Chapter 12.
Behavior of Gases
God made matter, but surfaces
were the work of the devil.
Wolfgang Pauli
Behavior of Gases
Gases are substances in which intermolecular forces are quite weak, and can be overcome by the kinetic energy of the molecules.
An "ideal" gas has no intermolecular
forces, and the "molecules" are tiny spheres
that undergo perfectly elastic collisions.
Behavior of Gases
The behavior of real gases can be approximated by the gas laws.
The gas laws are equations that quantitatively
describe behavior of certain properties of
gases.
Properties: Pressure, Temperature, Volume
the amount of gas is constant.
Pressure
Pressure = Force per unit area
Units of Pressure:
Pounds/square inch
Pascals, 1 Pa = 1 kg/(msec2)
Atmospheres
1 atm = 14.7 psi, 101 kPa
Millimeters of mercury
760. mm Hg, 29.9 in Hg
Pressure
Pressure
Temperature
Temperature is a measure of the hotness
or coldness of a body or environment.
Must be converted to Kelvins for gas law
calculations.
K = C + 273
There is no "below zero" or negative temperature on the Kelvin scale.
Temperature
Volume
Volume is the space occupied by a substance, in this case a gas.
Usually expressed in liters or milliliters
Boyle's Law
As the pressure on a gas is increased,
its volume will decrease,
and vice versa.
P x V = constant
P1 x V1 = P2 x V2
Temperature is constant
Boyle's Law
Boyle's Law
Boyle's Law
Problems:
An air mattress has a volume of 114 L in
the mountains, when it is put in the pickup truck. The atmospheric pressure is
0.925 atm. At the beach, the pressure is
0.975 atm. What is the volume of the air
mattress at the beach?
Boyle's Law
Problems:
An inflatable toy has a volume of 310. mL
when a child takes it aboard an airliner.
The atmospheric pressure is 0.995 atm.
As the airliner climbs, the cabin pressure
drops. The toy expands to a volume of
440. mL. What is the air pressure in the
airplane?
Charles' Law
As the temperature of a gas is increased,
its volume will increase, and vice versa.
V = constant
T
V1 = V2
T1
T2
Pressure is constant.
Charles' Law
Charles' Law
Charles' Law
Problems:
A balloon has a volume of 1.00 L while it
sits in a car on a sunny day. The temperature is 25C. The night is clear and
cold, and the temperature drops to 15C.
What is the volume of the balloon when
the air is cold?
Charles' Law
Problems:
A sample of nitrogen gas has a volume of
675 mL at 23C. To what temperature
must it be raised to increase its volume
to 710. mL?
Gay-Lussac's Law
As the temperature of a gas is increased,
its pressure will increase, and vice versa.
P = constant
T
P1 = P2
T1
T2
Volume is constant.
Gay-Lussac's Law
Problems:
A sample of nitrogen gas has a volume of
675 mL at 23C at 1.00 atm pressure.
It is warmed to 38C (about 100F).
What pressure will it reach if its
container has a constant volume?
The Combined Gas Law
Accounts for changes in pressure, temperature, and volume simultaneously.
P1V1 = P2 V2
T1
T2
The amount of gas is constant.
Memorize this formula, it contains all the others.
Combined Gas Law
Problems:
An individual has a lung capacity of 450 mL.
The air in the lungs is at body temperature
(37C) and 754 mm Hg. What volume
would the exhaled air have on a cold
winter day, with a temperature of –5C
and a pressure of 750. mm Hg?
Combined Gas Law
Problems:
A sample of argon gas occupies a volume of
80.0 mL at a pressure of 1.10 atm and a
temperature of 20C. What will the
temperature of the gas be, in C, if the
volume of the container is decreased to
40.0 mL and the pressure is increased to
2.20 atm?
…if the volume is decreased to 30.0 mL and
the pressure is increased to 3.00 atm?
Standard Temperature
and Pressure
Gases expand and contract freely with
changes in temperature and pressure.
Liquids and solids don’t do this.
Therefore we define a standard temperature and pressure for measurement
and comparison.
Standard Temperature
and Pressure
Temperature = 0.0C, 273 K
Pressure = 1.00 atm, 760. mm Hg
Standard Temperature
and Pressure
Problems:
A sample of neon gas has a volume of
23.4 L at STP. What would its volume
be at 0.750 atm and –20.C?
Gay-Lussac’s Law of
Combining Volumes
Volumes of gases that participate in chemical
reactions combine in the same ratios as the
coefficients for the compounds if all the
gases are at the same temperature and
pressure.
N2(g) +
1 volume
3 H2(g) 
3 volumes
2 NH3(g)
2 volumes
Gay-Lussac’s Law of
Combining Volumes
Problems:
N2(g) +
1 volume
3 H2(g) 
3 volumes
2 NH3(g)
2 volumes
What volume of ammonia will be formed
from 60. L of H2 and excess nitrogen?
What volume of nitrogen will be required
to react with 60. L of H2?
Avogadro’s Law
Equal volumes of different gases, at the
same temperature and pressure, contain equal numbers of molecules.
This explained Gay-Lussac’s Law.
It led to the discovery that the common
gaseous elements were diatomic
molecules.
Avogadro’s Law
The water puzzle:
4 g hydrogen + 32 g oxygen  36 g water
2 L hydrogen + 1 L oxygen  2 L water vapor
2 H2(g) + 1 O2(g)  2 H2O(g)
Standard Molar Volume
One mole of an ideal gas will occupy
22.414 L at STP.
This is roughly 5 1/2 gallons.
Conversion factors (like molar mass, g/mol)
1 mol gas
22.41 L gas
22.41 L gas
1 mol gas
The Ideal Gas Law
Relationship between P, V, T, and number
of moles of gas.
PxV
T
=
kn
P x V = k = 22.41 L x 1.00 atm
nxT
1.00 mol x 273K
k = 0.0821 L  atm = R
mol  K
The Ideal Gas Law
Relationship between P, V, T, and number
of moles of gas.
PV
=
nRT
P = Pressure in atmospheres
V = Volume in liters
n = number of moles of gas molecules
T = temperature in Kelvins
The Ideal Gas Law
Problems:
A portable oxygen tank holds 2.00 L at a
pressure of 2000. psi. At room temperature, 25C, how many moles of gas
are present?
How many grams of oxygen are present?
What is the density of the oxygen?
The Ideal Gas Law
Problems:
What is the volume of 1.52 moles of carbon
monoxide in a container at 0.992 atm and
a temperature of 65C?
The Ideal Gas Law
Problems:
A few milliliters of acetone are put in a vented
flask that holds 100. mL. The flask is placed
in a boiling water bath at 1.00 atm pressure,
and the acetone vaporizes. Most of the vapor escapes, but 0.183 g remains.
How many moles of acetone are present?
What is its molar mass?
Dalton’s Law of
Partial Pressures
The total pressure exerted by a mixture of
gases is the sum of the partial pressures
of the individual gases.
The partial pressure of a gas in a mixture is
the pressure it would exert if it occupied
the space alone.
Ptotal = p1 + p2 + p3 + …
Dalton’s Law of
Partial Pressures
Partial pressures of gases in a mixture are
proportional to the number of moles of
each gas in the mixture.
A mixture of 5.00 mol He, 2.00 mol O2, and
7.00 mol N2 has a pressure of 4.50 atm.
What are the partial pressures of the
gases?
If the gases occupy a volume of 10.0 L,
what is the temperature of the mixture?
Dalton’s Law of
Partial Pressures
Collecting a Gas over Water
Collecting a Gas over Water
The volume of gas collected must be corrected for the partial pressure of water
vapor at that temperature.
The vapor pressure of water at room temperature is about 20. mm Hg, and won’t
cause a substantial error.
How big an error will it cause?
Collecting a Gas over Water
Vapor Pressure of Water as a function of Temperature
1
Vapor Pressure,
Atmospheres
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
70
Temperature, degrees C
80
90
100