AP Chemistry
Unit 3
1
Gases
Kinetic-Molecular Theory
 Provides a model for gases at the microscopic level.
1. Gas molecules have negligible volume compared with space
between molecules (they are spread out).
2. Gas molecules are in constant, random motion. When they hit
the side of their container they contribute to pressure.
3. All collisions are elastic (molecules behave like billiard balls,
not soggy softballs).
4. Gas molecules have no attraction or repulsion for each other
(gas molecules don’t know other molecules are around).
5. The speed of gas molecules is proportional to temperature
(kinetic energy is related to speed).

1.
2.
3.
4.
5.
6.
Explains many properties of gases:
Gases are compressible.
Gases have low densities.
Gases mix completely.
Gases fill a container uniformly.
Gases exert pressure on side of container.
Gases flow easily (have low viscosity).
Variables that Describe Gases




2
Pressure (P): collision of gas molecules with wall of container
(force per unit area). Pa, kPa, atm, torr, mmHg
Temperature (T): related to average speed of gas molecules. K,
ºC, ºF
Volume (V): amount of space occupied by a gas. L, mL, cm3
Moles (n):the amount of gas. Moles, grams, molecules
Temperature Conversions
 K = C + 273
 F = 9/5(C) + 32
 C = 5/9 (F – 32)
Gas Laws

Boyle’s Law - as pressure increases volume decreases
(P1V1=P2V2)

Charles Law – as temperature increases volume increases
(V1/T1=V2/T2)

Gay-Lussac’s Law – as temperature increases pressure
increases (P1/T1=P2/T2)

Combined Gas Law – involves temperature, pressure, and
volume (P1V1)/T1=(P2V2)/T2)
Crash Course Notes:
3
Avogadro’s Law: Mole-Volume Relationship

At a fixed temperature and pressure, the volume of a gas is
directly proportional to the amount of gas in moles (n) or to the
number of molecules of gas.

Standard temperature and pressure (STP) is equal to…

The molar volume of a gas is…

At STP, molar volume of an ideal gas is _________________.

Example 5.8 Calculate the volume occupied by 4.11 kg of
methane gas, CH4(g), at STP.

The Combined Gas Law (including moles):
The Ideal Gas Law
 Equation:

4
P in atm, V in L, n in moles, T in Kelvin.

If any other units are used for these variables, CONVERT, or a
different value for R can be used…
Example 5.10 What is the pressure exerted by 0.508 mol O2 in a
15.0-L container at 303 K?
Example 5.11 What is the volume occupied by 16.0 g ethane gas
(C2H6) at 720 Torr and 18 °C?

5
Molecular Mass Formula:
Example 5.12 If 0.550 g of a gas occupies 0.200 L at 0.968 atm
and 289 K, what is the molecular mass of the gas?
Example 5.13 Calculate the molecular mass of a liquid that, when
vaporized at 100. °C and 755 Torr, yields 185 mL of vapor that has
a mass of 0.523 g.

Density Formula:

Density of a gas is directly proportional to its molar mass and
pressure, and is inversely proportional to Kelvin temperature.
6
Example 5.14 Calculate the density of methane gas, CH4, in
grams per liter at 25 °C and 0.978 atm.
Example 5.15 Under what pressure must O2(g) be maintained at
25 °C to have a density of 1.50 g/L?
Gases in Reaction Stoichiometry

7
When gases measured at the same temperature and pressure
are allowed to react, the volumes of gaseous reactants and
products are in small whole-number ratios.

Example: At a given temperature and pressure, 2.00 L of H2
will react with 1.00 L of O2 (Why 2:1? Balance the equation
…)

Example: At a given temperature and pressure, 6.00 L of H2
will react with 2.00 L of N2 to form 4.00 L of NH3 (Why
6:2:4? Balance the equation …)

We don’t need to know ______________conditions for the
reaction … as long as the _____________conditions apply to
all the gases.
Example 5.16 How many liters of O2(g) are consumed for every 10.0
L of CO2(g) produced in the combustion of liquid pentane, C5H12, if all
volumes are measured at STP?
8

We can use the law of combining volumes for stoichiometry
only for gases and only if the gases are at the same temperature
and pressure.

Otherwise, we must use stoichiometric methods from Chapter
3 combined with the ideal gas equation.
Handy Flow Chart:
Example: What volume of SO2 (g) is produced at STP, when 10.0
g of sulfur burns with an excess of oxygen according to the
reaction?
S8 (s) + 8 O2 (g) → 8 SO2 (g)
9
Example: How much NaN3 is needed to inflate a 50.0 L air bag to
1.15 atm at 25.0 ºC given the following chemical reaction?
2 NaN3 (s) → 2 Na (s) + 3 N2 (g)
10
Example 5.17 In the chemical reaction used in automotive air-bag safety
systems, N2(g) is produced by the decomposition of sodium azide, NaN 3(s), at a
somewhat elevated temperature:
2 NaN3(s) --> 2 Na(l) + 3 N2(g)
What volume of N2(g), measured at 25 °C and 0.980 atm, is produced by the
decomposition of 62.5 g NaN3?
11
Molar Mass Determination Using the Dumas Method:
Dalton’s Law of Partial Pressures

Dalton’s law of partial pressures is used in dealing with
__________________ of gases.

The total pressure exerted by a mixture of gases is equal to the
sum of the ________________________ exerted by the
separate gases:

Partial pressure:
12
Example 5.18 A 1.00-L sample of dry air at 25 °C contains 0.0319
mol N2, 0.00856 mol O2, 0.000381 mol Ar, and 0.00002 mol CO2.
Calculate the partial pressure of N2(g) in the mixture.

The ________________________________ of a gas is the
fraction of all the molecules in a mixture that are of a given
type.

An example: 0.100 mole of NaCl is dissolved into 100.0
grams of pure H2O. What is the mole fraction of HCl?
13

Since pressure (at constant T and V) is directly proportional to
number of moles:
Example 5.19 The main components of dry air, by volume, are
N2, 78.08%; O2, 20.95%; Ar, 0.93%; and CO2, 0.04%. What is the
partial pressure of each gas in a sample of air at 1.000 atm?
Collection of Gases over Water

As (essentially insoluble) gas is bubbled into the container for
collection, the water is _______________________.

The gas collected is usually saturated with _____________
____________________ because water is constantly
evaporating. The amount that evaporates depends on the
temperature of the water.
14

The water vapor in the container causes pressure. This is
called the ____________________________ of water. It can
be determined based on temperature from a table:
http://faculty.sdmiramar.edu/fgarces/zCourse/All_Year/Ch100_OL/aMy_FileLec/04OL_LecNotes_Ch100/07_Gas/701_GasLa
ws/701_pic/vaporpressure.jpg

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The total pressure of the container, then is the sum of the
partial pressure of the ___________________ and the
_____________________ produced:
Example 5.21 Hydrogen produced in the following reaction is
collected over water at 23 °C when the barometric pressure is 742
Torr:
2 Al(s) + 6 HCl(aq) → 2 AlCl3(aq) + 3 H2(g)
What volume of the “wet” gas will be collected in the reaction of
1.50 g Al(s) with excess HCl(aq)?
Example: 4.84 g of CaCO3 decomposes in a dilute HCl solution.
The CO2 gas is collected over water into a volume of 1.16 L. The
atmospheric pressure is 755 Torr. The temperature is 21 ºC. The
vapor pressure of water is 18.65 Torr at 21 ºC.
a. Find the volume of CO2 collected.
b. Calculate the percent yield.
16
Velocity of Gases

Velocity is difficult to calculate for gases because the particles
move….

We can consider velocity 2 ways:
o Net velocity –
o Average velocity –

What affects the velocity of gases:
o Temperature –
o Size of the particles (mass) –

There are formulas that can be used to calculate the speed of
molecules. It is known as ___________________________
____________________.
•
Kinetic Energy and Velocity are ________________________
______________________________.
–
Velocity is how ____________ the molecules are
moving
–
Kinetic energy is based on temperature __________.
•
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The higher the temperature, the greater the
kinetic energy.
•
–
Two different gases at the same temperature
have the same kinetic energy no matter the size
of their molecules, pressure, volume, etc.
As stated before, velocity _____________________
kinetic energy (temperature)
Effusion

Effusion is the process in which a gas…

Effusion is (mathematically) simpler than diffusion since
effusion does not involve ____________________________.

At a fixed T, the rates of effusion of gas molecules are
______________________ proportional to the square roots of
their molar masses:

The formula:
18
AP Test Question Equal numbers of moles of He(g), Ar(g), and
Ne(g) are placed in a glass vessel at room temperature. If the
vessel has a pinhole-sized leak, which of the following will be true
regarding the relative values of the partial pressures of the gases
remaining in the vessel after some of the gas mixture has effused.
a)
b)
c)
d)
e)
PHe< PNe< PAr
PHe < PAr < PNe
PNe < PAr < PHe
PAr < PHe < PNe
PHe = PAr = PNe
Example 5.23 If compared under the same conditions, how much
faster than helium does hydrogen effuse through a tiny hole?
Example 5.24 One percent of a measured amount of Ar(g)
escapes through a tiny hole in 77.3 s. One percent of the same
amount of an unknown gas escapes under the same conditions in
97.6 s. Calculate the molar mass of the unknown gas.
19
Diffusion

Gas molecules move from areas of __________ concentration
to areas of ________ concentration. They move to where it is
less crowded until they spread out evenly.

Diffusion is the process by which…

Diffusion of gases is much slower than would be predicted by
molecular speeds due to the frequent collisions of molecules.

The rate of diffusion, like effusion, depends on the mass of the
molecules.
Crash Course Notes:
20
Real Gases

Under some conditions, real gases do not follow the ideal gas
law:
1. Intermolecular forces of attraction cause the measured
pressure of a real gas to be less than expected.
(_________________________________________)
2. When molecules are close together, the volume of the
molecules themselves becomes a significant fraction of
the total volume of a gas. (______________________
_________________________)
3.

________________________ behave most like the ideal gases.

Which would deviate most from ideal behavior and why? H2,
H2O, or He
21
AP Free Response Example: A student was assigned the task of determining
the molar mass of an unknown gas. The student measured the mass of a sealed
843 mL rigid flask that contained dry air. The student then flushed the flask
with the unknown gas, resealed it, and measured the mass again. Both the air
and the unknown gas were at 23.0 C and 750. torr. The data for the experiment
are shown in the table below.
Volume of sealed flask
843 mL
Mass of sealed flask and dry air
157.70 g
Mass of sealed flask and unknown
gas
158.08 g
a)
Calculate the mass, in grams, of the dry air that was in the sealed flask. (The density
of dry air is 1.18 g/L at 23.0 ºC and 750. torr.)
b)
Calculate the mass, in grams, of the sealed flask itself (i.e. if it had no air in it).
c)
Calculate the mass, in grams, of the unknown gas that was added to the sealed flask.
22
d)
Using the information above, calculate the value of the molar mass of the unknown
gas.
e)
After the experiment was completed, the instructor informed the student that the
unknown gas was carbon dioxide. Calculate the percent error in the value of the
molar mass calculated in part d.
f)
For each of the following two possible occurrences, indicate whether it by itself
could have been responsible for the error in the student’s experimental result. You
need not include any calculations with your answer. For each of the possible
occurrences, justify your answer.

Occurrence 1: The flask was incompletely flushed with CO2 (g), resulting
in some dry air remaining in the flask.

Occurrence 2: The temperature of the air was 23.0 ºC, but the temperature
of the CO2 (g) was lower than the reported 23.0 ºC
23
g)
24
Describe the steps of a laboratory method that the student could use to verify that
the volume of the rigid flask is 843 mL at 23.0 ºC. You need not include any
calculations with your answer.