1. Gases Chapter 5 Lesson 3

2. Kinetic Molecular Theory of Gases
Postulates of the KMT Related to Ideal Gases
The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be zero
The particles are in constant motion. Collisions of the particles with the walls of the container cause pressure.
Assume that the particles exert no forces on each other
The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas

3. Kinetic Molecular Theory of Gases
Explaining Observed Behavior with KMT
P and V (T = constant)
As V is decreased, P increases:
V decrease causes a decrease in the surface area. Since P is force/area, the decrease in V causes the area to decrease, thus increasing the P

4. Kinetic Molecular Theory of Gases
P and T (V = constant)
As T increase, P increases
The increase in T causes an increase in average kinetic energy. Molecules moving faster collide with the walls of the container more frequently, and with greater force.

5. Kinetic Molecular Theory of Gases
V and T (P = constant)
As T increases, V also increases
Increased T creates more frequent, more forceful collisions. V must increase proportionally to increase the surface area, and maintain P

6. Kinetic Molecular Theory of Gases
V and n (T and P constant)
As n increases, V must increase
Increasing the number of particles increases the number of collisions. This can be balanced by an increase in V to maintain constant P

7. Kinetic Molecular Theory of Gases
Dalton’s Law of partial pressures
P is independent of the type of gas molecule
KMT states that particles are independent, and V is assumed to be zero. The identity of the molecule is therefore unimportant

8. Kinetic Molecular Theory of Gases
Root Mean Square Velocity
Velocity of a gas is dependent on mass and temperature
Velocity of gases is determined as an average
M = mass of one mole of gas particles in kg
R = J/K•mol
joule = kg•m2/s2
urms = 3RT M

9. Kinetic Molecular Theory of Gases
Example: Calculate the root mean square velocity for the atoms in a sample of oxygen gas at 0°C.
MO2 = 32g/mol
32g 1 kg = kg
1000g
T = = 273K
R = J/K•mol

10. Kinetic Molecular Theory of Gases
Urms = 3( kg•m2 •s-2•K-1 •mol-1)(273 K) = 461m•s-1
0.032 kg•mol-1
Answer 461m•s-1 or 461 m/s
Recall 1 Joule = 1 J = 1 kg• m2/s2 = 1 kg• m2• s-2

11. Kinetic Molecular Theory of Gases
Mean Free Path – distance between collisions
Average distance a molecule travels between collisions
1 x m for O2 at STP

12. Effusion and Diffusion
Movement of a gas through a small opening into an evacuated container (vacuum)
Graham’s law of effusion
Rate of effusion for gas 1 = √M2
Rate of effusion for gas 2 √M1

13. Effusion and Diffusion
Example: How many times faster than He would NO2 gas effuse?
MNO2 = g/mol larger mass
MHe = g/mol effuses slower
Rate He = = He effuses 3.39
Rate NO times faster

14. Real Gases and van der Waals Equation (Johannes van der Waals, 1873)
Volume
Real gas molecules do have volume
Volume available is not 100% of the container volume
n= number of moles
b = is an empirical constant, derived from experimental results

15. Real Gases and van der Waals Equation
Ideal: P = nRT V
Real: P = nRT
V-nb
V = Volume of the container
nb = Volume correction

16. Real Gases and van der Waals Equation
Pressure
Molecules of real gases do experience attractive forces
a = proportionality constant determined by observation of the gas
Pobs = Pideal – a(n/V)2  Pressure correction

17. Real Gases and van der Waals Equation
Combining to derive van der Waals equation
Pobs = nRT - n2a
V-nb V2
And then rearranging…
(Pobs + n2a/V2)(V-nb) = nRT

18. Real Gases: Deviations from Ideality
Real gases behave ideally at ordinary temperatures and pressures.
At low temperatures and high pressures real gases do not behave ideally.
The reasons for the deviations from ideality are:
The molecules are very close to one another, thus their volume is important.
The molecular interactions also become important.
J. van der Waals, , Professor of Physics, Amsterdam. Nobel Prize 1910.

19. Real Gases: Deviations from Ideality
van der Waals’ equation accounts for the behavior of real gases at low temperatures and high pressures.
The van der Waals constants a and b take into account two things:
a accounts for intermolecular attraction
For nonpolar gases the attractive forces are London Forces
For polar gases the attractive forces are dipole-dipole attractions or hydrogen bonds.
b accounts for volume of gas molecules
At large volumes a and b are relatively small and van der Waal’s equation reduces to ideal gas law at high temperatures and low pressures.

20. Real Gases: Deviations from Ideality
Calculate the pressure exerted by 84.0 g of ammonia, NH3, in a 5.00 L container at 200. oC using the ideal gas law.
PV = nRT
P = nRT/V n = 84.0g * 1mol/17 g T =
P = (4.94mol)( L atm mol-1 K-1)(473K)
(5 L)
P = 38.3 atm

21. Real Gases: Deviations from Ideality
Calculate the pressure exerted by 84.0 g of ammonia, NH3, in a 5.00 L container at 200. oC using the van der Waal’s equation. The van der Waal's constants for ammonia are: a = 4.17 atm L2 mol-2 b =3.71x10-2 L mol-1
n = 84.0g * 1mol/17 g T =
P = (4.94mol)( L atm mol-1 K-1)(473K) (4.94 mol)2*4.17 atm L2 mol-2
5 L – (4.94 mol*3.71E-2 L mol-1) (5 L)2
P = atm – 4.07 atm = (Using van der Waal’s Eq)
P = 38.3 atm (Using IGL)
7% error

22. Chemistry in the Atmosphere
Composition of the Troposphere
The atmosphere is composed of 78% N2, 21% O2, 0.9%Ar, and 0.03% CO2 along with trace gases.
The composition of the atmosphere varies as a function of distance from the earth’s surface. Heavier molecules tend to be near the surface due to gravity.

23. Chemistry in the Atmosphere
Upper atmospheric chemistry is largely affected by ultraviolet, x ray, and cosmic radiation emanating from space. The ozone layer is especially reactive to ultraviolet radiation
Manufacturing and other processes of our modern society affect the chemistry of our atmosphere. Air pollution is a direct result of such processes.