Question

The gas phase decomposition of dimethyl ether follows first order kinetics.
$C{H}_{3}OC{H}_3\left(g\right)\to C{H}_4\left(g\right)+H_2\left(g\right)+CO\left(g\right)$
The reaction is carried out in a constant volume container at ${500}^{\circ }C$ and has a half life of 14.5 min. Initially, only dimethyl ether is present at a pressure of 0.40 atm. What is the total pressure of the system after 12 min? Assume ideal gas behaviour.

• A. 0.74 atm
• B. 7.4 atm
• C. 74 atm
• D. none

Answer 1

The correct option is A 0.74 atm

For first order reaction,
Half life = $\frac{0.693}{k}$
or 14.5 = $\frac{0.693}{k}$
or k = $\frac{0.693}{k}=4.78\times {10}^{-2}mi{n}^{-1}$
Also,
$k=\frac{2.303}{t}log\frac{A_0}{A_t}=\frac{2.303}{t}log\frac{P_0}{P}$
or $\frac{0.693}{14.5}=\frac{2.303}{12}log\frac{0.40}{(0.40-x)}$
or x = 0.1746 atm
Total pressure of container after 12 min is
(0.40 - x) + x + x + x = 0.4 + 2x
= 0.4 + 2 $\times$ 0.1746
= 0.7492 atm