Gas Laws

GAS LAWS

Properties of Gases
Gases expand into any available volume
• gas molecules escape from open containers.
Gases are completely miscible
• once mixed they will not spontaneously separate.

Gases are described in terms of T, P, V and n

Volume, Amount and Temperature
• A gas expands uniformly to fill the container in which it is placed
– The volume of the container is the volume of the gas – Volume may be in liters, mL, or cm3

• The temperature of a gas must be indicated on the Kelvin scale
– Recall that K = °C + 273.15

• Amount of a gas is the number of moles

Pressure
• Pressure is force per unit area
– In the English system, pounds per square inch or psi – Atmospheric pressure is about 14.7 psi
Pressure Units
SI:
1 pascal (Pa) = 1 kg m-1s-2 = 1N m-2 others: 1 bar = 105 Pa = 100 kPa
1 atm = 101.325 kPa = 1.01325 bar
1 atm = 760 torr = 760 mm Hg
1 atm = 14.7 lb/in2

KINETIC MOLECULAR THEORY
A gas consists of tiny molecules in rapid, random motion. Gas molecules:
• are small compared to the distances between them
 easily compressed.
 mix completely with other gases.
• move randomly at very high speeds.
• have small attractions/repulsions for each other.
 all gases behave the same way.
• make elastic collisions with each other.
 don’t slow over time & fall to bottom of container

KINETIC MOLECULAR THEORY
Kinetic energy Ek = 1/2 mv2
• When gas molecules collide, their speed and direction changes.

• All gas molecules are constantly moving:
– average speed is directly proportional to T (K).
– the distribution of speeds can be calculated.

The Ideal Gas Law
The ideal gas law is a combination of:

Boyle’s Law
V 1
P
fixed n and T

Charles’s Law
VT
fixed n and P

IDEAL GAS LAW
PV = nRT or V = nRT
P

Avogadro’s Law
Vn
fixed P and T

Methods in Solving Gas Law’s Problem
Given: P, V
Constant: n and T
Given: T, V
Constant: n and P
Analyze the problem
(What are the given and the required)

Boyle’s Law
P1 V1 = P2 V2
Charles Law
V1 / T 1 = V 2 / T 2

Given: T, P
Constant: n & V

Gay-Lussac’s Law
P1 / T 1 = P 2 / T2

Given: n, V
Constant: T and P

Avogadro’s Law
V1 / n 1 = V 2 / n 2

Given: T, P, V
Constant: n

Combined Gas
P1V1 /T1 = P2V2 / T2

T, P, V, n

Ideal Gas Eq’n
PV = nRT

Rewriting the Ideal Gas Law in Density
Terms
m
PV 
RT
MM m P  MM d 

V
R T

Sample Problems:
1. A gas sample contained in a cylinder equipped with a moveable piston occupied 300. mL at a pressure of 2.00 atm.
What would be the final pressure if the volume were increased to 567 mL at constant temperature?
2. Several balloons are inflated with helium to a volume of 0.82
L at 26°C. One of the balloons was found several hours later; the temperature had dropped to 21°C. What would be the volume of the balloon when found, if no helium has escaped? 3. A sample of gas occupies 363. mL at STP. Under what pressure would this sample occupy 236. mL if the temperature were increased to 819°C?

4. Calculate the pressure needed to contain 2.54 mol of an ideal gas at 45°C in a volume of 12.75 L.
5. Nitrogen is slightly less dense than is a sample of air at the same temperature and pressure.
(a) Calculate the density of N2, in g/L, at 1.25 atm and 35°C.
(b) If the average molecular weight of the air is 29.2, what is the density of air at the same conditions?

Gas Mixtures & Partial Pressures
Dalton’s law of partial pressures
“The total pressure of mixture of gases is the sum of the partial pressure of the individual gases in the mixture.”

Ptotal = P1 + P2 + P3 + …

Gas Mixtures & Partial Pressures

Mole Fractions
Ptotal = n1RT / V + n2RT / V + ...
= (n1+ n2 + ...) RT / V
Ptotal = ntotalRT / V
So
P1 / Ptotal = n1/ntotal = X1
P2 / Ptotal = n2 /ntotal = X2

etc.

with X1 = mole fraction of gas 1 = (n1 / ntotal ) etc.

Notice that:

X1 + X2 + X3 + ….. = 1

Sample Problem:
6. A gaseous mixture contains 3.23 g of chloroform, CHCl3 , and 1.22 g of methane,
CH4 . Assuming that both compounds remain as gases, what pressure is exerted by the mixture inside a 50.00-ml metal container at
275o C? What pressure is contributed by the
CHCl3.

Collecting Gases Over Water
Gases are often collected over water.

gas

Ptotal = Pgas + Pwater
Pgas? Subtract the water vapor pressure from Ptotal

gas + H2O vapor Sample Problem:
7. A nitrogen sample occupies 249 mL at STP. If the same sample were collected over water at
25°C and 750. torr, what would be the volume of the gas sample? *VP of water at 25oC is 23.8 mmHg. * Taken from Vapor Pressure –Temperature data/list

GAS STOICHIOMETRY
MASS (g) of
Compound B

Assume that the gas behaves Ideally

Use Ideal Gas Equation to solve for MOLE of Gas A

MOLE of Gas A

Use mole ratio of
B and A
Use mole ratio of
A and B

Use Molar mass (g/mol) of compound
B

MOLE of
Compound B

Sample Problem:
8. During a collision, automobile air bags are inflated by the N2 gas formed by the explosive decomposition of sodium azide, NaN3.
2NaN3 2Na + 3N2
What mass of sodium azide would be needed to inflate a 25.0-L bag to a pressure of 1.40 atm at 25°C?

9. What mass of KNO3 would have to be decomposed to produce
21.1 L of oxygen measured at STP?
2KNO3(s) + heat  2KNO2(s) + O2(g)

Effusion of Gases
• Diffusion
– Gases move through space from a region of high concentration to a region of low concentration
• You can smell an apple pie baking as the particles responsible for the odor diffuse through the room

• Effusion
– Gas particles will escape through a small hole
(orifice) in a container
• Air will slowly leak out of a tire or balloon through pores in the rubber

Graham’s Law of Effusion rate of effusion of B  MMA 

 MM 

rate of effusion of A 
B 

1
2

• The rate at which gas B escapes divided by the rate at which gas A escapes is equal to the square root of the ratio of the molar mass of gas A to gas B

Effusion of Gases

Ammonia and Hydrogen Chloride

Sample Problem
10. A student of CHM12-3L performed an experiment on Graham’s Law using concentrated HCl and
NH4OH, placed in two separate test tubes. A diffusion tube, 13.1 cm in length, was inserted simultaneously to the two test tubes and allowed the reaction to proceed. A few minutes later, a white appeared on the diffusion tube. Using these data, calculate the distance travelled by the two gases.

REAL GASES
A gas behaves ideally at low P (≤ a few atm.) and at high T (well above the boiling point).
N2

2.0

CH4

1.0

1.5

H2

ideal gas

0 0.5

PV/nRT

At high P and/or low
T, gases deviate significantly from ideal behavior.

2.5

Ideal gas:
PV/nRT = 1 at all P

0

200
400
600
Pressure (atmosphere)

800

REAL GASES
Deviations from ideality occur because:
• (Weak) molecular attraction is accentuated at:
 high P = close together.
 low T = low energy = slow moving.
• Gas molecules have a finite volume.
The van der Waals equation: n2a P + 2 V – nb = nRT
V
Attraction correction finite V correction VAN DER WAALS CONSTANTS

Atoms:
London only

Molecules:
London only

London + dipole

Gas
He
Ne
Ar
H2
N2
O2
Cl2
CO2
CH4
NH3
H2O

a
L2 atm mol-2
0.034
0.211
1.35
0.244
1.39
1.36
6.49
3.59
2.25
4.17
5.46

b
L mol-1
0.0237
0.0171
0.0322
0.0266
0.0391
0.0318
0.0562
0.0427
0.0428
0.0371
0.0305

a and b both grow larger as molecule size and complexity increase.

Sample Problem
11. You want to store 165 g of CO2 gas in a 12.5-L tank at room temperature (25°C). Calculate the pressure the gas would have using (a) the ideal gas law and (b) the van der Waals equation. For CO2, a = 3.59 atm L2/mol2 and b = 0.0427 L/mol.

Homework No. 1
Page 159 Chemistry for Eng’g Students by Brown
5.19
5.29
5.31
5.47
5.57
5.77