6.6 - Molecular Kinetic Theory Model

Question 1

What is the difference between the gas laws and kinetic theory?

Answer 1

The gas laws are based on empirical evidence and kinetic theory is purely theory, so is based on assumptions and derivations.

Question 2

What do ideal gases not have that solids and liquids do have?

Answer 2

Potential energy. Ideal gases only have kinetic energy.

Question 3

What is the relationship between internal energy and temperature?

Answer 3

They are directly proportional.

Question 4

What is Brownian motion?

Answer 4

When small particles (like smoke particles) suspended in a liquid or gas are observed to move around in a random, erratic fashion.

Question 5

How can Brownian motion be observed?

Answer 5

Under a microscope.

Question 6

What does Brownian motion provide evidence for?

Answer 6

The existence of molecules in a gas or liquid.

Question 7

How do you describe the random motion of particles in Brownian motion?

Answer 7

• A range of speeds
• No preferred direction of movement
• Unpredictable

Question 8

Use the smoke particle model and explain how particular particles are observable.

Answer 8

• The larger, heavier smoke particles are visible under a microscope and are moved with Brownian motion by smaller, lighter particles travelling at high speeds.
• Smoke particles appear to move randomly as they are hit by all the tiny air particles that can’t be observed.

Question 9

What are 6 assumptions of kinetic theory?

Answer 9

• No intermolecular forces act on the molecules
• The duration of collisions is negligible in comparison to time between collisions
• The motion of molecules is random
• Perfectly elastic collisions
• Motion of molecules follows Newton’s laws
• Molecules move in straight lines between collisions

Question 10

What is stage 1 of the derivation of the kinetic theory of gases equation?

Answer 10

p = mv
Δp = final p – initial p = −mv − (+mv) = −mv − mv = −2mv

Question 11

What is stage 2 of the derivation of the kinetic theory of gases equation?

Answer 11

• Calculate the number of collisions per second by the molecule on a wall
• time = distance / speed = 2L / v

Question 12

What is stage 3 of the derivation of the kinetic theory of gases equation?

Answer 12

• Calculate the force exerted by the molecule on the wall
  F = Δp/Δt = 2mv / 2L/v = mv²/ L

Question 13

What is stage 4 of the derivation of kinetic theory of gases equation?

Answer 13

• Calculate the pressure exerted on one wall
  p = F/A (A = L²)
  = mv²/L/L² = mv²/L³
  L³ = V
  so therefore
  p = mv²/V

Question 14

What is stage 5 of the derivation of kinetic theory of gases equation?

Answer 14

• Consider the direction in which the number of molecules are moving within the box at all times
• Split velocity into its 3 components =
  cx² = cy² = cz² (x,y,z are the vector directions)
  therefore cx² = 1/3 c²

Question 15

What is stage 6 of the derivation of kinetic theory of gases equation?

Answer 15

• Consider the speed of the molecules as an average speed
• root-mean-square-speed (Crms)
  N(Crms)²

Question 16

What is stage 7 of the derivation of kinetic theory of gases equation?

Answer 16

• Consider the volume of the box
• the pressure on the wall
  p = 1/3 Nm(Crms)² / V

Question 17

How do you prove Ek = 3/2 kT?

Answer 17

1/3 Nm(Crms)² = NkT
1/3 m(Crms)² = kT
2/3 x 1/2 m(Crms)² = kT
1/2m(Crms)² - 3/2kT