionic compounds
are there?
•
Which techniques would you use to separate
each of the substance in this system? In which
sequence would you use them?
T = 277 K
P= 2 atm
The ball-and-stick representation of a molecule of one
of the substances in the drink is also shown in this
page:
•
What is its chemical formula?
Share and discuss you ideas with a classmate.
CLICK AND DRAG TO ROTATE
Chemical Thinking
U1
How do we distinguish substances?
41
Dynamics
In which of the different phases present in this system:
•
Are the attractive forces between particles the strongest?
•
Is the average potential energy per particle the lowest (most
negative)?
•
Is the average particle speed the highest?
•
Is the average kinetic energy per particle the lowest?
T = 277 K
P= 2 atm
•
Which of the components in this system has seems to have
the lowest vapor pressure? What does this tell you about the
strength of the attractive interaction forces between its particles?
Share and discuss your ideas with one of your classmates. Don’t forget to clearly justify your reasoning.
Change
Imagine that you were to take the soda can out of a
cooler and open it on the beach in a warm day at 300 K:
•
How would the average kinetic energy per particle
in each of the phases of this the system change?
•
How would the average potential energy per particle in each of the phases change?
•
How would the chemical composition of each of
the phases change?
•
Use the interactive tool on this page to build a
particulate representation of a nanoscopic portion
of the opened drink.
When cold pressurized beverages such as this are
opened, it is common to observe the formation of small
“cloud” around the opening (see image):
•
CLICK TO USE
How would you explain this phenomenon using
the particulate model of matter?
Share and discuss your ideas with one of your classmates. Don’t forget to clearly justify your reasoning.
ASSESS WHAT YOU KNOW
Based on the information provided in the representation:
42
MODULE 2
Modeling Matter
Let’s Apply
ASSESS WHAT YOU KNOW
Fighting Intuition
The properties and behavior of matter at the submicroscopic level sometimes defies our intuition.
We are not used to build explanations about the things that we observe in our daily lives based
on the movement and interactions of myriads of submicroscopic particles that we cannot see with
our eyes. Testing and recognizing the limits of our intuitive ways of describing and explaining the
world is crucial in the process of becoming a better chemical thinker. Thus, in these pages we pose
a few challenges to test your reasoning.
•
Evaluate the answer given by some students to the following questions. Share and discuss
your ideas with a classmate. Discuss what misunderstandings or intuitive ideas may lead
students to make mistakes and select incorrect answers.
Substances or Mixtures
Each of the following images is a particulate representations of a single substance or a mixture
of substances. Which of them represents a single substance?
1
2
3
4
A chemistry student chose representations 2 and 3. What do you think?
Cooling
The following diagram represents a magnified view of a small portion of a
steel tank filled with helium gas at 20 °C and 3 atm pressure. The dots represent the distribution of helium atoms. Which of the following diagrams
best illustrates the distribution of helium atoms in the steel tank if the temperature is lowered to -100 °C (helium is still a gas at this temperature)?
a.
b.
c.
A chemistry student chose representation a. What do you think?
d.
Chemical Thinking
U1
How do we distinguish substances?
43
Properties
Following is a list of properties of a sample of solid sulfur:
i. Brittle, crystalline solid. ii. Melting point of 113 oC.
iii. Density of 2.1 g/cm3. iv. Reacts with oxygen to form sulfur dioxide.
Which, if any, of these properties would be the same for one single atom of sulfur obtained from
the sample?
A chemistry student thinks that all of these properties of solid sulfur would be the same for
one single atom. What do you think?
Which of the following processes will make water molecules larger?
a. Freezing
b. Boiling
c. Condensing
e. None of them
A chemistry student selected a (freezing). What do you think?
Boiling
A sample of the liquid compound A2B
is heated up and completely evaporated
(changed to a gas) in a closed container as
shown in the figure. Which of the following
diagrams best represents what you would
“see” in the same area of the magnified view
of the vapor?
a.
b.
c.
d.
A chemistry student selected representation c. What do you think?
Particle Speed
Solid, liquid, and gaseous water coexist at the triple point (0.01 oC and 0.006 atm). In which
of these phases do water molecules have the lowest average speed at 0.01 oC and 0.006 atm?
a. Gas
b. Liquid
c. Solid
d. The average speed is the same in the three phases
A chemistry student selected d (the average speed is the same in the three phases). What
do you think?
ASSESS WHAT YOU KNOW
Phase Change
44
MODULE 3
Comparing
Masses
The atomic model of matter has proven to be a very powerful tool to describe,
explain, and predict the properties of chemical substances. The model suggests
that if we are able to characterize the specific nature of the particles that compose
a substance, we can make qualitative and quantitative predictions about its behavior. But how can we analyze, measure, or calculate the specific characteristics of
individual atoms, molecules, or ions? These are nanoscopic entities that
we cannot isolate and investigate in a conventional chemistry
lab. The characterization of the properties of the particles
that make up chemical substances is thus one of the major challenges in chemistry. The task is accomplished
in a variety of clever and creative ways that allow us to
generate information about three basic properties of the
What is the mass of
a single molecule of
particles of matter: their mass, their chemical composition, and
butane (C4H10)?
their three dimensional structure. In this module, we will analyze the
type of thinking that is used to determine the first of these properties.
The ability to measure, or calculate by some means, the mass of the atoms,
molecules, or ions that make up a substance is of central importance in many
fields. For example, this information is needed in the analysis of the environmental
effects of different substances in our world. Knowing atomic and molecular masses
is key in the prediction of the number of particles of each type present in a system,
information that can be, in some cases, matter of life or death.
THE CHALLENGE
Air Pollution
Modern technology allows us to quantify the concentration of different types
of pollutants in the atmosphere.
•
If someone told you that the concentration of ozone, O3(g), in the place
you live is 2 x 10-4 mg/L, what would you need to know to determine
how many molecules of O3 you breathe per liter of air that you take in?
•
Why would these numbers be important to know?
Share and discuss your ideas with one of your classmates.
This module will help you develop the type of chemical thinking that is needed
to make calculations similar to those describe in this challenge. In particular, the
central goal of the module is to discuss how to use information about atomic
and molecular masses to calculate the number of particles of different types
present in a system of interest.
Chemical Thinking
U1
How do we distinguish substances?
45
Relative Masses
Atoms, molecules, and ions have masses and sizes so small that cannot be measured directly with a balance or similar instruments. It is thus necessary to rely on
indirect measurement techniques to accomplish the task. In particular, the problem has been solved by comparing the masses of macroscopic samples of different
substances containing the same number of particles. For example, imagine that
you had two tanks of gas containing the same number of particles but two different substances such as helium and argon. If you measured the mass of the gas in
each tank you would find out that the argon gas sample is ten times heavier than
the helium gas sample with the same number of particles. What does this means
from the perspective of the atomic model of substances? Given that argon and
helium are chemical elements made up of single atoms, it implies that each atom
of argon (Ar) should be ten times more massive than each atom of helium (He). If
we knew the mass of a helium atom, we could calculate the mass of an argon atom
or vice versa. If we could measure or calculate the number of atoms in any of the
samples, we could also calculate the mass of the individual atoms.
The problem of determining atomic or molecular masses is intimately connected to the challenge of figuring out how to collect samples of different substances with the same number of particles, and how to determine the actual number of particles in these samples. The application of the particulate model of matter
provides a nice solution to these challenges. Let’s investigate how.
Mass Effect?LET’S THINK
We can use a simulation of an ideal gas to explore the effect of changing the
mass of the particles on the pressure of the system at any given temperature
and volume. In this computer simulation, particles with different masses can
be used to model different chemical substances. Click on the image to run the
simulation of an ideal gas and begin your analysis.
•
Explore the effect of the mass of the particles on the average pressure of
an ideal gas at constant temperature, volume, and number of particles. Remember to
wait until fluctuations in the
value of the average pressure
are minimal before collecting
any data.
•
Use the results of your investigation to propose an strategy
to experimentally prepare two
samples of different gases with
the same number of particles.
CLICK TO RUN
Share and discuss your ideas with a classmate. Don’t forget to clearly justify
your reasoning.
Figure 1.24 If these gas tanks
contain the same number of
particles of each substance, how
many times heavier is an oxygen
atom than a hydrogen atom?
46
MODULE 3
Comparing Masses
The results of our exploration suggest that under the conditions in which
the ideal gas model provides a good description of the behavior of gaseous substances, equal volumes of two different gases at the same temperature and pressure
will contain the same number of particles. In fact, we could have predicted this
outcome by simply analyzing equation (1.2) for the ideal gas law, which can be
re-expressed as:
(1.4)
Figure 1.25 Why could we not
expect equal volumes of different gases to have the same number of particles at T and P values
where the gases are no ideal?
N = P V / ( kB T ).
This model predicts that the number of particles for an ideal gas is solely determined by the values of P, V, and T independently of the mass of the particles.
Thus, in order to calculate the relative masses of the particles that made up any
pair of gaseous substances, this means how many times one type of particle weighs
more than the other, we can simply compare the masses of equal volumes of the
two gases at the same temperature and pressure; this should work as long as the
gases behave ideally. This approach to determining the relative masses of the particles of matter was first proposed by Amadeo Avogadro in 1811, who was also the
first to suggest based on experimental data that equal volumes of different gases
at the same temperature and pressure would have the same number of particles
(Avogadro’s Hypothesis).
LET’S THINK
Unknown Masses
Imagine that the mass of three identical tanks separately containing hydrogen
gas (H2(g)) and two unknown chemical elements were measured at the same
temperature and pressure:
•
How many times more massive an
A atom is than a H atom?
•
How many times more massive a
B atom is than a H atom?
•
If you were to assign a mass of “1”
to an hydrogen atom in an arbitrary unit, what would the relative
masses of the A and B atoms be
when expressed in that unit?
How would your relative masses change if you decided to arbitrarily assign a relative mass of “2” to a A atom?
Is one of the two scales of relative masses that you generated better than
the other? If yes, how?
•
•
Share and discuss your ideas and results with one of your classmates.
Using methods similar to the ones you applied in the past activity, together
with careful measurements of the proportions in which different types of atoms
chemically react with each other, chemists have been able to determine the “average relative atomic mass” of all of the known atoms. These values are expressed
Chemical Thinking
U1
How do we distinguish substances?
in so-called “atomic mass units” (amu) and are listed in the Periodic Table of the
Elemental Atoms in Figure 1.26. These numbers are determined using one type of
atom as a reference (as you used the H or the A atoms in the last activity), and can
be used to determine how much massive one atom is with respect to another. In
module 4 of this course unit we will we analyze in more detail how these different
numbers have been determined using modern analytical techniques.
47
Figure 1.26 Periodic Table of the
Elemental Atoms listing the average relative mass of each atom.
CLICK AND ROLL OVER TO DISPLAY MASSES
Number of AtomsLET’S THINK
The list of average relative atomic masses is very useful in chemistry and many
other disciplines in which it is important to figure out the relative number of
particles of different species in a system. To understand it, imagine that you
were in the business of buying and selling precious metals and had the following samples: 107.9 g of Ag(s), 197.0 g of Au(s), and 195.1 g of Pt(s).
•
Which of the three samples would have more atoms? Why?
•
How many grams of palladium metal, Pd(s), would you need to weigh
to have as many atoms as in 107.9 g of Ag(s)?
•
How many grams of copper metal, Cu(s), would you have to weigh to
have half the number of atoms that you have in 197.0 g of Au(s)?
•
Based on these results, why do you think it is useful to know the relative
masses of the different atoms in the periodic table?
Share and discuss your ideas with one of your classmates. Don’t forget to
clearly justify your answers.
48
MODULE 3
Comparing Masses
Number of Particles
http://www.kokogiak.com/megapenny/
Figure 1.27 Many people has
problems visualizing very large
numbers. This sequence of images based on number of pennies
may help you grasp how large
Avogadro’s Number is.
CLICK TO
CHANGE NUMBERS
One can think of the relative masses of the different atoms in the Periodic Table
in Figure 1.26 as indicative of how much more massive each type of atom is than
a reference atom with an assigned mass of 1 amu (one atomic mass unit). For example, helium atoms (He), with a relative mass of 4.003 amu are, on average, four
times more massive than the reference atoms while argon atoms (Ar), with a relative mass of 39.95 amu, are close to forty times heavier than the reference particles.
This implies that if we were to weigh 1.000 g of the reference atoms and 4.003 g of
He atoms, both samples should have the same number of atoms. In fact, a sample
of 39.95 g of Ar atoms should also be composed of the same number of atoms. So,
whenever we weigh masses of different types of atoms and these masses are equal
in magnitude to each atom’s average relative atomic mass, we should have samples
with the same number of atoms. This fact is very useful as it allows us to use the
mass of our samples, a quantity that we can measure, to compare number
of particles without having to know how many of them are present in each
system. In this way, based on the data listed in the Periodic Table we can
predict that 20.0 mg of calcium, with a relative atomic mass of 40.08 amu,
will have approximately half the number of atoms present in 9.0 mg of
beryllium, with a relative atomic mass of 9.012 amu.
Although comparing number of particles using relative masses is useful, it would be easier if we could just measure or calculate the actual number of particles in any given sample. Fortunately,
chemists have devised approaches to do so. In particular, they have
experimentally determined the number of atoms in samples of substances with a mass equal in magnitude to their average relative mass
expressed in grams. For example, the number of particles in 4.003
g of helium, 9.012 g of beryllium, or 40.08 g of calcium. This number, called
Avogadro’s Number NA, is very large (see Figure 1.27) and has a constant value
equal to 6.022 x 1023 particles.
LET’S THINK
Molecular Elements
Some chemical elements are made up of molecules rather than single atoms.
That is the case of hydrogen, H2, nitrogen, N2, oxygen, O2, fluorine, F2, phosphorus, P4, sulfur, S8, chlorine, Cl2, bromine, Br2, and iodine, I2. For this
reason, some people have difficulties figuring out the relative mass of their
particles or the number of molecules in a given sample. What about you?
•
If the average relative atomic mass of oxygen atoms is 16.00, what is the
average relative mass of oxygen molecules O2?
•
How many grams of phosphorus should you weigh to have 6.022 x 1023
molecules of this substance?
•
How many molecules should we expect to have in 35.45 g of chlorine
gas?
Share and discuss your ideas and results with one of your classmates.
Chemical Thinking
U1
How do we distinguish substances?
From the chemical point of view, having information about the number of
particles in a sample of a given substance is frequently more relevant than knowing
its mass. Thus, it is convenient to define a unit of measurement that can be used
to simplify the quantification of the number of particles in a system of interest.
Avogadro’s Number, NA = 6.022 x 1023, has been chosen as the base to build such
unit of measurement. In particular, the new unit measurement, called a mole
(1 mol), is defined as the amount of substance that contains one Avogadro’s Number of particles of such substance. Thus, based on our previous discussion, together
with the information provided in the periodic table in Figure 1.26, we can say that
4.003 g of helium is 1 mol of helium, 39.95 g of argon is 1 mol of argon, and
38.00 g of fluorine (made up of F2 molecules) is 1 mol of this chemical element.
One mole of any substance always contains 6.022 x 1023 particles.
Measuring the amount of substance using the mole as a unit is a way of expressing how many times, or what fraction of, an Avogadro’s Number of particles
of a given substance we have in our hands. For example, if someone indicates that
they have 3.0 mol of metallic copper (Cu(s))in a bag, we know the bag contains
3.0 x (6.022 x 1023) = 1.8 x 1024 Cu atoms.
On the other hand, if they have 0.10 mol of metallic silver (Ag(s)) in the same
bag, there will be
0.10 x (6.022 x 1023) = 6.0 x 1022 Ag atoms
in the system. In general, if n is the number of moles of substance that we have,
the number of atoms in the sample N can be calculated using the following relationship:
(1.5) N = n x NA
The MoleLET’S THINK
Understanding the concept of “mole” and how to use it in the quantification
of the number of particles in any given sample of a substance is critical to be
an effective chemical thinker. To assess your own understanding, evaluate the
veracity of the following statements:
•
The mass of one mole of neon (Ne) atoms is 20.18 amu;
•
The mass of one potassium atom is 39.10 g;
•
The mass of 1.2 x 1023 aluminum (Al) atoms is 53.96 g;
•
One mole of O2 molecules weighs 16.00 g;
•
Three moles of metallic palladium are made up of three atoms;
•
106.4 g of Pd(s) have the same number of atoms as one mole of He(g).
Share and discuss your ideas with a classmate. If you judge that an statement
is incorrect, rewrite it to make it true.
Figure 1.28 The dozen,
as the mole, is a unit of
amount of substance. It
allows us to simplify the
counting in systems composed of discrete things.
49
50
MODULE 3
Comparing Masses
ONE MOLE
26.98 g Al
The mass of one mole of any substance is called its molar mass M and it corresponds to the mass of 6.022 x 1023 particles of the substance. M is traditionally
expressed using the units g/mol. The molar mass of chemical elements made up
of atoms has the same magnitude as their average relative atomic mass. Thus, the
molar mass of helium is 4.003 g/mol and that of calcium is 40.08 g/mol. These are
the masses of 6.022 x 1023 atoms of each of these chemical elements. For molecular
elements, such as hydrogen and oxygen, the molar mass corresponds to the mass of
one mole of molecules and has to be calculated taking into account the number of
atoms present in each molecule:
M(H2) = 2 x M(H) = 2 x 1.008 = 2.016 g/mol
256.6 g S8
24.31 g Mg
MOLAR MASS
The same procedure can be applied to calculate the molar mass of any molecular
compound, using the chemical formula to determine the number of atoms of each
type in its molecules. For example, the molar mass of carbon dioxide is:
M(CO2) = M(C) + 2 x M(O) = 12.01 + 2 x 16.00 = 44.01 g/mol
The molar mass of an ionic compound, such as aluminum chloride AlCl3(s), represents the mass of 6.022 x 1023 formula units of this substance:
M(AlCl3) = M(Al) + 3 x M(Cl) = 26.98 + 3 x 35.45 = 133.33 g/mol
M(H2O) =
18.02 g/mol
The molar mass of a substance is a useful quantity as it can be used to calculate the number of moles n present in any sample; once n is calculated we can use
equation (1.5) to determine the number of particles in the system. The number
of moles n results from determining how many times larger or smaller the mass of
the sample m is compared to the molar mass of the substance M:
(1.6) n=m/M
For example, if we know that a medium-size car releases around 400. g of CO2(g)
to the atmosphere per mile that it moves, we can calculate the number of moles n
and the number of particles N that it emits along that distance:
Figure 1.29 The transformation from mass (m) to number
of particles (N), or vice versa,
is facilitated by calculating the
moles of substance using the
molar mass M and Avogadro’s
Number NA.
n = m / M = 400. / 44.01 = 9.08 moles of CO2(g)
N = n x NA = 9.08 x 6.022 x 1023 = 5.47 x 1024 CO2 molecules.
n=m/M
m=nxM
MASS
m
MOLES
n
N = n x NA
n = N / NA
NUMBER OF
PARTICLES
N
Chemical Thinking
U1
How do we distinguish substances?
LET’S THINK
Breathing AIr
As we move to higher altitudes, the density of oxygen gas in the atmosphere decreases as
shown in the following table. This reduces the likelihood of oxygen molecules, O2, entering in our blood causing hypoxia, or oxygen deprivation.
h (km)
0 (Sea level)
0.7 (City of Tucson)
8.8 (Top of Mount Everest)
12.5 (Airplane cruising altitude)
•
r (g/L)
0.283
0.260
0.111
0.065
n (mol/L)
N (molecules/L)
Use the information in the table to calculate the number of moles n and the number
of molecules N per liter of air at different altitudes. Analyze how many times fewer
molecules there are at the different altitudes compared with the number at sea level.
Share and discuss your ideas with a classmate.
USEFUL TOOLS
tity is expressed. To do the conversion one
needs to:
One critical chemical thinking skill is the
ability to use experimental results for the
mass or volume of different substances and
calculate the number of moles or particles in
the system. One can use equations (1.5) and
(1.6) to accomplish the task, but sometimes
it is easier to rely on appropriate conversion
factors. Let’s analyze how to do it.
Factor-Label Method. This problem-solving
strategy is based on the fact that any number can be multiplied by one without changing its value. The challenge is to express the
multiplicative “one” as a proper unit conversion factor.
Unit conversion factors can be built
from any two terms that describe equivalent
amounts of a physical or chemical quantity.
For example, we can use the identity
1 mol of atoms = 6.022 x 10 atoms
a) Identify the original and the new units of
the quantity to transform. For example, if we
want to know how many atoms of carbon
are present in 0.030 moles of this chemical
element, we can set the problem as:
0.030 mol (old unit) = ? atoms (new unit)
b) Multiply the original quantity by the proper unit conversion factor that will replace the
old units by the new ones by cancellation:
0.030 mol C(s) x
6.022 x 1023 C atoms
1 mol C(s)
c) Perform the mathematical operations indicated by the resulting expression:
0.030 x 6.022 x 1023 = 1.8 x 1022 C atoms
23
to build these two unit conversion factors:
1 mol of atoms
6.022 x 1023 atoms
or
Using this approach we can directly transform from mass to number of atoms, or vice
versa, using a single unit conversion factor:
6.022 x 1023 atoms
1 mol of atoms
These types of unit conversion factors can be
used to transform the units in which a quan-
1.8 x 1022 C atoms x
12.01 g of C(s)
6.022 x 1023 C atoms
= 0.36 g of C(s).
51
52
MODULE 3
Comparing Masses
Back to Gases
Our knowledge about the macroscopic and submicroscopic properties of gases
can be applied to develop alternative strategies to estimate the number of moles
or the number of particles in a sample of a given gaseous substance. For example,
if we assume that the gases behave ideally, we can use equation (1.4) to determine
the number of particles N given information about the temperature T, pressure P,
and volume V of the system. Using the relationship between number of moles n
and number of particles as expressed by equation (1.5), we could also calculate the
value of n given by:
n = N / NA = P V / ( NA kB T ) = P V / ( R T )
(1.7) R values
Units
-1
8.314 J K mol-1
0.08206 L atm K-1 mol-1
1.986 cal K-1 mol-1
Figure 1.30 The universal
gas constant R can be expressed in different units.
where the constant R = NA x kB is known as the universal gas constant (see Figure
1.30). This expression can also be used to make quick estimations about the volume that will occupy, or the pressure that will exert, certain mass m of a gaseous
substance with a molar mass M at any temperature. For this purpose we can combine equations (1.6) and (1.7) to generate the following alternative expressions for
the equation of state of an ideal gas:
(1.8)
P V = n R T = m R T / M.
To illustrate how to use this relationship, we will estimate the volume in liters
(L) occupied by 1 mol of gas at certain pressure and temperature. In particular,
let’s take T = 273.15 K (0 oC) and P = 1 atm (760 mmHg), which are traditionally identified as standard conditions for temperature and pressure (STP) in experimental measurements. Using equation (1.8), together with the value of R in
proper units (see Figure 1.30), we get:
V=
nRT
P
=
1 x 0.08206 x 273.15
1
=
22.41 L
If we assume that gases behave ideally, this volume will be the same independently
of the type of substance that we have.
LET’S THINK Identification
The equation of state of the ideal gas as expressed in equation (1.8) can also be used to find the identity of unknown gases by using their molar mass M as differentiating characteristic. Imagine that you
measured the volume occupied by 2.8 x 10-3 g of an unknown pollutant at standard temperature and
pressure. Your results indicate that the gas sample occupies a volume of 2.24 mL.
•
What is the molar mass of the pollutant?
•
If you knew that the pollutant is a chemical compound made of carbon and oxygen, could
you infer what its chemical formula is?
Share and discuss your ideas with a classmate. Don’t forget to clearly justify your ideas.
Chemical Thinking
U1
How do we distinguish substances?
Gaseous substances in our environment are normally mixed with other components forming homogeneous solutions, as is the case of the air that surrounds
us. Thus, it is common to use concentrations rather than total amounts when
quantifying their presence in any given system. The concentration give us information about how much of a substance we have per unit volume of the mixture.
For example, we could indicate how many micrograms per cubic meter (mg/m3),
how many moles per liter (mol/L), or how many molecules per cubic centimeter
(molecules/cm3) of a certain substance we have. No matter what units we use, the
ideas discussed in this module can be applied to convert from one unit to another.
One useful way to quantify the concentration of substances, particularly when
present in low concentrations, is using mixing ratios. These ratios describe the
proportion in which the substance is present in the mixture relative to all of the
components. In the case of gases, it is common to use volume-mixing ratios such
as part per million in volume (ppmv) and part per billion in volume (ppbv) to
indicate concentrations. For example, 1 ppmv of nitrogen monoxide gas in air
implies that in one million volume units of air, one volume unit consists of NO(g)
if this substance were to be separated from the gas mixture. This is the same as saying that we have 1 L of NO(g) per every 106 L of air, or 1 mL of the pollutant per
liter of air. Similarly, 1 ppbm corresponds to one part in one billion parts, which
can be expressed, for example, as 1 mL of the substance per 1000 liters or 1 m3.
If we assume that gases behave ideally, then equal volumes of gas should have
equal number of particles at the same temperature and pressure. So, the number of
particles of any substance in the gas phase should be proportional to the volume it
occupies (see equation (1.7)). This implies that concentrations expressed in ppmv
or ppbv also give information about the ratio of particles in the system. Thus, 1
ppmv of NO(g) in air indicates that there is 1 molecule of NO per every million
molecules of air, or that there is 1 mol of NO per every million moles of air.
Clean Air
1
106
Figure 1.31 1 ppm corresponds to one part in one
million parts.
LET’S THINK
The Environmental Protection Agency (EPA) has set National Ambient Air Quality
Standards for various pollutants. These standards set the maximum concentrations not
to be exceeded in certain average time:
Pollutant
CO(g)
NO2(g)
SO2(g)
•
Level
9 ppmv
53 ppbv
0.03 pmmv
Average Time
8-hour
Annual
Annual
mg/m3
How would you use the following conversion factors, together with the molar mass
of each of the substances in this table, to express the concentrations in mg/m3 assuming standard conditions of temperature and pressure in the atmosphere?
1 m3 =1000 L
1 mol of gas at STP = 22.41 L of gas at STP
1 g = 1000 mg
Share and discuss your ideas with a classmate. Complete the calculations and discuss
whether you expect the results to depend on the atmospheric temperature and pressure.
53
54
MODULE 3
Comparing Masses
The proportionality between number of particles and volume occupied for
ideal gases greatly simplifies the task of converting from mass of substance to
amount of substance expressed either in moles or number of particles. For example, the concentration of methane gas, CH4(g), in our atmosphere is close to 1.8
ppmv. This concentration is equivalent to 1.8 moles of CH4(g) per every million
moles of air. Given that the molar mass for CH4 is M(CH4) = 16.04 g/mol and
that 1 mol of air has a volume close to 22.41 L at STP, we can estimate the mass in
micrograms of methane per liter of air using the following approach:
Moles to Mass of CH4
1.8 mol CH4(g)
106 mol Air
x
16.04 g CH4(g)
1 mol CH4(g)
x
Grams to Micrograms of CH4
1 mol Air
x
22.41 L Air
106 mg
1g
=
1.3 mg/L
Moles to Volume of Air
Concentrations in gases are also commonly expressed in percent volume of
a substance with respect to the total volume of the mixture. So, for example, the
concentration of argon gas, Ar(g), in the atmosphere is close to 0.934% in volume. This implies that we have 0.934 L of Ar(g) per every 100 L of air. Assuming that the gases are ideal, we can also say that of every 100 particles of air, only
one of them is an Ar atom on average. This corresponds to a concentration of
9, 340 Ar atoms in 1,000,000 molecules of air, or 9.34 x 103 ppmv. To convert
from %volume to ppmv in gases we just need to multiply by 104.
LET’S THINK
Harvesting Air
As we analyzed it in module 2 of this same unit, most of the nitrogen and oxygen that we use for practical purposes are extracted from air. But exactly how
much of each of these chemical elements can we get from every liter of air?
•
Based on what you have learned in this module, design and implement a
strategy to calculate the mass in grams of oxygen and nitrogen that can
be extracted per liter of air at standard temperature and pressure.
•
Analyze how your results would change at higher altitudes, where the
pressure may decrease to half its value at sea level and the absolute temperature may be lower by 10%.
The following information may be useful in completing this task:
a. The %volume of N2(g) and
O2(g) in the atmosphere are
78.08% and 20.95%, respectively.
b. The volume of one mole of
ideal gas at STP is 22.41 L.
c. For an ideal gas, V = nRT/P.
Discuss and share your ideas with one of your classmates.
Chemical Thinking
FACING THE CHALLENGE
Clean Air?
Our ability to monitor the quality of the air we
breathe strongly depends on the clever application of many of the ideas discussed in this module.
Ambient monitoring, this is the determination of
pollutant concentration in ambient air, can now
be done in real-time using
instruments that can measure concentrations as low
as 1 ppbv with very fast
response times (seconds to
minutes). Many of these
measurements are based
on the determination of
the amount of light absorbed by individual pollutants, absorption that is
frequently proportional to the concentration of
molecules of that substance in an air sample. Information about number of moles or number of
molecules can then be expressed in terms of mass
per unit volume if we know the molar mass of
the pollutant and the temperature and pressure at
which the measurements were taken.
Most major cities and towns in the world are
equipped with air-quality monitoring stations that
track the concentration of pollutants, some times
on an hourly basis. These concentrations are then
compared to the air-quality standards in force and
alerts, warnings or emergencies may be declared
if the air quality is not satisfactory. In the United
States, the Clean Air Act passed in
1970 requires the Environmental Protection Agency (EPA) to
set National Ambient Air Quality
Standards for pollutants considered harmful to public health and
the environment. These standards
define maximum expected concentrations of six major pollutants
in clean outdoor air. These pollutants include four atmospheric
gases: carbon monoxide (CO(g)),
nitrogen dioxide (NO2(g)), ozone
U1
How do we distinguish substances?
(O3(g)), and sulfur dioxide (SO2(g)).
Carbon monoxide is a toxic substances rather
difficult to detect with our senses. Once it enters into the bloodstream, it disrupts the delivery
of oxygen throughout the body. CO(g) is often
produced when carbon-containing compounds
are burned in closed spaces with limited oxygen
supply, such as in stoves or inside the combustion
engines of our cars. Carbon monoxide poisoning
is responsible for the death
of millions of people every
year in developing countries.
Thus, monitoring its concentration in local environments
is of central importance. In
the US, emissions of CO(g)
by cars dropped 60% from
1990 to 2005 thanks to technological advances in car
manufacturing.
Ozone is a gas with a sharp odor, one that can
be smelled around photocopier and electric motors. It is a toxic substance that harms lung function and irritates the respiratory system. O3(g) is
produced through the interaction of other pollutants with high-energy radiation from the Sun. This
substance is one of the most closely monitored in
urban areas, and one of the main causes of environmental alerts in large cities.
Nitrogen dioxide and sulfur dioxide are also
toxic substances that cause irritation of the respiratory system. One of the main sources of NO2(g) is
the burning of gasoline in car engines. The burning
of coal for the production of electric power is the
major source of SO2(g) emissions.
Regulations enacted through the
Clean Air Act have helped reduce local average concentrations
of NO2(g) by 46% and those of
SO2(g) by 71% in the last thirty
years in the US.
The concentrations of these
major pollutants in metropolitan
areas are used to calculate the socalled Air Quality Index (AQI)
traditionally listed in the daily
forecast section of newspapers.
55
56
MODULE 3
Comparing Masses
Let’s Apply
Some chemical elements can exist in different forms, or allotropes. That is the case of oxygen,
which in its most stable form is made up of O2 molecules, but can also exist as ozone, a substance
composed of molecules with three oxygen atoms, O3. Ozone gas affects the respiratory system even
at very low concentrations and damages the leaves and needles of trees.
O3(g) is called a secondary pollutant because it is not directly emitted into the atmosphere, but
produced from chemical reactions between O2(g) and other pollutants such as NO2(g), stimulated
by the presence of sunlight. Ozone concentrations are monitored regularly in major cities across
the world. In the US, the EPA has set the clean air quality standard for this substance at an average
of 80 ppbv over an 8-hour period.
Concentrations
The following map shows the evolution of O3(g) concentrations in Tucson, Arizona on August
18, 2010.
CLICK TO PLAY
•
Analyze the variations
in the concentrations
of O3(g) along the
day. How would you
explain these changes?
•
Estimate the lowest
and the highest concentrations of O3(g) in
ppbv during the entire
day.
•
Estimate the lowest
and highest concentrations of ozone in
mg/m3 assuming STP
conditions.
•
Discuss how concentrations of O3(g) in
ppbv and mg/m3 will change if you take into account that the atmospheric pressure in
Tucson is 0.918 atm and that average temperatures are between 23.9 oC (lowest)and 37.2
o
C (highest) in the month of August.
ppbv
Share and discuss you ideas with a classmate. Don’t forget to clearly justify your reasoning.
http://www.airinfonow.com/html/ozone.html
ASSESS WHAT YOU KNOW
Ozone Matters
Chemical Thinking
U1
How do we distinguish substances?
57
Breathing
On average, people take 24,000 breaths each day. One single breath has a volume
close to 0.5 L.
Estimate the total number of particles in one single breath of air at STP conditions.
•
Estimate the total number of O3 molecules breathed by one person living in
Tucson on August 18, 2010 assuming STP conditions. Use the map on the
previous page to estimate the average O3(g) concentration during the day.
•
Estimate the total number of O2 molecules breathed by the same person during the day. What percentage of all of the oxygen particles breathed by this
person were O3 molecules?
Share and discuss your ideas with one of your classmates. Don’t forget to clearly justify your reasoning and procedures.
Good Ozone
•
Estimate the volume of one mole
of air at the temperature and pressure where ozone concentrations
reach their maximum.
Altitude (km)
The EPA has a saying about ozone: “Good up high, bad nearby.” This is based
on the fact that while ozone is a pollutant of concern in the troposphere,
where we live, the same substance protects us from harmful high-energy radiation from the Sun at high altitudes, in the stratosphere.
The graph on this page shows the 100
concentration of ozone as a function of
altitude in the atmosphere. The region
80
T = -40 oC
with high ozone concentrations defines
60
P = 2 x 10-3 atm
the so-called “ozone layer.”
Thermosphere
Mesosphere
40
20
Stratosphere
Troposphere
0
0
3
Ozone (ppmv)
•
Estimate the concentration of
O3(g) in that same region in moles/L.
•
Imagine you could take the number of moles of O3 in one liter of air
in that region of the ozone layer and “inject” it into a liter of air at sea
level, under STP conditions. What would the concentration of ozone
be in ppbv? Would this concentration exceed EPA standards?
Share and discuss your ideas with one of your classmates. Don’t forget to
clearly justify your reasoning and procedures.
6
9
ASSESS WHAT YOU KNOW
•
58
MODULE 3
Comparing Masses
Let’s Apply
ASSESS WHAT YOU KNOW
Greenhouse Gases
Some atmospheric gases, such as CO2(g) and CH4(g), absorb infrared radiation emitted by both
the Sun and our own planet, trapping thermal energy in the atmosphere. They are called greenhouse gases and help sustain average global temperatures favorable to life on Earth. They are also
thought to be responsible for the current increase in average temperatures across the world (global
warming) due to their much higher concentration in the atmosphere compared to pre-industrial
times. The following table includes important information for the analysis of the properties and
effects of major greenhouse gases in our planet:
Substance
CO2(g)
CH4(g)
N2O(g)
CCl2F2(g)
Concentration
(Pre-1750)
280 ppmv
700 ppbv
270 ppbv
0
Concentration
(Recent Times)
386 ppmv
1866 ppbv
323 ppbv
537 pptv*
Lifetime
(Years)
variable
12
114
100
GWP
(over 100 years)
1
25
298
10,900
*pptv- parts per trillion in volume.
The lifetime in this table is a measure of the average time it takes for concentrations of a given
substance to return to its natural value following an increase in its concentration in the atmosphere. The global warming potential (GWP) is a measure of the thermal energy trapped per unit
mass of the greenhouse gas relative to that of a reference gas (CO2(g)). The GWP is calculated over
a specific time interval as its value depends on the lifetime of each species.
Concentrations
Using the concentrations provided in the table for the different greenhouse gases:
•
Calculate the percent increase in the concentration of each gas in
the atmosphere from pre-industrial to present time. Investigate
what are the main sources of these four substances in modern societies, and propose an explanation for why some concentrations
have increased more than others.
•
Express all of the concentrations in the table in mg/L. Is this a
convenient unit to report concentrations of these gases in mass
per unit volume? If it is not, which unit would be better? Why?
Share and discuss you ideas and calculations with a classmate. Don’t
forget to clearly justify your reasoning and procedures.
Chemical Thinking
U1
How do we distinguish substances?
59
GWP
The scale for the global warming potential (GWP) of a substance is set using CO2(g)
as a reference; in particular, the GWP for this gas is taken to be equal to one. Thus, if
the GWP for CH4(g) is 25, this implies that 1.0 g of methane traps the same amount
of thermal energy in the atmosphere as 25.0 g of CO2(g) do. Based on this information:
•
Estimate the number of molecules of CO2 that would be needed to trap as
much thermal energy as:
•
a) 1 molecule of CH4;
b) 1 molecule of N2O;
c) 1 molecule of CCl2F2;
Which would be the advantages and disadvantages of expressing GWP as thermal energy trapped per molecule rather than per gram of substance?
Share and discuss your ideas with one of your classmates. Don’t forget to clearly justify your reasoning and procedures.
CFC’s
Chlorofluorocarbons (CFC’s), such as CCl2F2, are synthetic substances that
were used as refrigerants in cars and air conditioning systems but have been
banned due to their ability to react with ozone in the stratosphere and thus
destroy the ozone layer. Although present in very small concentration in the
atmosphere, CFC’s tend to have a very high GWP and are responsible for
close to 10% of atmospheric warming.
Despite the fact that chlorofluorocarbons (CFC’s) were banned in 1996,
there are still approximately 100 million functioning air conditioning units
that use CCl2F2. If each of these air conditioning units contains 1.1 kg of this
compound and leaks 25% a year:
•
How many moles of CCl2F2 are added to the atmosphere yearly?
•
What number of moles of CO2 would have a warming effect equivalent to that of the amount of CFC released every year?
•
Americans produce close to 1.97 x 103 kg of CO2(g) per capita every year. How many people would be needed to produce CO2(g) in
amounts that could have the same warming effect as the CFC released?
Share and discuss your ideas with one of your classmates. Don’t forget to
clearly justify your reasoning.
CClF3
CCl3F
CHClF2
ASSESS WHAT YOU KNOW