Equal masses of Helium (He), Methane ($\mathrm{CH}_4$), and Sulphur dioxide ($\mathrm{SO}_2$) gases

Question

Equal masses of Helium (He), Methane ($\mathrm{CH}_4$), and Sulphur dioxide ($\mathrm{SO}_2$) gases have been taken in a rigid container. The ratio of the partial volumes they would occupy individually under identical conditions of temperature and pressure is

Professor PC Thomas Classes · Answer

(a) : According to Avogadro's hypothesis, the volume ratio of gases under identical conditions is equal to their mole ratio ($V \propto n$). Moles = Mass / Molar Mass. Let the equal mass be $w$. Molar masses are He=4, $\mathrm{CH}_4$=16, $\mathrm{SO}_2$=64. The mole ratio is $(w/4) : (w/16) : (w/64)$. Multiplying the entire ratio by 64 gives $16 : 4 : 1$.