Question

The gas phase decomposition of dimethyl ether follows first order kinetics:
$C{H}_3-O-C{H}_3\left(g\right)\to C{H}_4\left(g\right)+H_2\left(g\right)+CO\left(g\right)$

The reaction is carried out in a constant volume container at ${50}^{0}C$ and has a half life of 14.5 minutes. Initially, only dimethyl ether is present at a pressure of 0.40 atm. What is the total pressure of the system after 12 minutes? (Assume the ideal gas behaviour.)

• A. 0.946 atm
• B. 0.785 atm
• C. 0.777 atm
• D. 0.749 atm

Answer 1

The correct option is D 0.749 atm

$t_{\frac{1}{2}}=\frac{0.693}{k}\Rightarrow k=\frac{0.693}{14.5}=0.0478$
$P_t=P_o\left[e^{kt}\right]$
$P_t=0.225$
$C{H}_{3}OC{H}_3\to C{H}_4+H_2+CO$
$\begin{array}{ccccc}f=0& .40& 0& 0& 0\\ f=t& .40-x& x& x& x\end{array}$
$0.40-x=0.225$
$x=0.40-0.225=0.1746$ atm
total pressure$=0.40+2x$
$=0.40+0.349$
$=0.749$ atm