1. 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

2. 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
P1 = 224 mm Hg
T1 = 293 K
V2 = ?
P2 = 760 mm Hg
T2 = 273 K
P1V1/T1 = P2V2/T2
(224 mmHg)(201L)/293 K = (760 mmHg)V2/273 K
(224mmHg)(201L)(273 K)
= V2
(760mmHg)(293 K)
55 L= V2
Episode 903

3. 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

4. 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 = kPa•L/mol•K
Value of R when using atm and liters
R = atm•L/mol•K
Episode 903

5. Ex: The average lung capacity for a female student is 3. 9 L
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
n = ?
R = kPa•L/mol•K
(310 K)
PV = nRT
(110 kPa)(3.9 L) = n(8.314 kPa•L/mol•K)(310 K)
0.17 mol = n
Episode 903

6. 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

7. Mole Ratio Molar Volume
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  O KNO2
? Liters O2 = 3.2 moles KNO3
3.2 mol KNO3
1 mol O2
22.4 L O2
= 36 L O2
2 mol KNO3
1 mol O2
Mole Ratio
Molar Volume
Episode 903

8. 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

9. PT = PH2O + PO2 95.0 kPa = 3.17 kPa + PO2 91.8 kPa = PO2
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
95.0 kPa = 3.17 kPa + PO2
PT = 95.0 kPa
91.8 kPa = PO2
25⁰C = 3.17 kPa
(Look on water vapor chart)
Episode 903