Dimethyl ether decomposes as ${\mathrm{CH}}_3{\mathrm{OCH}}_3\left(\mathrm{g}\right)⟶{\mathrm{CH}}_4\left(\mathrm{g}\right)+\mathrm{CO}\left(\mathrm{g}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)$ When CH₃OCH₃, decomposes to 20% extent at certain fixed conditions, what is the ratio of diffusion of pure CH₃OCH₃ with methane?

$$\begin{gathered} {\mathrm{CH}}_3{\mathrm{OCH}}_3\left(\mathrm{g}\right)\to {\mathrm{CH}}_4\left(\mathrm{g}\right)+\mathrm{CO}\left(\mathrm{g}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right) \\ \mathrm{Initial} \mathrm{press}.: 1 0 \\ \mathrm{at} \mathrm{euilibrium}: 1-\mathrm{x} \mathrm{x} \\ 1-0.2 0.2 \\ \because \mathrm{x}=20\% = 0.2 \end{gathered}$$
$\begin{array}{r}\frac{{\mathrm{r}}_{{\mathrm{CH}}_3{\mathrm{OCH}}_3}}{{\mathrm{r}}_{{\mathrm{CH}}_4}}=\sqrt{\frac{{\mathrm{M}}_{{\mathrm{CH}}_4}}{{\mathrm{M}}_{{\mathrm{CH}}_3{\mathrm{OCH}}_3}}}\times \frac{{\mathrm{P}}_{{\mathrm{CH}}_3{\mathrm{OCH}}_3}}{{\mathrm{P}}_{{\mathrm{CH}}_4}}\\ =\sqrt{\frac{16}{46}}\times \frac{0.8}{0.2}=2.36:1\end{array}$