The ratio of rate of diffusion of $\mathrm{SO}_2$ to $\mathrm{CH}_4$ is

The ratio of rate of diffusion of $\mathrm{SO}_2$ to $\mathrm{CH}_4$ is
  1. $1: 1$
  2. $1: 2$
  3. $2: 1$
  4. $4: 1$

Solution

Rate of diffusion of gas (r) $\propto \frac{1}{\sqrt{\text { Molecular weight of gas }}}$ Molecular weight of $\mathrm{SO}_2=32+16 \times 2=64$ $\therefore \quad r_{\mathrm{SO}_2} \propto \frac{1}{\sqrt{64}}$ Molecular weight of $\mathrm{CH}_4=12+1 \times 4=16$ $\therefore \quad r_{\mathrm{CH}_4} \propto \frac{1}{\sqrt{16}} \Rightarrow \frac{r_{\mathrm{SO}_2}}{r_{\mathrm{CH}_4}}=\frac{\sqrt{16}}{\sqrt{64}}=\frac{1}{2}=1: 2$

Asked in: AP EAMCET 2022 (07 Jul Shift 1)

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