Calculate the relative molecular mass [molecular weight] of 290 ml. of a gas 'A' at 17 °C and 1520 mm pressure which weighs 2.73 g at s.t.p. [1 litre of hydrogen at s.t.p. weighs 0.09 g.]

Convert the volume to s.t.p. using gas equation

Using the gas equation,

$\dfrac{P${1}V{1}}{T{1}} = \dfrac{P{2}V{2}}{T{2}}

Substituting the values we get,

$\dfrac{1520 \times 290}{290} = \dfrac{760 \times x}{273} \\[0.5em] x = \dfrac{1520 \times 273}{760} \\[0.5em] x = 546 \text{ ml}$

546 ml of gas at s.t.p. weighs 2.73 g

∴ Wt. of 1000 ml of gas = $\dfrac{2.73}{546} \times 1000 = 5 \text { g}$

Vapour density of gas X =

$\dfrac{\text{Wt. of 1 lit of gas X}}{\text {Wt. of 1 lit of H}_2} \\[0.5em] = \dfrac{5}{0.09} \\[0.5em] = 55.55$

Hence, vapour density of gas is 55.55

Molecular weight = 2 x Vapour Density
= 2 x 55.555
= 111.11 g

Hence, molecular weight of gas is 111.11 g