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Chemical
Quantities
Chapter 10
Introduction
• Counting and measuring quantities of
atoms and molecules
• Convert between units of volume, mass,
and quantities of molecules, atoms, etc.
• Calculate the percent composition of
compounds and derive the empirical and
molecular formulas and masses
The Mole: A Measurement of
Matter (Section 10.1)
• Measuring
matter
• What is a
mole?
• The mass of
a mole of an
element
• The mass of
a mole of a
compound
I. Measuring Matter
•
Measure matter in
three ways:
1. Mass
2. Volume
3. Counting
• Recall the SI Units for
mass and volume
1. Mass: kg
2. Volume: L
• Remember how to use
the prefixes
Matter: Anything that has
Mass and occupies
space. (Ch. 1)
Units that indicate a specific
number of objects.
• Dozen = 12
• Pair = 2
• Ream = 500
• Gross = 144
A relationship can be established
between count units and mass or
volume.
• Let’s say 1 dozen apples = 2.0 kg and
1 dozen apples = 0.20 bushels
• We can use these relationships to set up 3
conversion factors:
1 dozen
1dozen
1 dozen
12 apples 2.0 kg apples 0.20 bushels
Let’s quickly review dimensional
analysis.
• Dimensional analysis is a tool for solving
conversion problems (going from one unit
to a different unit)
• A conversion factor (a ratio relating the
two units involved in the conversion) is
used.
• Simple multiplication of the ratios will yield
the desired conversion.
Three basic questions to ask when
doing dimensional analysis:
1. What unit do I start out with?
2. What unit do I want to end up
with?
3. What conversion factor relates
those two units?
Let’s try a problem.
What is the mass of 90 average-sized
apples if one dozen of the apples has a
mass of 2.0 kg?
II. What is a Mole?
A mole (mol) of a substance is 6.02 x 1023
representative particles of that substance
and is the SI unit for measuring the amount
of a substance.
• The mole makes counting atoms and
molecules more feasible.
• 6.02 x 1023 is known as Avogadro’s number.
• Representative particle: the species present
in a substance (i.e. atoms, molecules).
What would a mole of stuff look
like?
1 mole of atoms would
cover the entire Earth
to a depth of 50 miles.
A mole of dollars would guarantee
every person in the world
(~ 6 billion people) an income of
over $3 million dollars each second
for 100 years.
And how about a mole of moles?
• The mass of a mole of
moles would be 60
times greater than the
mass of all the water in
all the oceans.
• A mole of moles lined
up end-to-end would
stretch from here to the
nearest star more than
2 million times.
What are these “representative
particles?”
• Most
Elements
• Some
Elements
• Molecular
Compounds
• Ionic
Compounds
Atoms
(Fe, Na, P)
Diatomic Molecules
(O2, N2, Cl2)
Molecules
(CH4, H2O)
Formula Unit
(NaCl, CaCl2)
We can use the mole to particle
relationship as a conversion factor.
• The equivalence is:
1 mole = 6.02 x 1023 representative particle
• Which gives us the following conversion
factors:
1 mole
6.02 x 1023 particles
6.02 x 1023 particles
1 mole
• We can use these conversion factors to go
from moles to particles and vice versa.
# of Particles to Moles
• What is the “unit” that we start out with?
# of particles
• What “unit do we want to end up with?
mole
• Which conversion factor would we use?
1 mole
6.02 x 1023 particles
Let’s try a problem.
Magnesium is a light metal used in the
manufacture of aircraft, automobile
wheels, tools, and garden furniture. How
many moles of magnesium is
1.25 x 1023 atoms of magnesium?
Moles to # of Particles
• What is the “unit” that we start out with?
mole
• What “unit do we want to end up with?
# of particles
• Which conversion factor would we use?
6.02 x 1023 particles
1 mole
Let’s try a problem.
Propane gas is used for cooking and
heating. How many atoms are in 2.12 mol
of propane (C3H8)?
III. The Mass of a Mole of an
Element
• Atomic masses are expressed
in atomic mass units (amu).
– Remember these are
“weighted averages.”
• By converting this relative scale
to the more convenient mass
scale in grams, we get values
that are easier to measure out.
• Thus, the atomic mass of an
element expressed in grams
is the mass of one mole of
the element.
Mass of 1 mole of marbles
(if 1 marble = 1 g.)
6.02 x 1023 g.
Molar Mass
The mass of 1 mole of an element.
• These masses are essentially the same as
the average atomic masses given in the
periodic table.
• If you take one mole of any element and
weigh it, the mass will be equal to the
molar mass.
IV. The Mass of a Mole of a
Compound
• In order to find the mass of a mole of a
compound, we must know the formula of the
compound.
• Calculate the mass of a compound by adding
the atomic masses of the atoms that make up
the compound.
• The molar mass of any compound is the mass in
grams of 1 mole of that compound.
Let’s try a problem.
The decomposition of hydrogen peroxide
(H2O2) provides sufficient energy to
launch a rocket. What is the molar mass
of hydrogen peroxide?
Mole-Mass and Mole-Volume
Relationships (Section 10.2)
Representative
Particles
• The MoleMass
Relationship
• The MoleVolume
Relationship
Mole
Mass
Volume
I. The Mole-Mass Relationship
• The mole-mass relationship is essentially
the relationship between # of particles to
mass they have.
• In section 10.1 we saw how the mole is
related to mass by the molar mass of a
substance (element or compound).
• We can use the molar mass to convert
between the moles of a substance and its
mass (more dimensional analysis!).
Let’s see how this is done.
What is the mass of 3.00 mol of NaCl?
1. Calculate the molar mass of NaCl.
2. Use this as the conversion factor.
3. Solve for the answer using dimensional
analysis.
Let’s convert from mass to moles.
How many moles is 10.0 g. of sodium
sulfate?
II. The Mole-Volume Relationship
• The mole-volume relationship is
essentially a relationship between # of
particles and the volume they occupy.
• For gases the mole-volume relationship is
not as straight forward as the mole-mass
relationship.
• For gases, volume is dependent upon
temperature and pressure.
The mole-volume relationship in
gases is straight forward if we
define the specific conditions the
gases are in.
• This is because gases occupy different
volumes at different temperatures and
pressures.
• To compare the mole-volume relationships
of different gases we must compare at the
same temperature and pressure (“STP”)
Avogadro’s Hypothesis
Equal volumes of gases at the same
temperature and pressure contain the
same number of particles.
• Though gas molecules are not the same
sizes, the spaces between gas molecules,
for any gas is so large, it makes the sizes
of the individual gas molecules
insignificant.
• All three gases occupy the same volume
(22.4 L) and have the same number of
particles (1 mol) because they are all at the
same temperature and pressure.
What is STP?
• STP = “Standard Temperature and
Pressure”
– Temperature = 0O C.
– Pressure = 101.3 kPa or 1 atm.
• At STP the following relationship exists
between moles and volume:
I mole = 22.4 L (“Molar Volume”)
or
6.02 x 1023 particles = 22.4 L
Calculating the volume of a gas at
STP.
• The molar volume is used to convert a
known number of moles of gas to the
volume of the gas at STP.
• The conversion factors are:
22.4 L
1 mol
1 mol
22.4 L
• The choice of conversion factor depends
on whether you start with mol or L.
Let’s try a problem.
If you have 0.375 mol of O2, what volume
would it occupy at STP?
Calculating the molar mass of a
gas from its density.
• Different gases have different densities
(d= m/v).
• For gases the density is measured in
grams per liter (g/L) at a specific
temperature.
• We can use this density of a gas to
calculate its molar mass.
• molar mass = density (STP) x molar vol.
Let’s analyze the units and see
how we can determine molar mass
from density and molar volume.
1. What are the units of density?
2. What are the units of molar volume?
3. What happens when we multiply them?
4. What do these units describe?
Let’s try a problem.
The density of a gaseous compound
containing carbon and oxygen is found to
be 1.964 g/L at STP. What is the molar
mass of the compound?
A Summary of the Mole
• A unit equivalent to 6.02 x 1023 particles.
• The “particles” are atoms, ions, molecules,
and formula units.
• It’s relationships to mass and volume allow
us to convert between mass, volume, and
number of particles.
The Mole and Conversions
1. Four types of conversion problems:
• mol
particles (atoms,etc)
– 1 mol = 6.02 x 1023 particles
•
mol
mass
– molar mass (g/mol)
•
mol
volume
– molar volume (1 mol = 22.4 L @ STP)
•
density
– molar volume
molar mass
Percent Composition and
Chemical Formulas (Section 10.3)
• The Percent
Composition of
a Compound
• Empirical
Formulas
26.8% Cr
40.3% K
32.9% O
• Molecular
Formulas
Potassium Chromate, K2CrO4
I.
The Percent Composition of
a Compound
The relative amounts of the elements
in a compound.
• In other words, the % composition is the
percent by mass of each element in a
compound.
• This consists of the percent value for each
element of a compound.
Let’s look at an example.
• Each
percentage
represents the
percent by
mass of each
element.
• The total has
to equal 100.
26.8% Cr
40.3% K
32.9% O
Potassium Chromate, K2CrO4
Obtaining % Composition from
mass data.
• We can obtain the percent composition of
a compound if we have information on the
masses of the elements that make up the
compound and the total mass of the
compound.
• We can obtain these masses
experimentally.
In other words, plug numbers into
the following equation.
% mass
= mass of the element x 100
of an element
mass of compound
Let’s try a problem.
When a 13.60 g. sample of a compound
containing only magnesium and oxygen is
decomposed, 5.40 g. of oxygen is
obtained. What is the percent composition
of this compound?
Obtaining the percent composition
from the chemical formula.
• The chemical formula allows us to
determine the percent composition of a
compound.
• This is because the % composition of a
compound stays the same regardless of
how much of it we have.
• The subscripts in the formula is used to
calculate the mass of each element in 1
mole of a compound.
Let’s look at an example.
Water = H2O
11.1% H and 88.9% O by mass regardless
of the volume of water
We can use the following equation
to obtain the percent composition
from the chemical formula:
% mass = mass of element in 1 mole
of compound
molar mass of compound
x 100
Obtaining % Composition from the
chemical formula.
1. Know what the chemical formula is.
2. Determine the molar mass of each
element.
3. Calculate the total mass of the
compound.
4. Divide the molar mass of each element
by the total mass of the compound and
divide by 100.
Let’s try a problem.
Propane (C3H8), the fuel commonly used
in gas grills, is one of the compounds
obtained from petroleum. Calculate the
percent composition of propane.
II. Empirical Formulas
• Formulas for some molecular compounds
show a basic ratio of elements.
• Multiplying that ratio by any factor can
produce formulas for other compounds.
• This “basic ratio” is known as the empirical
formula.
Defining “empirical formula”
A formula which gives the lowest
whole-number ratio of the
atoms of the elements in a compound.
• The percent composition is required to
calculate the basic ratio of the elements
contained in a compound.
• The empirical formula, like any chemical
formula, may be interpreted in terms of
number of atoms and in terms of moles of
each atom.
Interpreting the empirical formula.
Ethyne (aka: acetylene)
C2H2
Polystyrene
(aka: packing material)
C8H8
What is the empirical
formula
for ethyne and
styrene?
Determining empirical formulas
1.
2.
3.
4.
5.
6.
7.
Identify the percent composition of each element in
a compound.
Assume 100 g. total molar mass for the compound.
Convert percentages to masses.
Use molar masses of the elements to convert
masses to moles
Divide all moles by the smallest number of moles.
The numbers obtained will give us the smallest
whole number ratio for each element in the
compound.
If a whole number is not obtained, multiply each ratio
by the smallest whole number that will convert both
subscripts to whole numbers.
Let’s try a problem
A compound is analyzed and found to
contain 25.9% nitrogen and 74.1%
oxygen. What is the empirical formula of
the compound?
III. Molecular Formulas
• Many compounds share the same
empirical formula, however they may have
different molar masses.
• The difference in the molar masses of
these compounds are usually simple
whole-number multiples of the molar mass
of the empirical formula.
Let’s look at some examples.
Glucose
C6H12O6
(180g/mol)
Acetic acid
C2H4O2
(60g/mol)
Formaldehyde
CH2O
(30g/mol)
What can we conclude about the
molecular formula?
The molecular formula of a
compound is either the same as its
experimentally determined
empirical formula, or it is a simple
whole-number multiple of its
empirical formula.
To determine the molecular formula
from the empirical formula, we need
to know the compounds molar mass.
• We can obtain
this molar
mass
experimentally
using a
machine
known as a
mass
spectrometer.
Determining the molecular formula.
1. Determine the empirical formula.
2. Calculate the molar mass of this formula.
3. Obtain the molar mass of the compound
in question.
4. Divide this molar mass by the molar
mass of the empirical formula.
5. This is the multiplier used to obtain the
molecular formula from the empirical
formula.
Let’s try a problem.
Calculate the molecular formula of a
compound whose molar mass is 60.0g/mol
and empirical formula is CH4N.
Chemical
Quantities
Chapter 10
The End