1. BEHAVIOR, LAWS, AND KINETIC MOLECULAR THEORY
GASES
BEHAVIOR, LAWS, AND KINETIC MOLECULAR THEORY
Kenneth E. Schnobrich

2. Properties of Gases
Particles are traveling in straight-line paths and are randomly distributed
No definite shape or volume
Relatively large distances between the particles
Low densities
Can be compressed
Can be liquefied at low temperatures and high pressures

3. Units that Apply Pressure Temperature Densities Volume
Standard pressure
101.3 kPa, 760 Torr, 1 atm
Temperature
Standard temperature
0°C or 273K
Densities
Normally in g/L
Volume
Liters or milliliters

4. Gas Behavior and the Gas Laws
Boyle’s Law
This law examines the relationship between volume and pressure
The volume occupied by a gas is inversely proportional to the pressure exerted on the gas
V a 1/P

5. Sample Problem Always identify the variables - P1, P2, V1, and V2.
Use the relationship on “Table T” (P1V1 = P2V2) - note temperature is constant.
What volume will 500. mL of a gas occupy if the pressure is changed from kPa to kPa?
What do you definitely know??

6. Solution
You definitely know that the volume should decrease because pressure is increasing
P1V1 = P2V2
(101.3 kPa)(500 mL) = (502.4 kPa)(V2)
V2 = 500. mL(101.3 kPa/502.4 kPa)
V2 = mL

7. *temperature is constant
Sample Problems
Example P1 P2 V V2 1
2 atm
4 atm 4L ?L 2 ?
3 atm 5L 8L 3
101.3 kPa
400 kPa
500 mL
?mL 4
200 kPa
600 kPa 5
100 kPa
0.05 kPa 2L
*temperature is constant

8. Gas Behavior and the Gas Laws
Charles’s Law
This law examines the relationship between Volume and Temperature
The volume occupied by a gas is directly proportional to the Kelvin temperature
V a T(K)

9. Sample Problem Always identify the variables - T1, T2, V1, and V2.
Use the relationship on “Table T” (V1/T1 = V2/T2) - note pressure is constant.
What volume will 500. mL of a gas occupy if the temperature is changed from 0°C to 50°C ?
Make sure that you convert °C - K
What do you definitely know??

10. Solution
You definitely know that the volume should increase because temperature is increasing
V1/T1 = V2/T2
0.00°C = 273 K and 50.0°C = 323 K
V2 = 500. mL(323 K/273 K)
V2 = 592 mL

11. Sample Problems Example V1 V2 T1 T2 1 400 mL ?mL 25°C 50°C 2 4 L 10 L?K
819K 3
8 L
273K 4 ?L
20 L 5
3 L
10°C
*Pressure is constant

12. 1 New York State Reference Tables for Chemistry
The Combined Gas Law
The combined gas law simply deals with both change in pressure and change in temperature (Table T)1.
P1V1/T1 = P2V2/T2
In this problem, as we have with Charles’s and Boyle’s Laws, the number of mols of gas remains constant.
1 New York State Reference Tables for Chemistry

13. Sample Problem
20. L of H2 gas is at a pressure of kPa and 20°C. What volume will this gas occupy at a pressure of 20.6 kPa and a temperature of 0°C?
Start by identifying your variables in the problem: P1, V1, T1, P2, T2 - solve for V2
# mols of gas is constant

14. Solution What are the known values: V1 = 20 L T1 = 20°C = 293 K
P1 = kPa
P2 = 20.6 kPa
V2 = ??

15. Solution (cont.) V2 = V1(T2/T1)(P1/P2) Notice -
Since the temperature is decreasing it will decrease the value for V1 (direct relationship)
Since the pressure is decreasing it will increase the value for V1 (inverse relationship)
V2 = 20. L(273 K/293 K)(101.3 kPa/20.6 kPa)
V2 = 92 L (to the correct # of significant figures)

16. Sample Problems V1 P1 T1 V2 P2 T2 1 10 L 2 atm 373 K ?L 4 atm 456 K 2
Trial V1 P1 T1 V2 P2 T2 1
10 L
2 atm
373 K ?L
4 atm
456 K 2
5 L
?atm
200 K
400 K 3
2 L
20°C
0.5 atm
**mols of gas constant

17. Daltons Law of Partial Pressures
If you have a mixture of non-reacting gases each gas will exert a partial pressure depending on the amount (mol fraction) of that gas present.
The total pressure of the gas mixture will be the sum of the partial pressures of each of the gases in the mixture.
Pt = P1 + P2 + P3 …….
The mol fraction is simply the #mols of a gas divided by the total # of mols of gas in the mixture.

18. Partial Pressures
Let’s say I have a mixture of N2, O2, and H2O gas exerting a total pressure of 6 atmospheres in a closed container.
The total number of mols of gas would be 10 and the total pressure is 6 atm.
6 atm
each molecule represents a mol of that gas

19. Partial Pressures The mol fraction of each gas is as follows :
H2O = 3/10
So the partial pressure of each gas would be:
N2 = 3/10(6 atm) = 1.8 atm
O2 = 4/10(6 atm) = 2.4 atm
H2O = 3/10(6 atm) = 1.8 atm
6 atm
each molecule represents a mol of that gas

20. Ideal Gas Law
The ideal gas law also takes into account the number of mols of gas -
PV = nRT
P = pressure (atmospheres)
V = volume (Liters)
n = # mols of gas
T = temperature (K)
R = Universal Gas Law constant (.082 L•atm/mol•K

21. Ideal Gas Law (cont.)
If you were to solve for V at STP and one mol of gas you should get what we call “molar volume of a gas”
V = nRT/P
V = (1 mol)(.082 l•atm/mol•K)(273 K)/(1 atm)
V = 22.4 L

22. Molar Volume
Experimentally it can be determined that one mol of any gas, at STP, will occupy a volume of 22.4 L
STP = standard temperature & pressure = 0°C(273 K) and 1atm(101.3 kPa)

23. One Mol of Each Gas
All at STP
22.4 L H2 O2
CO2
SO2

24. Avogadro’s Hypothesis
Equal volumes of gases under the same conditions of temperature and pressure will contain equal #’s of particles
EQUAL NUMBER OF PARTICLES
1.0 L
Same Temperature & Pressure
Same Volume

25. EQUAL NUMBER OF PARTICLES
Avogadro (cont.)
Note: In the example given there are the same # of particles, there are not the same # of atoms
EQUAL NUMBER OF PARTICLES
1.0 L
Same Temperature & Pressure
Same Volume He
HCl

26. Graham’s Law of Diffusion
Diffusion - the movement of particles from a region of high concentration to a region of low concentration
Effusion - the movement of particles from a region of high concentration to a region of low concentration through a small orifice (small opening)

27. Graham’s Law (cont.)
In very simple terms, the law suggests that lighter particles (atoms or molecules) move faster than heavier particles.
NH3
HCl

28. Kinetic Molecular Theory
The volume of a gas molecule is negligible compared to the volume it can occupy as a result of its motion
Gas molecules are in constant, rapid, random straight-line motion
Collisions between gas molecules are perfectly elastic (T a KE) so there is no net loss of energy
There are no attractive forces between the gas molecules

29. Gases & Solubility
Henry’s Law describes how pressure changes the solubility of a gas
as the partial pressure of the gas above a liquid increases its solubility increases
Pressure increasing
Solubility increasing

30. Gases & Solubility
As temperature increases the solubility of a gas will decrease
when gases normally go into solution it is an exothermic process and for that reason when the temperature of solutions of gases in liquids increases the solubility decreases
Like your soda going flat when you leave it out on a warm day - the increased temperature causes the CO2 to come out of solution

31. Ideal vs Real
We assume that the volume of a gas molecule is negligible and there are no attractive forces between gas molecules under “normal” conditions. In reality, gas molecules do have a measureable volume and there are weak attractive forces (either dipole-dipole or van derWaals forces or possibly both). So, under “normal” conditions, both the attractive forces and the molecule volume are considered negligible.
Under conditions of – high pressure and low temperature gas behavior varies from the gas laws.
High pressure – molecules are pushed close together and the attractive forces, although weak, pull the molecules together.
Low temperature – molecules move more slowly (lower KE) and the weak attractive forces become more important as molecules come close to each other.

32. Ideal vs Real
So, gases behave most ideally at high temperatures (molecules are moving too fast for the weak attractive forces to have an effect) and low pressures/large volumes (molecules are so far apart that the attractive forces and molecule volume are insignificant).
There are only two gases that behave close to ideally under all conditions and they are – H2 and He. They both have very small molecule volumes and extremely weak van der Waals forces. H2 He

33. Critical Temperatures (°C)
Ideal vs Real
Critical temperature – above this temperature the substance cannot exist as a liquid.
Critical pressure – at the critical temperature, the pressure that must be applied to cause that gas to condense H2 He
-240°C
-268°C
Critical Temperatures (°C)