Download States of Matter and Charles* Law

STATES OF MATTER AND
BOYLE’S LAW
Text 9.1: Page 418-428
Uses of Gases
States of Matter
Examples of States

There are examples of elements that exist in
each of the 3 states at the room temperature
What Determine State?

What state each compound is in is
dependent on the strength of the
intermolecular bonds
 Bond
between molecules in the solid
state are the strongest of the three
 Bond between molecules in the
gaseous state are the weakest of
the three
Kinetic Molecular Theory

Called this because any
moving object has kinetic
energy
 The
energy of movement
or motion
 Different states are
associated with different
amounts of kinetic energy
Kinetics of Gases?
Movement of Molecules

Molecules can move in 3
directions
 Translational:
straight line
 Rotational: spinning
 Vibrational: back-andforth motion of atoms
within the molecules
Movement of States

If molecules are restricted to
vibrational they will stay as
solids and in a ordered state
 Both
gases and liquids will
display all 3 types of motion
but to different degrees
Movement Between States
Gas Laws: Boyle’s Law

Is a mathematical equation that describes how
pressure alters the volume of a gas
p1v1=p2v2
Gas Laws: Boyle’s Law

Is a mathematical equation that describes how
pressure alters the volume of a gas
p1v1=p2v2
What Does this Mean?
…as the pressure on a gas increases, the volume of the
gas decreases proportionally, provided that the
temperature and amount of gas stays constant…

Relationship between pressure and volume:
 As
pressure increases, volume decreases
 i.e. when pressure is doubled, volume is halved
What Does this Mean?
…as the pressure on a gas increases, the volume of the
gas decreases proportionally, provided that the
temperature and amount of gas stays constant…

Relationship between pressure and volume:
 As
pressure increases, volume decreases
 i.e. when pressure is doubled, volume is halved
Measure Pressure?

Pressure is measures in
Pascal’s (Pa)
 This
represents I newton
(N) on an area of 1 m2
 Atmospheric pressure =
1000 Pa or 1 kPa
 Also at times measured in
mm Hg because of an
instrument we used to use
to measure pressure
STP and SATP

For many years did all calculations at STP
(standard temperature and pressure)
0

⁰ C and 101.325 kPa
Now generally use SATP (standard ambient
temperature and pressure
 25⁰
C and 100 kPa
 This is also much closer to many laboratory
conditions
STP and SATP

For many years did all calculations at STP
(standard temperature and pressure)
0

⁰ C and 101.325 kPa
Now generally use SATP (standard ambient
temperature and pressure
 25⁰
C and 100 kPa
 This is also much closer to many laboratory
conditions
Practise Problem
A 2.0L party balloon at 98 kPa is taken to a top of a mountain
where the pressure is 75 kPa. Assume the temperature is the same.
What is the new volume of the balloon?
(Page 428)
Homework!
CHARLES', GAY-LUSSAC’S
AND COMBINED GAS LAW
Text 9.1: Page 429- 438
Learning Goals

By the end of this class, the students will be able to:
 Describe
how temperature and volume in gases are
related in terms of Charles’ Law and kinetic molecular
theory
 Describe how temperature and pressure in gases are
related in terms of Gay-Lussac’s Law and kinetic
molecular theory
Gas Laws: Charles’ Law

Is a mathematical equation that describes how
temperature alters the volume of a gas
V1
V2
=
T1
T2
What Does this Mean?
…as the temperature of a gas increases, the volume of
the gas increases proportionally, provided that the
pressure and amount of gas stays constant…

Relationship between temperature and volume:
 As
temperature increases, volume increases
 i.e. when temperature is doubled, volume is doubled
Temperature

Many times temperature
measured in Kelvins
 Another
unit to measure
temperature
 Measure from absolute
zero
 Where
there is absolutely
no kinetic movement in
molecules
K
= ⁰ C + 273
Standards

For many years did all calculations at STP
(standard temperature and pressure)
 273.15

K (0 ⁰ C) and 101.325 kPa
Now generally use SATP (standard ambient
temperature and pressure
K (25⁰ C) and 100 kPa
 Both of these values of K have more digits but
reduced to 3 significant digits
 298.15
Practise Problems
A gas inside a cylinder with a movable piston is heated
from 25⁰C to 315 ⁰C . What is the new volume of the
gas knowing the initial volume was 0.30L? (Text 433)
Gas Laws: Gay-Lussac’s Law

Is a mathematical equation that describes how
temperature alters the pressure of a gas
P1
P2
=
T1
T2
What Does this Mean?
…as the temperature of a gas increases, the pressure of
the gas increases proportionally, provided that the
volume and amount of gas stays constant…

Relationship between pressure and temperature:
 As
temperature increases, pressure increases
 i.e. when temperature is doubled, pressure is doubled
Practise Problems
A sealed storage tank contains argon gas at 18⁰ C and
a pressure of 875 kPa at night. What is the new
pressure if the tank and its contents warm to 32⁰ C
during the day?
(Text 435)
Gas Laws: Combined Gas Law

Is a summary mathematical equation that
describes how pressure, temperature and volume
all interact
P 1 V1
P 2 V2
=
T1
T2
What Does this Mean?

You can use this equation
to remember all three of
the other equations.
 Simple cancel out the
variables that stay
constant!
Boyle’s Law
P 1 V1
P 2 V2
=
T1
T2
Charles’s Law
P 1 V1
P 2 V2
=
T1
T2
Gay-Lussac’s Law
P 1 V1
P 2 V2
=
T1
T2
Practise Problems
A balloon contains hydrogen gas at 20⁰ C and a pressure of 100
kPa and a volume of 7.50L. Calculate the volume of the balloon
after it rises to an upper atmosphere with a pressure of 28 kPa
and a temperature of -36 ⁰ C ?
(Text 437)
MIXTURES, PARTIAL
PRESSURES AND REACTIONS
Text 10.1-10.2: Pages 460-471
Mixtures of Gases

Many years ago scientists
believed that the atmosphere
was made of only one chemical
compound
 Antoine
Lavoisier (1743-1794)
was the first to give evidence
that the atmosphere was made
of a mixture of gases
 He was also known as the father
of modern chemistry
Antoine Lavoisier

He did a series of
experiments that involved
burning different compounds
in the presence of air
 Based
on these experiments he
concluded the atmosphere was
made of at least 2 gases
 One that supported combustion
and one that did not
Antoine Lavoisier

Lavoisier also noticed if he
burned something in a sealed
container when that container
was opened to air would rush in
 This
is because there was a lower
pressure in the container because
of the volume of gas consumed in
the combustion
John Dalton

John Dalton more
specifically did work on
the properties of gases
 He
hypothesized that
gas molecules work
independently and will
produce the same
pressure whether in a
mixture or on its own
Experimental Design
Dalton’s Law of Partial Pressures

From his experiments he came up with his law…
“The total pressure of a mixture of non-reacting
gases is equal to the sum of the partial pressures of
the individual gases”
ptotal = p1 + p2 + p3 … pn

A partial pressure , p, a gas in a mixture would
exert if it were the only gas present in the same
volume and at the same temperature
Kinetic Molecular Theory… Again?

This law can be explained
via kinetic molecular theory
 The
collisions are what cause
the pressure
 It doesn’t matter what type of
gaseous molecules are causing
the collisions, just that a specific
number of collisions are
happening
Practise Problems
“ A compressed air tank for scuba diving to a depth of
30 m, a mixture with an oxygen partial pressure of 28
atm and a nitrogen partial pressure of 110 atm is used.
What is the total pressure of the tank?”
(Page 461)
Reactions of Gases

Even though gases occur in mixtures around us, they
also can react with one another!
 But always follow The Law of Combining Volumes
 Volumes
of gases combine according to mole ratios
“When measured at the same temperature and
pressure, volumes of gaseous reactants and
products of chemical reactions are always in simple
ratios of whole numbers”
Avogadro’s Theory

Even more fully explained by Avogadro’s Theory
 “Equal
volumes of gases at the same temperature
and pressure contain equal numbers of molecules”
 Thus we can still use mole ratios to predict volumes of
products produced in chemical equations
Practise Problems
“A catalytic converter in the exhaust system of a car uses
oxygen (from the air) to convert carbon monoxide to
carbon dioxide, which is released through the tailpipe. If
we assume the same temperature and pressure, what
volume of oxygen is required to react with 125 L of
carbon monoxide produced during a 100km trip?”
(Page 468)
Moles of Gases?!?

We can determine moles of a gas from the volume
it takes up
 Molar
volume (MV): is the volume that one mole of a
gas takes up at a specified temperature and
pressure
At SATP 24.8 L/mol
At STP 22.4 L/mol
n = V / MV
Or
Moles = volume / molar volume
Practise Problem
“What volume is occupied by 0.024 mol of carbon
dioxide gas at SATP?”
(Page 469)
IDEAL GAS LAW
Text 9.4: Page 443-445
Make Sense?

One last relationship described how volume and
number of moles relate
 It
makes sense that as the number of moles increases so
does the volume it takes up
 More moles, more molecules, more volume!
vαn
Assumptions…
 All
calculations we have
done have made one main
assumption:
 That
we are dealing with an
IDEAL gas
 An
ideal gas is a
hypothetical gas that obeys
all the gas laws perfectly
under all conditions
An Ideal Gas

The problem is…
Ideal Gases DONT Exist!


They don’t condense into a liquid when cooled
They perfectly graph relationships between
pressure, temperature and volume they would
have exactly linear relationships
Ideal Gas Law

There is an equation that summarizes the
characteristics of ideal gases
PV= nRT
P = Pressure in kPa
V= Volume in L
R= 8.31 kPa L/ mol K
n= Moles in… moles
T= Temperature in K
The Gas Constant

R = The Gas Constant
 8.31

kPaL/ mol K
The constant of variation
that relates the pressure
in kPa, volume in L,
amount in Moles and
Temp in K
 Of
an Ideal Gas
An Example of Ideal Gas Relationships
The Real Gas Equation:

Note: You do not need to know this equation, just that
ideal gases don’t exist and they actually behave like:
(P+ n2a/V2)(V-nb)= nRT


This is also known as the van der Waals equation
Where:


a = is a measure of attraction between particles
b = is the average volume of gas particles
Van Der Waals Again?

This equation is also known as
the Van Der Waals equation
 Taking
into account the two new
variables:
a
= is a measure of attraction
between particles
 b = is the average volume of
gas particles
…
Why do you think this is
called the Van Der Waals
equation?
Ideal vs. Real Gases


The Difference Between Ideal and Real Gases can
be done by calculating the Pressure Difference. In
the case below this is the pressure exerted by
0.3000 mol of helium in a 0.2000 L container at 25 °C.
Pnon-ideal - Pideal = 32.152 atm - 30.55 atm
Pnon-ideal - Pideal = 1.602 atm
Practice Problems
What mass of neon gas should be introduced into an
evacuated 0.88L tube to produce a pressure of 90 kPa at
30⁰ C?
(Page 444)
Practice Problems
What amount of methane gas is present in a sample that
has a volume of 500 mL at 35.0 ⁰C and 210 kPa?
(Page 445)
Homework!