Chapter 14
Gas Laws
Standards
Students know how to apply the
gas laws to relations between the
pressure, temperature, and
volume of any amount of an ideal
gas or any mixture of ideal gases.
Dalton’s Law of Partial Pressures
For a mixture of gases in a
container,
PTotal = P1 + P2 + P3 + . . .
This is particularly useful in calculating
the pressure of gases collected over
water.
Dalton’s Law of Partial Pressure
• The total pressure in a container is
the sum of the pressure each gas
would exert if it were alone in the
container.
• The total pressure is the sum of
the partial pressures.
• PTotal = P1 + P2 + P3 + P4 + P5 ...
• For each P = nRT/V
Dalton’s Law Continued
• In the same container R, T and V
are the same.
• PTotal = n1RT + n2RT + n3RT +...
V
V
V
The Mole Fraction
• Ratio of moles of the substance to
the total moles.
• symbol is Greek letter chi

c1 =
n1 =
nTotal
P1
PTotal
c
Examples
• The partial pressure of nitrogen in
air is 592 torr. Air pressure is 752
torr, what is the mole fraction of
nitrogen?
• What is the partial pressure of
nitrogen if the container holding the
air is compressed to 5.25 atm?
.
Gas Density and Molar Mass
•
•
•
•
•
D = m/V
Let M stand for molar mass
M = m/n
n= PV/RT
M = m
PV/RT
• M = mRT = m RT = DRT
PV
V P
P
• PTotal = (n1+ n2 + n3+...)RT
V
• PTotal = (nTotal)RT
V
Examples
•• What
is the density of ammonia at
.
23ºC and 735 torr?
• A compound has the empirical
formula CHCl. A 256 mL flask at
100.ºC and 750 torr contains .80 g
of the gaseous compound. What is
the molecular formula?
Boyle’s Law
Pressure is inversely proportional to
volume when temperature is held
constant.
P1V1  P2V2
Examples
1. 20.5 L of nitrogen at 25ºC and 742
torr are
compressed to 9.8 atm at
constant T. What is the new volume?
2. 30.6 mL of carbon dioxide at 740
torr is expanded at constant
temperature to 750 mL. What is the
final pressure in kPa?
A Graph of Boyle’s Law
Charles’s Law
The volume of a gas is directly proportional
to temperature, and extrapolates to zero at
zero Kelvin.
(P = constant)
V1 V2

T1 T2
Temperature MUST be in KELVINS!
Examples
1.What would the final volume be if
247 mL of gas at 22ºC is heated to
98ºC , if the pressure is held
constant?
2. At what final temperature would 40.5
L of gas (23.4ºC) have a volume of
81.0 L at constant pressure?
A Graph of Charles’ Law
Gay Lussac’s Law
The pressure and temperature of a gas are
directly related, provided that the volume
remains constant.
P1 P2

T1 T2
Temperature MUST be in KELVINS!
Examples
1. A sample of nitrogen gas has a pressure of
6.58 kPa at 539 K. If the volume does not
change, what will the pressure be at 211 K ?
2. The pressure in a car tire is 198 kPa at
27°C. After a long drive, the pressure is
225 kPa. What is the temperature of the
air in the tire? Assume that the volume is
constant.
A Graph of Gay-Lussac’s Law
The Combined Gas Law
The combined gas law expresses the
relationship between pressure, volume and
temperature of a fixed amount of gas.
P1V1 P2V2

T1
T2
Examples
• A deodorant can has a volume of
175 mL and a pressure of 3.8 atm
at 22ºC. What volume of gas could
the can release at 22ºC and 743
torr?
Ideal Gases
Ideal gases are imaginary gases that
perfectly fit all of the assumptions of
the kinetic molecular theory.
Gases consist of tiny particles that
are far apart relative to their size.
Collisions between gas particles
and between particles and the walls
of the container are elastic collisions
No kinetic energy is lost in elastic
collisions
Ideal Gases
(continued)
Gas particles are in constant, rapid
motion. They therefore possess
kinetic energy, the energy of motion
There are no forces of attraction
between gas particles
The average kinetic energy of gas
particles depends on temperature, not
on the identity of the particle.
Real Gases Do Not Behave Ideally
Real gases DO experience inter-molecular
attractions
Real gases DO have volume
Real gases DO NOT have elastic collisions
Deviations from Ideal Behavior
Likely to behave
nearly ideally
Gases at high
temperature and low
pressure
Small non-polar gas
molecules
Likely not to behave
ideally
Gases at low
temperature and high
pressure
Large, polar gas
molecules
IDEAL GAS LAW





PV = nRT
P = pressure in atm, kPa, mm Hg
n = number of moles
V = volume in Liters
R is the ideal gas constant;
depends on the pressure unit
R = 0.0821 Latm/ Kmol or
R = 8.314 LkPa/ Kmol or
R = 62.36 LmmHg/ Kmol
Examples
1.A 47.3 L container containing 1.62 mol
of He is heated until the pressure
reaches 1.85 atm. What is the
temperature?
2.Kr gas in a 18.5 L cylinder exerts a
pressure of 8.61 atm at 24.8ºC What is
the mass of Kr?
3.A sample of gas has a volume of 4.18 L
at 29ºC and 732 torr. What would its
volume be at 24.8ºC and 756 torr?
Diffusion
 Diffusion describes the mixing
of gases. The rate of diffusion
is the rate of gas mixing.
 Diffusion is the result of
random movement of gas
molecules
 The rate of diffusion
increases with temperature
 Small molecules diffuse faster
than large molecules
Graham’s Law of Diffusion
Distance traveled by gas 1
M2

Distance traveled by gas 2
M1
M1 = Molar Mass of gas 1
M2 = Molar Mass of gas 2
Examples
1. Which gas effuses faster: hydrogen
or chlorine, and by what factor?
2. Calculate the ratio of the velocity of
helium atoms to fluorine molecules at
the same temperature.