Gases

Question 1

Define the pressure of a gas and give its units

Answer 1

The pressure of a gas is the force per unit area that the gas exerts normally (90°) on a surface
Units: Pascals (Pa) 1Pa = 1Nm⁻²

Question 2

Define isothermal change

Answer 2

An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0.

Question 3

State Boyle’s law

Answer 3

For a fixed mass of gas at constant temperature:
pV = constant
where p is gas pressure and V is gas volume

Question 4

Name the 3 experimental gas laws

Answer 4

1) Boyle’s law
2) Charle’s law
3) The Pressure Law

Question 5

For a constant temperature, describe the graphs of:

i) Pressure vs. Volume
ii) Pressure vs. 1 / Volume

Answer 5

i) A curved line which tends towards each axis

ii) A straight line passing through the origin

Question 6

Describe the apparatus to test Boyle’s law

Answer 6

A foot pump attached to a sealed tube of oil enclosing a volume of gas under pressure in a volume graded tube. A pressure gauge is attached to the system to measure the change in pressure associated with the changing volume of gas

Question 7

State Charle’s law

Answer 7

The volume of a fixed mass of gas at a constant pressure varies with absolute temperature T (in Kelvins)
V / T = constant

Question 8

Describe the apparatus to test Charle’s law

Answer 8

A glass tube open at one end containing dry air trapped by a suitable liquid can be used to find how the volume of a fixed mass of gas at constant pressure varies with temperature

Question 9

State the pressure law

Answer 9

For a fixed mass of gas at a constant volume, the relationship between the pressure p and temperature T can be written as:
P / T = constant

Question 10

Describe the apparatus to test the pressure law

Answer 10

A sealed boiling flask containing dry gas is placed in a water bath whilst the gas is connected to a pressure gauge to measure the change in pressure, with a thermometer in the water bath to measure the change in temperature

Question 11

Describe and explain Brownian motion of gas particleS

Answer 11

The motion of each particle is due to it being bombarded unevenly and at random by individual molecules.
The particle is therefore subjected to a force due to the impacts which changes its magnitude and direction at random

Question 12

Define an ideal gas and give the equation for the 3 experimental gas laws combined

Answer 12

An ideal gas obeys Boyle’s law
For a fixed mass of ideal gas:
pV = nRT
where V is the volume of n moles of gas at temperature

Question 13

Define and explain the molar gas constant

Answer 13

The molar gas constant is 8.31 Jmol⁻¹K⁻¹ for 1 mole of an ideal gas at STP
This is because 1 mole of any ideal gas at 273K and 101kPa has a volume of 0,0224m³ so the pV/T value is constant

Question 14

Give the equation for the mass of an ideal gas from the molar mass and the number of moles using the ideal gas equation

Answer 14

Since mass = Molar mass M x moles n
And n = pV / RT
Mass of a gas = M(pV/RT)

Question 15

Give the equation for the density of an ideal gas of molar mass M

Answer 15

ρ = Mass / Volume = nM/V = pM/RT

Question 16

Give the equation for the Boltzmann constant and relate it to the ideal gas equation

Answer 16

Boltzmann constant k = R / Nᴬ
Since n = N / Nᴬ
pV = NkT

Question 17

Explain Boyle’s law in terms of molecular collisions

Answer 17

The pressure of a gas at constant temperature is increased by reducing its volume because the gas molecules travel less distance between impacts at the walls due to the reduced volume. Hence there are more impacts per second so the pressure is greater

Question 18

Explain the pressure law in terms of molecular collisions

Answer 18

The pressure of a gas at constant volume is increased by raising its temperature. The average speed of the molecules is increased by raising the gas temperatures so the impacts of the molecules on the container walls are harder and more frequent. Hence the pressure is raised as a result

Question 19

Give the equation for the rms of gas molecules

Answer 19

c(rms) = √(c₁² + c₂² + … + c(N)² / N)

where c₁, c₂, … c(N) represent the speeds of individual molecules and N is the number of molecules in the gas

Question 20

Give the kinetic theory equation for a gas

Answer 20

pV = ⅓Nmc(rms)²

Question 21

Name 5 assumptions made for the kinetic theory equation for a gas

Answer 21

1) The molecules are point molecules (the volume of each molecule is negligible compared with the volume of gas)
2) They do not attract each other
3) The move about in continual random motion
4) The collision they undergo with each other and with the container surface are elastic collisions
5) Each collision with the container surface is of much shorter duration than the time between impacts

Question 22

Give the equation for the mean kinetic energy of a molecule of gas

Answer 22

KE for a molecule = Total KE / number of molecules

Question 23

Give the equation for the mean kinetic energy of a gas

Answer 23

KE = ½m(c₁² + c₂² + … + c(N)² / N) = ½mc(rms)²

Question 24

Give the equation for the mean kinetic energy of a gas in terms of the Boltzmann constant

Answer 24

½mc(rms)² = ³∕₂kT
Since k = R / Nᴬ
3kT = mc(rms)²

Question 25

Give the equation for the total kinetic energy of n moles of an idea gas

Answer 25

Total KE = ³∕₂nkT