Problem : $SO_2Cl_2 \rightleftharpoons SO_2 + Cl_2 $ is the first order gas reaction with K = 2.2 × 10^{–5} sec^{–1} at 320°C. The percentage of SO_{2}Cl_{2} decomposed on heating for 90 minutes is

(A) 1.118

(B) 0.1118

(C) 18.11

(D) 11.30

Solution: $\large K = \frac{2.303}{t} log\frac{a}{a-x}$

$\large log\frac{a}{a-x} = \frac{K t}{2.303} $

$\large log\frac{a}{a-x} = \frac{2.2 \times 10^{-5}\times 60 \times 60}{2.303} = 0.0516$

$\large \frac{a}{a-x} = 1.127$

$\large \frac{a-x}{a} = 0.887$

$\large 1- \frac{x}{a} = 0.887$

$\large \frac{x}{a} = 0.113 $

= 11.3 %

Ans: (D)