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 as 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 its 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 (for an ideal gas)

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.