1. Gas Densities, Partial Pressures, and Kinetic-Molecular Theory
Sections

2. Objectives Apply the ideal-gas equation to real gas situations.
Interpret the kinetic-molecular theory of gases

3. Gas Densities and Molar Mass
Rearrange the ideal-gas equation :
n = P
V RT
Multiply both sides by molar mass, M
nM = PM
V RT
Product of n/V and M = density in g/L
Moles x grams = grams
Liter mole liter

4. Gas Densities and Molar Mass
Density is expressed:
D = PM RT
Density depends on pressure, molar mass, and temperature

5. Gas Mixtures and Partial Pressure
Dalton’s Law of Partial Pressures:
Total pressure of a mixture equals sum of the pressures that each would exert if present alone.
Pt = P1 + P2 + P3 + ….

6. Gas Mixtures and Partial Pressures
Thus:
P1 = n1 (RT); P2 = n2 (RT); P3 = n3 (RT);…
V V V
And
Pt = (n1 + n2 + n3 + ….) RT = nt (RT)
V V

7. Mole Fraction, X P1 = n1 RT/ V = n1 Pt = nt RT/ V = nt Thus…
P1 = (n1/nt)Pt = X1Pt

8. Example
Mole fraction of N2 in air is 0.78 (78%). If the total pressure is 760 torr, what is the partial pressure of N2?

9. Homework
59-67, odd only

10. Kinetic-Molecular Theory
Explains why gases behave as they do
Developed over 100 year period
Published in 1857 by Rudolf Clausius

11. Kinetic Molecular Theory
* Theory of moving molecules
You Must Know the 5 Postulates of the Kinetic Molecular Theory of Gases (page 421).

12. Root-mean-square speed, u
Speed of a molecule possessing average kinetic energy
Є = ½ mu2
Є is average kinetic energy
m is mass of molecule
Both Є and u increase as temperature increases

13. Application to Gas Laws
Effect of a V increase at constant T:
- Average kinetic energy does not change when T is constant. Thus rms speed is unchanged. With V increase, there are fewer collisions with container walls, and pressure decreases (Boyle’s Law).

14. Application to Gas Laws
2. Effect of a T increase at constant V:
- Increase T means increase of both average kinetic energy and rms speed. No change in V means there will be more collisions with walls.

15. Molecular Effusion & Diffusion
u = 3RT M
*Derived equation from the k-m theory
**Less massive gas molecules have higher rms speed

16. Effusion
Escape of gas molecules through a tiny hole into an evacuated space

17. Diffusion
Spread of one substance throughout a space or throughout a second substance

18. Graham’s Law of Effusion
Effusion rate of a gas is inversely proportional to the square root of its molar mass.
Rates of effusion of two gases:
* At same T and P in containers with identical pinholes

19. Graham’s Law of Effusion

20. Diffusion and Mean Free Path
Similar to Effusion (faster for lower mass molecules)
BUT diffusion is slower than molecular speeds because of molecular collisions
Mean Free Path: average distance traveled by a molecule between collisions

21. Homework
69, 71, 73, 75, 76, 77, and 79