1. CHEMISTRY 161
Chapter 5

2. REVISION 1. ideal gas equation p × V = n × R × T R = 8.314 J / mol / K
2. molar volume
Vm = 22.4 l
3. Dalton’s Law
p = p1 + p2 + …

3. 1. Kinetic Molecular Theory of Gases
macroscopic
(gas cylinder)
microscopic
(atoms/molecules)
Maxwell
( )
Boltzmann
( )

4. Kinetic Energy of Gases
physical properties of
gases can be described
by motion of individual
gas atoms/molecules
each macroscopic and
microscopic particle in
motion holds an energy
(kinetic energy)

5. kinetic energy = energy of an object in motion
SI Units of Energy
energy = force × distance
W = F × Δs
[W] = [F] × [s]
[W] = N m = kg m2 s-2 = J
Joule
( )
kinetic energy = energy of an object in motion

6. Assumptions of the Kinetic Theory of Gases
gases are composed of atoms/molecules which are
separated from each other by a distance l much more than their
own diameter d
d = m
l = 10-3 m….. few m
molecules are mass points with negligible volume l

7. 2. gases are constantly in motion in random reactions
and hold a kinetic energy
gases collide and transfer energy
(billiard ball model)

8. F(inter) = 0 p(inter) = 0 3. gases atoms/molecules
do not exert forces on each other
(absence of intermolecular interactions)
F(inter) = 0
p(inter) = 0

9. Gas Diffusion

10. Ekin = ½ m u2 Ekin = ½ m u2 T ∞ ½ m u2 const T = ½ m u2
4. the average kinetic energy of a gas molecule/atom
is proportional to the temperature
Ekin = ½ m u2
Ekin = ½ m u2
u12 + u22 + u32 + … + uN2
u2 = N
T ∞ ½ m u2
const T = ½ m u2

11. 1. Compressibility of gases
Applications
1. Compressibility of gases
p ∞ 1/V

12. 2. Kinetic energy of gases
Ekin = ½ m u2 ∞ T
p ∞ T

13. 2. Distribution of Molecular Speeds
Maxwell-Boltzmann distribution

14. activation energy

15. Quantification Ekin = ½ m u2 = const T Ekin = ½ M u2 = const’ T
Ekin = ½ M u2 = 3/2 R T
root mean square speed
urms =√ (3 R T / M)

16. Calculate the RMS of molecular helium at 25oC
1. apply
urms =√ (3 R T / M)
2. calculate numbers and SI units
1360 ms-1

17. deviation of ideal gas law
3. Real Gases
p × V = n × R × T (n = 1)
deviation of ideal gas law
at high pressures
p ≈ 90 atm

18. North America Nebula
p << atm

19. (van der Waals equation) (p + (a n2 / V2) ) (V – n b) = n R T
ideal gas law
p V = n R T
real gas law
(van der Waals equation)
(p + (a n2 / V2) ) (V – n b) = n R T
corrected volume
(volume occupied by molecules)
corrected pressure
(additional pressure/force from attraction)

20. REVISION 1. Kinetic Molecular Theory of Gases
2. Distribution of Molecular Speeds
Ekin = ½ M u2 = 3/2 R T
3. Real Gas Law
(p + (a n2 / V2) ) (V – n b) = n R T

21. Homework
Chapter 5, p `
problems