Ideal Gases

Question 1

What is the Avogadro Constant?

Answer 1

The number of particles that make up one mole of any gas

Question 2

What is the Boltzmann Constant?

Answer 2

A constant relating the average kinetic energy of the particles in a gas, to the gas’ temperature

Question 3

What is Boyle’s Law

Answer 3

As volume decreases the pressure on a gas at a constant temperature increases

Question 4

what is Charles’ law

Answer 4

As temperature increases the volume of a gas at constant pressure increases

Question 5

What is an ideal gas?

Answer 5

A hypothetical gas that has molecules with no interactions and occupies negligible space so it obeys the ideal gas law.

Question 6

What is the ideal gas law?

Answer 6

A combination of Boyle’s, Charles’ and the Pressure Law that describes the relationship between pressure, volume and temperature of an ideal gas

Question 7

What is the Pressure Law?

Answer 7

As temperature increases the pressure of a gas of constant volume increases.

Question 8

What is the SI unit for an amount of given susbtance?

Answer 8

• amt of substance is measured in moles
• unit: mol

Question 9

how many molecules comprise one mole of a substance?

Answer 9

• One mole of any substance contains Avogadro’s number of constituent molecules
• 6.02 x 10^23 molecules

Question 10

What is an ideal gas #2

Answer 10

An ideal gas is one that can be considered to obey the principle that the product of the pressure and volume of the gas will be proportional to its temperature (pV ∝ T)

Question 11

What are the key assumptions in the kinetic theory of gases?

Answer 11

• there are a large number of molecules in random, rapid motion.
• Particles have a negligible volume compared to the total
  volume of the gas
• All collisions are perfectly elastic
• The time taken for a collision is negligible compared to the time between collisions
• Between collisions there are no forces between particles

Question 12

Why do gases exert a pressure on the container they’re in?

Answer 12

• Gas particles collide with the surfaces of the container
• The container exerts a force in the particles to change their direction
• the particles exert an equal and opposite force on the container
• pressure is force applied (in total, by all particles) per unit area

Question 13

What is the ideal gas equation?

Answer 13

• pV = nRT
• where:
• ‘p’ is the pressure, Pa
• ‘R’ is the molar gas constant, 8.31 Jmol^-1K^-1
• ‘n’ is the number of moles, mol
• T is the temperature, K
• V is the volume, m^3

Question 14

Give an alternative form of the ideal gas equation

Answer 14

• pV = NkT
• where:
• ‘p’ - pressure, Pa
• ‘k’ - the Boltzmann constant, Jmol^-1
• ‘N’ - the number of molecules
• ‘T’ - temperature, K
• ‘V’ - volume, m^3

Question 15

Define the Boltzmann constant k

Answer 15

• k = R/ N(a)
• where:
• ‘R’ is the molar gas constant, 8.31 Jmol^-1
• ‘N(a) is the Avogadro’s constant (the number of particles in a mole), 6.02 x 10^23

Question 16

Explain how increasing the temperature of a balloon, while keeping the volume the same, will increase the pressure on the gas

Answer 16

• As the temperature increases, the avg KE of the particles increases, so the particles travel at a higher speed.
• This results in more frequent collisions
• This would cause an increased rate of change in momentum
• So the particles would exert a greater force
• therefore the pressure is increased

Question 17

True or False?
‘ All collisions between particles and between particles and the wall are elastic’ is an assumption of an ideal gas.

Answer 17

• True

Question 18

State an assumption of an ideal gas related to time?

Answer 18

The time for each collision is negligible in comparison to the time between collisions

Question 19

Describe 3 other assumptions of the ideal gas equation

Answer 19

• The particles move randomly
• They follow Newton’s laws of motion
• No intermolecular forces between particles
• Volume of container is negligible compared to the volume of the particles

Question 20

Use the kinetic theory of gases to explain why a temperature increase would lead to an increase in pressure for a gas that is contained within a container of invariant volume.

Answer 20

• A temperature increase means the particles have more kinetic energy
• More kinetic energy means a greater change in momentum during collisions with the container
• There are also more frequent collisions
• Change in momentum is proportional to force applied, and therefore to pressure as well

Question 21

What equation links N, V, p, m and c?

Answer 21

• pV = 1/3 Nmc^2
• where:
• ‘p’ - pressure
• ‘V’ - volume
• ‘N’ - number of particles
• ‘m’ - molecular mass of a particle
• ‘c^2’ - mean square speed

Question 22

What is meant by the root mean square speed?

Answer 22

• the square root of the mean of the squares of the speed of the molecules
• C (rms)

Question 22

What equation is used to determine the number of moles?

Answer 22

• n = m/M
• where:
• m is the mass of the substance
• M is the molar mass (in grams, which is the same as the nucleon number for the atom/molecule) of the particles that make up the substance

Question 23

Derive the relationship:
pV = 1/3 Nm(c^2)

Question 24

Show that the mean kinetic energy of gas molecules is proportional to T

Question 25

Show that the total translational kinetic energy of a mole of a monatomic gas is E(k) = 3/2 RT

Question 26

Assuming constant volume, how are the pressure and temperature of a gas related?

Answer 26

- They are directly proportional - i.e. P/T = constant

Question 27

True or False 'The internal energy of an ideal gas is proportional to absolute temperature.'

Answer 27

- True - In an ideal gas, there is no 'potential energy' component in the internal energy. - This means the internal energy is proportional to the kinetic energy (which is, in turn, dependent on temperature)