1. Chapter 9. Properties of Gases and the Kinetic Molecular Theory
Gas Mixtures: Partial Pressures
Pressure of a Gas
The Ideal Gas Law
Kinetic Molecular Theory
Maxwell-Boltzmann Velocity Distribution
Real Gases
Department of Chemistry, KAIST 1 1

2. An Overview of the Physical States of Matter
The Distinction of Gases from Liquids and Solids
1. Gas volume changes greatly with pressure.
2. Gas volume changes greatly with temperature.
3. Gases have relatively low viscosity.
4. Most gases have relatively low densities under normal conditions.
5. Gases are miscible.

3. The three states of matter

4. 9.1 Pressure of a Gas: Barometric Principles
1643, Torricelli
Force necessary to suspend
the barometric fluids comes from
the pressure of the atmosphere

5. r = m/V
independent of A !

6. at the same P, rHghHg = rH2OhH2O
Can you calculate how long the water tube would be ??
1 atm (standard atmosphere):
760 mmHg (0 oC, dry air, sea level)
760 Torr (independent of temperature)
101,325 Nm-2 (Pa) - SI unit
1,013,250 dyne cm-2
lb in-2

7. Effect of atmospheric pressure on objects at the Earth’s surface.

8. 9.2 The Ideal Gas Law Boyle’s Law Charles’s Law V a 1 P
n and T are fixed
V x P
= constant
V = constant / P
Charles’s Law
V a T
P and n are fixed V T
= constant
V = constant x T

9. Boyle’s Law

10. Department of Chemistry, KAIST
Boyle’s Law
Department of Chemistry, KAIST

11. Charles’ Law relationship between volume and temperature of a gas
(at constant moles and Pressure).

12. Boyle’s Law Charles’s Law V a 1 P n and T are fixed V x P = constant
V = constant / P
Charles’s Law
V a T
P and n are fixed V T
= constant
V = constant x T
Gay-Lussac showed that Boyle’s law continues to hold for different T, and Charles’ law for different P PV T
= constant

13. Gay-Lussac’s experiment & Avogadro’s Explanation
1 volume hydrogen +
1 volume of chlorine
 2 volumes of hydrogen chloride
Avogadro:
suggesting that
1) equal volumes of any gas
contain equal numbers of gas molecules
2) gaseous hydrogen and chlorine
are present as diatomic molecules
Avogadro’s Law
V a n
P, T are fixed V n
= constant N NA
n =

14. combine PV T = constant & V n = constant we get Ideal Gas Law
(equation of state)

15. Standard temperature and pressure (STP):
T = K (0 oC), P = 1 atm

16. Standard molar volume
Equation 9.14

17. 9.3 Gas Mixtures: Dalton’s Law of Partial Pressures
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18. Mixtures of Gases Dalton’s Law of Partial Pressures P1 = n1RT / V
Gases mix homogeneously in any proportions
Each gas in a mixture behaves as if it were the only gas present
Dalton’s Law of Partial Pressures
P1 = n1RT / V
P2 = n2RT / V, …
Ptotal = P1 + P2 + P
P1= c1 x Ptotal
where c1 is the mole fraction
c1 = n1
n1 + n2 + n3 +... = n1
ntotal
PO2 = (0.209)(760 Torr) = 159 Torr

19. 9.4 The Kinetic Molecular Theory
Maxwell’s idea;
molecules are in constant motion
(random and chaotic)
molecule’s coordinate is fixed
at a fixed position ~
equal to the vector distance
Translational kinetic energy
= (1/2)mv2
(Cartesian velocity components)
Probability of molecules for v ~ v+dv = 4 πv2dv

20. In a container of edge length L
Consider one molecule

21. Now consider all N molecules

23. When this is compared to
Molar kinetic energy
Average energy per molecule
kB = R/N
Boltzmann’s constant
absolute Temp is the measure of molecular motion !!

24. Apparatus for studying molecular velocity distribution

25. Maxwell-Boltzmann Distribution of Molecular Velocity
Average value of energy or velocity characterizes the group
average value is derived from a distribution of values

26. Department of Chemistry, KAIST
Velocity distribution function
as Temp increases,
peak velocity is shifted
to higher values
2) distribution is broadened
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27. Fraction of molecules with speeds in a given interval
Interval: a to b
approximation for small x

28. most probable molecular speed
The distribution of speeds
of three different gases
at the same temperature
The distribution of speeds
for nitrogen gas molecules
at three different temperatures
most probable molecular speed

29.  ū = most probable molecular speed Average speed
8RT ∏M 
ū =
root-mean-square (rms) speed

30. 8RT ∏M 
The path traveled by a single gas molecule:
ū =

31. Wall collision rate: -
Zwall = ¼ (N/V) v A
Molecular collision rate: -
Zmol = 2 (N/V) v d2
The path traveled by a single gas molecule:
Mean free path: -
 = v/Zmol = 1/[2 (N/V)d2]

32.  M2 M1 NH4Cl  NH3 17 g/mol HCl 36 g/mol
Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. M2 M1  r1 r2
r = flux of molecules along a concentration gradient =
NH4Cl
Effusion is the escape of gas through a pin hole. Effusion rate is inversely proportional to M. 
NH3
17 g/mol
HCl
36 g/mol

33. A molecular description of Boyle’s Law

34. A molecular description of Dalton’s law of partial pressures.

35. A molecular description of Charles’s Law

36. A molecular description of Avogadro’s Law

37. 9.5 The Behavior of Real Gases
The behavior of several real gases with increasing external pressure

38. The effect of intermolecular attractions on measured gas pressure
Pideal = P + a(n/V)2
(P: actual pressure)
actual pressure is smaller than the ideal pressure

39. Effect of excluded volume
The effect of molecular volume on measured gas volume
Effect of excluded volume
Videal = V - nb
actual volume is greater than the ideal volume

40. van der Waals Constants for Some Common Gases
van der Waals equation for n moles of a real gas
adjusts P up
adjusts V down
Gas a
atm*L2
mol2 b L
mol
0.034
0.211
1.35
2.32
4.19
0.244
1.39
1.36
6.49
3.59
2.25
4.17
5.46 He Ne Ar Kr Xe H2 N2 O2
Cl2
CO2
CH4
NH3
H2O
0.0237
0.0171
0.0322
0.0398
0.0511
0.0266
0.0391
0.0318
0.0562
0.0427
0.0428
0.0371
0.0305
See Example 9.5

41. Virial Equation of State
B= B(T) 2nd viral coeff. C=C(T), …
B= b-a/RT if for
van der Waals gas
(prove)
B=0
at the Boyle temp