Question

A vessel contains dimethyl ether at a pressure of 0.4 atm. Dimethyl ether decomposes as $C{H}_{3}OC{H}_3\left(g\right)\to C{H}_4\left(g\right)+CO\left(g\right)+H_2\left(g\right)$. The rate constant of decomposition is $4.78\times {10}^{-3}mi{n}^{-1}$. Calculate the ratio to initial rate of diffusion of rate of diffusion after 4.5 hour of initiation of decomposition. Assume the composition of gas present and composition of gas diffusing to be same.

• A. $0.26:1$
• B. $0.13:1$
• C. $1:0.26$
• D. $1:0.13$

Answer 1

Answer: (A)

$0.26:1$

$C{H}_{3}OC{H}_3\to C{H}_4+CO+H_2$
$t=00.4$
$t=4.5hr.$ 0.110.290.290.29
$kt=\ln \frac{P_0}{P}\Rightarrow 4.78\times {10}^{-3}\times 4.5\times 60=\ln \frac{0.4}{P}$
$P=0.11atm$
at$t=0P_0=0.4$
$M_0=46$
at $t=4.5hr.P=0.11+0.29\times 3=0.98atm$
$M=\frac{0.11\times 46+0.29(16+28+2)}{0.98}=18.77$
$\frac{r_0}{r}=\frac{P_0}{P}\sqrt{\frac{M}{M_0}}=\frac{0.4}{0.98}\sqrt{\frac{18.77}{46}}=0.26$