Question

The rate constant $k,$ for the reaction
$N_2{O}_5\left(g\right)\to 2N{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)$ 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. ${\left[N_2{O}_5\right]}_t={\left[N_2{O}_5\right]}_0+kt$
• B. ${\left[N_2{O}_5\right]}_0={\left[N_2{O}_5\right]}_t^{e^{kt}}$
• C. $lo{g}_{10}{\left[N_2{O}_5\right]}_t=lo{g}_{10}{\left[N_2{O}_5\right]}_0-kt$
• D. $\ln \frac{{\left[N_2{O}_5\right]}_0}{{\left[N_2{O}_5\right]}_t}=kt$

Answer 1

Answer: (D)

Rate constant $=2.3\times 10^{-2}se{c}^{-1}$
It means it is a first order reaction (because unit of rate constant is $se{c}^{-1}$)
For first order reaction $k=\frac{1}{t}ln\frac{a}{a-x}$
$kt=ln\frac{a}{a-x}=ln\frac{{\left[N_2{O}_5\right]}_0}{{\left[N_2{O}_5\right]}_t}$