The Ideal Gas Equation (DP IB Chemistry) : Revision Note

Calculate the volume, in dm³, occupied by 0.781 mol of oxygen at a pressure of 220 kPa and a temperature of 21 °C.

Answer:

• Step 1: Rearrange the ideal gas equation to find volume of the gas

• Step 2: Convert into the correct units and calculate the volume the oxygen gas occupies

P = 220 kPa = 220 000 Pa

n = 0.781 mol

R = 8.31 J K^-1 mol^-1

T = 21 ^oC = 294 K

= 0.00867 m³

= 8.67 dm³

A word about units...

Students often mess up gas calculations by getting their unit conversions wrong, particularly from cm³ to m³. Think about what a cubic metre actually is - a cube with sides 1 m or 100 cm long. The volume of this cube is 100 x 100 x 100 = 1 000 000 or 10⁶ cm³

So when you convert from m³ to cm³ you MULTIPLY by 10⁶ and when you convert from cm³ to m³ you DIVIDE by 10⁶  (or multiply by 10^-6 which is the same thing)

Calculate the pressure of a gas, in kPa, given that 0.20 moles of the gas occupy 10.1 dm³ at a temperature of 25 ^oC.

Answer:

• Step 1: Rearrange the ideal gas equation to find the pressure of the gas

• Step 2: Convert to the correct units and calculate the pressure

n = 0.20 mol

V = 10.1 dm³ = 0.0101 m³ = 10.1 x 10^-3 m³ 

R = 8.31 J K^-1 mol^-1

T = 25 ^oC = 298 K

P = 49 037 Pa = 49 kPa (2 sig figs)

Calculate the temperature of a gas, in ^oC, if 0.047 moles of the gas occupy 1.2 dm³ at a pressure of 100 kPa.

Answer:

• Step 1: Rearrange the ideal gas equation to find the temperature of the gas

• Step 2: Convert to the correct units and calculate the pressure

n = 0.047 mol

V = 1.2 dm³ = 0.0012 m³ = 1.2 x 10^-3 m³ 

R = 8.31 J K^-1 mol^-1

P = 100 kPa = 100 000 Pa

T = 307.24 K = 34.24 ^oC = 34 ^oC  (2 sig figs)

A flask of volume 1000 cm³ contains 6.39 g of a gas. The pressure in the flask was 300 kPa and the temperature was 23 °C.Calculate the molar mass of the gas.

Answer:

• Step 1: Rearrange the ideal gas equation to find the number of moles of gas

• Step 2: Convert to the correct units and calculate the number of moles of gas

P = 300 kPa = 300 000 Pa

V = 1000 cm³ = 0.001 m³ = 1.0 x 10^-3 m³ 

R = 8.31 J K^-1 mol^-1

T = 23 ^oC = 296 K

      n = 0.12 mol

• Step 3: Calculate the molar mass using the number of moles of gas

To calculate the temperature in Kelvin, add 273 to the Celsius temperature, eg. 100 ^oC is 373 Kelvin.