Question

The reaction $A\left(g\right) \rightarrow 2B\left(g\right)+C\left(g\right)$ follows first order kinetics. The reaction is started with pure ' $A$ ' in a rigid closed vessel maintained at constant temperature. After $10s$ , a pin hole is developed in the vessel. If the molar ratio of gases ' $A$ ' and ' $B$ ' coming out initially is $1:2$ the rate constant of reaction(in $s^{- 1}$ ) is $X$ . Calculate $100X$ ? (Molar masses of $A,B$ and $C$ are $16,4$ and $8g/mol$ respectively, ln $2=0.7$ , ln $3=1.1$ )

Answer 1

Now, $\frac{r_{A}}{r_{B}}=\frac{P_{A}}{P_{B}}\sqrt{\frac{M_{B}}{M_{A}}}\Rightarrow \frac{1}{2}=\frac{a - x}{2 x}\cdot \sqrt{\frac{4}{16}}$
$\Rightarrow x=\frac{a}{3}$
Now, $K=\frac{1}{t}\cdot ln\frac{a}{a - x}=\frac{1}{10 sec}\cdot ln\frac{a}{\frac{2 a}{3}}$
$=0.04sec^{- 1}100X=4$