Question

The rate constant $k$, for the reaction
$N _{2} O _{5}(g) \longrightarrow 2 NO _{2}(g)+\frac{1}{2} O _{2}(g)$
is $2.3 \times 10^{-2} s ^{-1}$. Which equation given below describes the change of $\left[ N _{2} O _{5}\right]$ with time?
$\left[ N _{2} O _{5}\right]_{0}$ and $\left[ N _{2} O _{5}\right]_{t}$ correspond to concentration of $N _{2} O _{5}$ initially and at time $t$.

• A. $\left[ N _{2} O _{5}\right]_{t}=\left[ N _{2} O _{5}\right]_{0}+k t$
• B. $\left[ N _{2} O _{5}\right]_{0}=\left[ N _{2} O _{5}\right]_{t} e^{k t}$
• C. $\log \left[ N _{2} O _{5}\right]_{t}=\log \left[ N _{2} O _{5}\right]_{0}+k t$
• D. $\ln \frac{\left[ N _{2} O _{5}\right]_{0}}{\left[ N _{2} O _{5}\right]_{8}}=k t$

Answer 1

Answer: (D)

From the unit of rate constant $\left( sec ^{-1}\right)$ it is clear that the reaction is of first order. For Ist order reaction $k=\frac{1}{t} \log _{e} \frac{a}{a-x}$
or $ k t=\log _{e} \frac{\left[ N _{2} O _{5}\right]_{0}}{\left[ N _{2} O _{5}\right] t}$
$k \propto \frac{1}{t}$ so,
$k \propto \frac{1}{\sec }= s ^{-1}$