Kinetic theory of Gas Molecules

Question 1

Explain Boyle’s Law

Answer 1

• The pressure of a gas at constant temperature is increased by reducing its volume.
• The gas molecules travel less distance between impacts at the wall due to the reduced volume.
• Therefore there are more impacts per second.

Question 2

Explain the pressure law

Answer 2

• The pressure of a gas at constant volume is increased by raising its temperature.
• Molecules travel faster so mean kinetic energy of molecules increases
• Momentum of molecules increases
• Impacts are harder and more frequent
• Each collision transfers more momentum
• More force per unit area on container walls
• So the pressure increases.

Question 3

Molecules in a gas have a spread of speeds.

Answer 3

• In a collision the speed of the molecules will change.
• If temperature does not change, distribution will stay the same.
• If the temperature of a gas is raised, its molecule move faster, on average. The root mean square speed of the molecules increases.
• The distribution curve become broader and flatter because the greater temperature, the more molecules there are moving at higher speeds.

Question 4

What is the root mean square speed, c_rms.

Answer 4

Square root of the mean value of the square of the molecular speeds of the molecules of a gas.

C_rms = (c₁²+c₂²+c₃²…+c_N²/N)^½

Question 5

What is the kinetic theory equation?

Answer 5

pV = 1/3Nm(c_rms)^{<span>2</span>}

Question 6

Assumptions of the kinetic theory equation

Answer 6

• All particles are identical / have same mass
• The collisions they undergo with each other and with the container of the surface are elastic collisions.
• Intermolecular forces are negligible except during collisions. If the forces are not negligible the force of the impact on the container walls would be reduced.
• Volume of molecules is negligible (point molecules) compared to volume of container/gas
• Time of collisions is negligible (duration of collision / time between collisions)
• They move about in continual random motion (range of speeds + no preferred direction of movement)
• Large no of molecules present / statistical laws apply

Question 7

Kinetic energy of the molecules of an ideal gas:

Answer 7

Mean kinetic energy of a molecule of an ideal gas= 3/2kt

Question 8

Total kinetic energy for one mole =

Answer 8

N_Ax(3/2)kT = 3/2RT

Question 9

Total KE for n moles =

Answer 9

3/2nRT