Chapter 20 - Gases

Question 1

What does Boyle’s law state?

Answer 1

• For a fixed mass of gas at a constant temperature:
  PV = constant
  where p = gas pressure and v = volume

Question 2

Why would you have to wait a few seconds to measure
the new volume in Boyle’s law experiment?

Answer 2

Work has been done on the gas, which increases temperature. We want to have constant temperature, so wait for thermal equilibrium to be reached

Question 3

What does Charles law state?

Answer 3

V/T = constant
For a fixed mass of gas at constant pressure

Question 4

How do you calculate the work done to keep the pressure constant when there is a change to the volume of a gas?

Answer 4

Work done = p x change in v

Question 5

What is an isobaric change?

Answer 5

Any change at constant pressure

Question 6

What does the pressure law state?

Answer 6

P/T = constant
for fixed mass of gas at constant volume

Question 7

What is brownian motion?

Answer 7

Random movement (range of speeds in no preferred direction) of particles due to being bombarded unevenly and randomly by individual molecules

Question 8

What experiment shows Brownian motion? (not required practical)

Answer 8

Observing smoke particles with a microscope when a beam of light is directed through

Question 9

What is avogadro constant? Give the value

Answer 9

N(A) - Number of atoms in exactly 12g of carbon isotope C-12.
- 6.023x10^23

Question 10

How many molecules of a substance is in 1 mole?

Answer 10

6.023 x 10^23

Question 11

What is an ideal gas?

Answer 11

Gas that obeys Boyle’s law

Question 12

Give the ideal gas equation

Answer 12

Pv = nRT

Question 13

What is the value for the Boltzmann constant (K)?

Answer 13

1.38 x 10^-23 JK^-1

Question 14

Whats the equation for boltzmann constant (K)?

Answer 14

K = R/Na

Question 15

Give the ideal gas equations, including boltzmann constant

Answer 15

Pv = NkT 
N = number of particles

Question 16

What is the root mean square speed?

Answer 16

Crms = (C1^2 +C2^2 +…+CN^2/N) ^1/2

Question 17

What is the kinetic theory equation?

Answer 17

Pv = 1/3 Nm(Crms)^2

Question 18

What are some assumptions that have to be made about an ideal gas to derive the kinetic theory equation?

Answer 18

1. ) The molecules are point molecules - volume of each molecules is negligible compared with the volume of the gas.
2. ) Do not attract each other.
3. ) Move in continual random motion
4. ) Elastic collisions
5. ) Collisions with container surface much shorter duration than the time between impacts. Collision time negligible
6. ) Newton’s laws apply
7. ) Negligible intermolecular forces
8. ) Molecules are identical
9. ) Large number of particles

Question 19

Derive the kinetic theory equation

Answer 19

C1^2 = u1^2 + v1^2 +w1^2 (perpendicular components of velocity)
distance to opposite face and back = 2lx
time between successive impacts = 2lx/u1
force = change in p/t
= -2mu1/2lx/u1 = -mu1^2/lx
P = mu1^2/lxlylz. lylz = area, so: mu1^2/v
P = mu1^2/v +mu2^2/v + mu3^2/v + ….+ muN^2/v
= m/v( u1^2 + u2^2 + u3^2+…+ uN^2) = Nmu*^2/v where u* is mean u and = u1^2 + u2^2+…. +uN^2/N
P = Nm/3v(u*^2+v*^2+w*^2)
Crms^2 = u*^2+v*^2+w*^2, therefore p = Nm/3v Crms^2 or Pv = 1/3NmCrms^2

Question 20

What is the internal energy equal to an ideal gas?

Answer 20

Kinetic energy

Question 21

What is the equation for the mean kinetic energy of a molecule of an ideal gas?

Answer 21

3/2kT
= 1/2m(Crms^2)
= 3RT/2Na

Question 22

how do you work out the internal energy of n moles of an ideal gas?

Answer 22

3/2 nRT

Question 23

What is thermal equilibrium?

Answer 23

When 2 bodies are the same temperature so there’s no net flow of thermal energy between them.

Question 24

What happens when hot gas is mixed with cool gas - eventually reaching thermal equilibrium?

Answer 24

(Kinetic) energy exchanged in molecular collisions until average kinetic energy of all molecules is the same

Question 25

Whats the equation for total kinetic energy in one mole of an ideal gas?

Answer 25

3/2RT (as k = R/Na)

Question 26

When the temperature of an ideal gas in a sealed container falls, what happens to the pressure of the gas?

Answer 26

Decreases as frequency of collsions decreases, so rate of change of momentum decreases.

Or using PV = nRT: if T decreases then as V, n and R are constants, P must decrease

Question 27

How is pressure exerted by a gas on the walls of a container?

Answer 27

Gas molecules move in random motion and when the collide with the walls they exert a force on the wall and the wall exerts an equal one back (Newton’s 3rd law). The molecules momentum changes and therefore creates pressure.

Question 28

Use kinetic theory of gases to explain why: pressure exerted by an ideal gas increases when it is heated at constant volume

Answer 28

Collision frequency (with wall) increases and rate of momentum change per collision increases. Greater force because more momentum change per seeond, meaning greater pressure