Find the relative molecular mass of a gas, 0.546 g of which occupies 360 cm3 at 87°C and 380 mm Hg pressure. (1 litre of hydrogen at s.t.p. weighs 0.09 g)

Using the gas equation,

⇒ P_1V_1\overT_1=P_2V_2\overT_2

Substituting the values we get,

⇒ 380 × 360\over 360=760 × x\over273

⇒ x = 380 × 360 × 273\over 360 × 760

⇒ x = 10273\over 76

⇒ x = 136.5 cm³ = 0.1365 lit.

At s.t.p. 0.1365 lit weighs 0.546 g

Therefore, 1 lit of gas weighs = 0.546\over 0.1365 × 1 = 4 g

Vapour density of gas = 4\over 0.09

= 44.444

Molecular weight = 2 × Vapour density

= 2 × 44.444

= 88.888 = 88.89 g

Hence, relative molecular mass of gas 88.89 g