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Ideal Gas Law

Key Concepts

An Ideal Gas (perfect gas)is one which obeys Boyle's Law and Charles' Law exactly.
An Ideal Gas obeys the Ideal Gas Law (General gas equation):
PV = nRT
where
P=pressure
V=volume
n=moles of gas
T=temperature
R = gas constant (dependent on the units of pressure, temperature and volume)
R = 8.314 J K^-1 mol^-1 if
Pressure is in kilopascals(kPa)
Volume is in litres(L)
Temperature is in kelvin(K)
R = 0.0821 L atm K^-1 mol^-1 if
Pressure is in atmospheres(atm)
Volume is in litres(L)
Temperature is in kelvin(K)
An Ideal Gas is modelled on the Kinetic Theory of Gases which has 4 basic postulates:

Gases consist of small particles (molecules) which are in continuous random motion
The volume of the molecules present is negligible compared to the total volume occupied by the gas
Intermolecular forces are negligible
Pressure is due to the gas molecules colliding with the walls of the container

Real Gases deviate from Ideal Gas Behaviour because:

at low temperatures the gas molecules have less kinetic energy (move around less) so they do attract each other
at high pressures the gas molecules are forced closer together so that the volume of the gas molecules becomes significant compared to the volume the gas occupies

Under ordinary conditions, deviations from Ideal Gas behaviour are so slight that they can be neglected
A gas which deviates from Ideal Gas behaviour is called a non-ideal gas.

Ideal Gas Law Calculations

Calculating Volume of Ideal Gas: V = (nRT) ÷ P

What volume is needed to store 0.050 moles of helium gas at 202.6kPa and 400K?

PV = nRT

P = 202.6 kPa
n = 0.050 mol
T = 400K
V = ? L
R = 8.314 J K^-1 mol^-1

202.6V = 0.050 x 8.314 x 400
202.6 V = 166.28
V = 166.28 ÷ 202.6
V = 0.821 L (821mL)

Calculating Pressure of Ideal Gas: P = (nRT) ÷ V

What pressure will be exerted by 20.16g hydrogen gas in a 7.5L cylinder at 20^oC?

PV = nRT

P = ? kPa
V = 7.5L
n = mass ÷ MM
mass = 20.16g
MM(H₂) = 2 x 1.008 = 2.016g/mol
n = 20.16 ÷ 2.016 = 10mol
T = 20^o = 20 + 273 = 293K
R = 8.314 J K^-1 mol^-1

P x 7.5 = 10 x 8.314 x 293
P x 7.5 = 24360.02
P = 24360.02 ÷ 7.5 = 3248kPa

Calculating moles of gas: n = (PV) ÷ (RT)

A 50L cylinder is filled with argon gas to a pressure of 10130.0kPa at 30^oC. How many moles of argon gas are in the cylinder?

PV = nRT

P = 10130.0kPa
V = 50L
n = ? mol
R = 8.314 J K^-1 mol^-1
T = 30^oC = 30 + 273 = 303K

10130.0 x 50 = n x 8.314 x 303
506500 = n x 2519.142
n = 506500 ÷ 2519.142 = 201.1mol

Calculating gas temperature: T = (PV) ÷ (nR)

To what temperature does a 250mL cylinder containing 0.40g helium gas need to be cooled in order for the pressure to be 253.25kPa?

PV = nRT

P = 253.25kPa
V = 250mL = 250 ÷ 1000 = 0.250L
n = mass ÷ MM
mass = 0.40g
MM(He) = 4.003g/mol
n = 0.40 ÷ 4.003 = 0.10mol
R = 8.314 J K mol^-1
T = ? K

253.25 x 0.250 = 0.10 x 8.314 x T
63.3125 = 0.8314 x T
T = 63.3125 ÷ 0.8314 = 76.15K

Practice Questions

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