1. Kinetic Molecular Theory of Gases
A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume.
Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic.
Gas molecules exert neither attractive nor repulsive forces on one another.
The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy
KE = ½ mu2

2. Kinetic theory of gases and …
Compressibility of Gases
Boyle’s Law
P a collision rate with wall
Collision rate a number density
Number density a 1/V
P a 1/V
Gay-Lussac’s Law
Collision rate a average kinetic energy of gas molecules
Average kinetic energy a T
P a T

3. Kinetic theory of gases and …
Compressibility of Gases
Charles’s Law
T a average kinetic energy of molecules
Collision rate a average kinetic energy of gas molecules
P a collision rate with wall
…. But! In Charles’s law, pressure stays constant…
To decrease the collision rate, the volume needs to be increased
V a T

4. Pressure and Volume (Boyle’s Law)
Figure 5.14 The Effects of Decreasing the Volume of a Sample of Gas at Constant Temperature
Decreasing the volume causes the particles to collide with the walls of the container more frequently, increasing the pressure
Copyright©2000 by Houghton Mifflin Company. All rights reserved.

5. Pressure and Temperature (Gay-Lussac’ Law)
Figure 5.15 The Effects of Increasing the Temperature of a Sample of Gas at Constant Volume
Increasing the temperature causes the particles to move faster increasing the frequency of collision with the walls of the container. If the volume is constant this results in and increase in pressure
Copyright©2000 by Houghton Mifflin Company. All rights reserved.

6. Volume and Temperature (Charles’s Law)
Figure 5.16 The Effects of Increasing the Temperature of a Sample of Gas at Constant Pressure
Increasing the temperature causes the particles to move faster increasing the frequency of collision with the walls of the container. If the pressure remains constant, the volume of the container will increase to compensate for the increased motion of the particles
Copyright©2000 by Houghton Mifflin Company. All rights reserved.

7. Kinetic theory of gases and …
Avogadro’s Law
P a collision rate with wall
Collision rate a number density
Number density a n
P a n
Dalton’s Law of Partial Pressures
Molecules do not attract or repel one another
P exerted by one type of molecule is unaffected by the presence of another gas
Ptotal = SPi

8. Volume and Number of Moles (Avogadro’s Law)
Figure 5.17 The Effects of Increasing the Number of Moles of Gas Particles at Constant Temperature and Pressure
Increasing the number of particles at constant temperature and pressure results in an increase in collisions. The volume of the container will increase to compensate for the increased number of collision.
Copyright©2000 by Houghton Mifflin Company. All rights reserved.

9. KMT – What happens in “real” gases
A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume.
Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic.
Gas molecules exert neither attractive nor repulsive forces on one another.
Under what conditions will gases most
likely exhibit nonideal behavior??

10. Deviations from Ideal Behavior
1 mole of ideal gas
Repulsive Forces
PV = nRT
n = PV RT
= 1.0
Attractive Forces

11. Effect of intermolecular forces on the pressure exerted by a gas.

12. Which element/molecule has the weakest attraction to each other??
Van der Waals equation
nonideal gas
P (V – nb) = nRT
an2 V2 ( ) }
corrected
pressure
volume
Pressure Correction: Takes into account the probability that a molecule will end up close enough to another molecule causing an intermolecular attraction
Volume Correction: Takes into account that molecules, while extremely small, do take up some amount of volume
Which element/molecule has the weakest attraction to each other??

13. Given that 3. 50 moles of NH3 occupy 5
Given that 3.50 moles of NH3 occupy 5.20 L at 47˚C, calculate the pressure of the gas (in atm) using the ideal gas law, and then the van der Waals equation.
Ideal gas law
Van der Waals Equation
V=5.20 L
T=( ) = 3.20x102 K
n=3.50 mol
R= L·atm/K·mol
V=5.20 L
T=( ) = 3.20x102 K
n=3.50 mol
a=4.17 atm·L2/mol2
b= L/mol

14. Homework: Problem 5.89
Calculate the pressure exerted by 2.50 moles of CO2 confined in a volume of 5.00 L at 450 K if the gas is behaving ideally. It has been shown that this gas exhibits non-ideal behavior. Calculate the actual pressure given a=3.59; b=

15. The Meaning of Temperature
Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)
Copyright©2000 by Houghton Mifflin Company. All rights reserved.

16. Kinetic Molecular Theory
Root mean square speed is an average molecular speed
For one mole of a gas KE = 3/2 RT
For one molecule
Therefore
KE = kinetic energy
R = universal gas constant
T = temperature (in K)
m = mass
u = speed
Bar over top = root mean square average
Copyright©2000 by Houghton Mifflin Company. All rights reserved.

17. Apparatus for Studying Molecular Speed Distributiona

18.  3RT urms = M The distribution of speeds of three different gases
at the same temperature
The distribution of speeds
for nitrogen gas molecules
at three different temperatures
urms =
3RT M 

19. Calculate the root mean squared speed of molecular chlorine in m/s at 20ºC.

20. Problem 5.78
The temperature in the stratosphere is -23ºC. Calculate the root mean square speeds of N2 molecules in this region. N2=____

21.  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. r1 r2 M2 M1  =
molecular path
NH4Cl
NH3
17 g/mol
HCl
36 g/mol

22. Gas effusion is the is the process by which gas under pressure escapes from one compartment of a container to another by passing through a small opening. = r1 r2 t2 t1 M2 M1 
Nickel forms a gaseous compound of the formula Ni(CO)x What is the value of x given that under the same conditions methane (CH4) effuses 3.3 times faster than the compound?
M2 = r1 r2 ( ) 2
x M1
r1 = 3.3 x r2
= (3.3)2 x 16 = 174.2
M1 = 16 g/mol
x • 28 = 174.2
x = 4.1 ~ 4

23. Justify the statement:
A helium-filled rubber balloon deflates faster than an air-filled one.

24. Problem 5.83
A gas evolved from the fermentation of glucose is found to effuse through a porous barrier in 15.0 min. Under the same condition of temperature and pressure, it takes an equal volume of N2 gas 12.0 min to effuse through the same barrier. Calculate the molar mass of the gas. What could this gas be?