A gas of mass 32 gms has a volume of 20 litres at S.T.P. Calculate the gram molecular weight of the gas.
Topic: Mole concept, gas volumes and stoichiometry
Answer
Given: mass = 32 g, volume at STP = 20 litres.
Gram molecular weight = mass of 22.4 litres of the gas at STP.
Moles of gas = volume at STP ÷ 22.4 = 20 ÷ 22.4 = 0.893 mol
Gram molecular weight = mass ÷ moles = 32 ÷ 0.893 = 35.84 g mol⁻¹
Gram molecular weight ≈ 35.8 g mol⁻¹
The single fact this question runs on: one mole of ANY gas occupies 22.4 litres at STP. So 20 litres is a little less than one mole, which means the gram molecular weight must be a little more than 32 — check your answer against that before you write it down.
The usual wrong answer is 35.84 the other way up, or simply 32, from assuming that 20 litres is one mole. It is not; only 22.4 litres is. A quick alternative route by proportion: 20 L weighs 32 g, so 22.4 L weighs 32 × 22.4 ÷ 20 = 35.84 g.