C15 Ideal Gases

Question 1

SI unit of measurement for the amount of a substance

Answer 1

The Mol (Mole)

Question 2

Define ‘one mole’

Answer 2

The amount of substance that contains are many elementary entities as there are atoms in 12g of carbon-12.

Question 3

State Avogrado’s Constant

Answer 3

6.022 x 10^23

Question 4

Formula to calculate number of particles in a substance, N

Answer 4

N = n x N(a)

n = number of moles
N(a) = Avogadro’s Constant

Question 5

Formula to calculate the molar mass of a substance, M

Answer 5

M = m / n

Question 6

State assumptions made in the kinetic model for an ideal gas

Answer 6

• The gas contains a very large number of particles moving in random directions with random speeds.
• The particles of the gas occupy a negligible volume compared with the volume of the gas.
• The collisions of the particles with each other and the container walls are perfectly elastic (no KE lost).
  The time of the collisions between the particles is negligible compared to the to the time between the collisions.
• Electrostatic forces between particles are negligible except during collisions.

Question 7

How does the speed/velocity/momentum of an atom change when it bounces off a boundary at?

Answer 7

• Speed remain the same, as it is a scalar.
• Velocity is the negative speed, as the direction is opposite.
• Change in momentum = -2mu

Question 8

State Boyle’s Law and conditions

Answer 8

P ∝ 1/V or pV = constant
Assuming constant temperature and mass of the gas.

Question 9

State the relationship between pressure and temperature and conditions

Answer 9

p ∝ T or p/T = constant
Assuming the volume and the mass of the gas remain constant.
T is always measured in kelvin

Question 10

Combining the gas laws formula and how it can be applied

Answer 10

• pV / T = constant
• Can be used when conditions are changing from an initial state to a final state
• P1V1 / T1 = P2V2 / T2

Question 11

State the equation of state for an ideal gas

Answer 11

• For one mole of an ideal gas, the constant in the combined temperature is the molar gas constant, R
• pV / T = nR or pV = nRT

Question 12

State the value/unit for R (molar gas constant)

Answer 12

8.31 J K-1 mol-1

Question 13

Describe the graph of pV against T

Answer 13

• This produces a straight line through the origin, as pV ∝ T
• By comparing y = mx + c and pV = nRT
• Gradient: nR
• The greater the number of moles, the steeper the line.

Question 14

Average velocity of particles in a gas

Answer 14

It would be 0 m/s, as the particles all move in random directions at different speeds, cancelling out.

Question 15

Average velocity of particles in a gas

Answer 15

It would be 0 m/s, as the particles all move in random directions at different speeds, cancelling out.

Question 16

How do we determine r.m.s speed

Answer 16

• The velocity of each particle is squared, and the average of these squares is calculated.
• The square root of the average is taken.

Question 17

Formula for pressure at the microscopic level

Answer 17

pV = 1/3 Nmc(squared bar)

where:
N = number of particles in the gas
m = mass of each particle
c (squared bar) = mean square speed of the particles

Question 18

Deriving pV = 1/3 Nmc(squared bar)

Answer 18

• Consider a single gas particle, mass m, velocity c, in a cube container of sides L.
• The time t between collisions is 2L / c
• Force = change in momentum / time
• Force = 2mc x c / 2L = mc(squared) / L
• If there are N particles, average force = mc(squared bar) / L, where c(squared bar) = mean square speed
• On average, about 1/3 of the particles are moving between opposite faces.
• CSA = L^2
• Force = mc(squared bar) x N x 1/3
• p = Nmc(squared bar) / 3L x 1 / L(squared)
• L(cubed) = volume
• pV = 1/3Nmc(squared bar)

Question 19

What is the Maxwell-Boltzmann distribution?

Answer 19

• In a container, gas particles will all be moving at different speeds, from very fast to very slow.
• The range of speeds the particles can take at a given temperature is the Maxwell-Boltzmann distribution.

Question 20

How does changing the temperature of a gas affect the Maxwell-Boltzmann distribution?

Answer 20

• The hotter that gas becomes, the greater the range of speeds.
• The modal speed and r.m.s increases.
• The distribution becomes more spread out.

Question 21

State the Boltzmann constant

Answer 21

k = R / N(a)
1.38 x 10^-23 J/K

Question 22

The second equation of the state of an ideal gas, by substituting the Boltzmann constant

Answer 22

pV = nRT —> pV = nKN(a)T
Number of particles in the gas, N = n x N(a)
pV = NkT

Question 23

Equation that relates the mean KE of a particle to the absolute temperature of the gas

Answer 23

1/3Nmc(squared bar) = NkT
Cancel out N, sub out 2/3
1/2mc(squared bar) = 3/2 kT

Question 24

Relationship between temperature and kinetic energy and conditions

Answer 24

E(k) ∝ T
Assuming the temperature is measured in kelvin.

Question 25

Internal energy of an ideal gas

Answer 25

• In an ideal gas, there are negiblible electrostatic forces between particles unless during a collision.
• This means the internal energy of a particle in an ideal gas is entirely its kinetic energy.
• Doubling temperature doubles K(e), so internal energy.