The Combined Gas Law
• Expresses the relationship between
pressure, volume, and temperature of a
fixed amount of gas.
• PV/T = k or P1V1/T1 = P2V2/T2
Charles’ Law
Episode 903
• Ex: A sample of gas has a volume of
201 L when its temperature is 293 K
and its pressure is 224 mm Hg. What
volume will the gas occupy at STP?
• Given:
–
–
–
–
–
–
V1 = 201 L
P1V1/T1 = P2V2/T2
P1 = 224 mm Hg
T1 = 293 K
(224 mmHg)(201L)/293 K = (760 mmHg)V2/273 K
V2 = ?
P2 = 760 mm Hg
(224mmHg)(201L)(273 K)
= V2
T2 = 273 K
(760mmHg)(293 K)
55 L= V2
Episode 903
Diffusion
• The spontaneous spreading or mixing of
a substance.
Graham’s Law of Diffusion
• Under the same conditions of
temperature and pressure, gases
diffuse at a rate inversely proportional
to the square root of their density (or
molar mass).
• v1/v2 or
d2/d1 or
m2/m1
Episode 903
Ideal Gas Equation
• PV = nRT
• New variables
– n = amount of gas in moles
– R = Universal Gas Constant
•
•
•
•
•
•
Proportionality constant
value depends on units used for pressure and volume
value of R when using kPa and liters
R = 8.314 kPa•L/mol•K
Value of R when using atm and liters
R = 0.0821 atm•L/mol•K
Episode 903
Ex: The average lung capacity for a female
student is 3.9 L. At normal body
temperature, 37⁰C, and 110 kPa, how many
moles of air could her lungs hold?
Given:
P = 110 kPa
V = 3.9 L
T = 37 ⁰C (310 K)
n=?
R = 8.314 kPa•L/mol•K
PV = nRT
(110 kPa)(3.9 L) = n(8.314 kPa•L/mol•K)(310 K)
0.17 mol = n
Episode 903
Avogadro’s Law
• Equal volumes of different gases
under the same conditions have
the same number of particles.
• Conversely, if samples of
different gases at the same
temperature and pressure contain
the same number of particles,
then the volumes of all the
samples must be equal.
• At STP, one mole of any gas
occupies a volume of 22.4 Liters.
• 22.4 Liters is the molar volume
of a gas.
Episode 903
Ex: 3.2 moles of KNO3 are heated,
producing O2 and KNO2. Calculate the
volume of O2 in liters, that could be
obtained at STP.
2KNO3  O2 + 2KNO2
? Liters O2 = 3.2 moles KNO3
3.2 mol KNO3
1 mol O2
22.4 L O2
2 mol KNO3
1 mol O2
= 36 L O2
Episode 903
Dalton’s Law of Partial Pressures
• The pressure of a gas mixture is the
sum of the individual pressure of each
gas alone.
• PT = P1 + P2 + P3 + …
Episode 903
Ex: Oxygen gas has been collected over
water at a total pressure of 95.0 kPa
and a temperature of 25⁰C. What is the
pressure of the dry oxygen gas?
PT = PH2O + PO2
PT = 95.0 kPa
95.0 kPa = 3.17 kPa + PO2
PH2O @ 25⁰C = 3.17 kPa
91.8 kPa = PO2
(Look on water vapor chart)
Episode 903