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In a flask, the weight ratio of \(\mathrm{CH}(\mathrm{g})\) and \(\mathrm{SO}_{2}(\mathrm{~g})\) at \(298 \mathrm{~K}\) and 1 bar is \(1: 2\). The ratio of the number of molecules off \(\mathrm{SO}_{2}(\mathrm{~g})\) and \(\mathrm{CH}_{4}(\mathrm{~g})\) is
(A) \(1: 4\)
(B) \(4: 1\)
(C) \(1: 2\)
(D) \(2: 1\)

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Ans: (C)
Weight ratio \(\quad \mathrm{w}_{\mathrm{CH}_{4}}: \mathrm{w}_{\mathrm{SO}_{2}}=1: 2\)
Number of moles, \(n=\frac{w}{M}, \frac{n_{1}}{n_{2}}=\frac{w_{1}}{M_{1}} \times \frac{M_{2}}{w_{2}}\)
\(\frac{\mathrm{n}_{\mathrm{SO}_{2}}}{\mathrm{n}_{\mathrm{CH}_{4}}}=\frac{\mathrm{w}_{\mathrm{SO}_{2}}}{\mathrm{M}_{\mathrm{SO}_{2}}} \times \frac{\mathrm{M}_{\mathrm{CH}_{4}}}{\mathrm{w}_{\mathrm{CH}_{4}}}=\frac{2}{64} \times \frac{16}{1}=\frac{1}{2} \therefore\) mole ratio \(\mathrm{SO}_{2}: \mathrm{CH}_{4}=1: 2\)
\(\therefore\) ratio of number of molecules of \(\mathrm{SO}_{2}\) and \(\mathrm{CH}_{4}=1: 2\)
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