Question

The rate constant $k,$ for the reaction
$N_{2}O_{5}\left(g\right)\to2NO_{2}\left(g\right)+\frac{1}{2}O_{2}\left(g\right)$ is $2.3\times10^{-2}s^{-1}$ 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 $N_2O_5$initially and at time, $t$?

• A. $\left[N_{2}O_{5}\right]_{t}=\left[N_{2}O_{5}\right]_{0}+kt$
• B. $\left[N_{2}O_{5}\right]_{0}=\left[N_{2}O_{5}\right]_{t}^{e^{kt}}$
• C. $log _{10}\left[N_{2}O_{5}\right]_{t}=log_{10}\left[N_{2}O_{5}\right]_{0}-kt$
• D. $\ln \frac{\left[N_{2}O_{5}\right]_{0}}{\left[N_{2}O_{5}\right]_{t}}=kt$

Answer 1

Answer: (D)

Rate constant $= 2.3 \times 10^{-2} sec^{-1}$
It means it is a first order reaction (because unit of rate constant is $sec^{-1}$)
For first order reaction $k=\frac{1}{t}ln\frac{a}{a-x}$
$kt=ln\frac{a}{a-x}=ln\frac{\left[N_{2}O_{5}\right]_{0}}{\left[N_{2}O_{5}\right]_{t}}$