Question

The rate constant for the reaction, $N_2{O}_5\left(g\right)⟶2N{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)$, is $2.3\times {10}^{-2}{sec}^{-1}$. Which equation given below describes the change of $\left[N_2{O}_5\right]$ with time, ${\left[N_2{O}_5\right]}_0$ and ${\left[N_2{O}_5\right]}_t$ corresponds to concentration of $N_2{O}_5$ initially and time $t$ respectively?

• A. ${\left[N_2{O}_5\right]}_0={\left[N_2{O}_5\right]}_t{e}^{kt}$
• B. ${\log }_e\frac{{\left[N_2{O}_5\right]}_0}{{\left[N_2{O}_5\right]}_t}=kt$
• C. ${\log }_{10}{\left[N_2{O}_5\right]}_t={\log }_{10}{\left[N_2{O}_5\right]}_0-kt$
• D. ${\left[N_2{O}_5\right]}_t={\left[N_2{O}_5\right]}_0+kt$

Answer 1

Answer: (A), (B), (C)

The correct options are
A ${\left[N_2{O}_5\right]}_0={\left[N_2{O}_5\right]}_t{e}^{kt}$
B ${\log }_e\frac{{\left[N_2{O}_5\right]}_0}{{\left[N_2{O}_5\right]}_t}=kt$
C ${\log }_{10}{\left[N_2{O}_5\right]}_t={\log }_{10}{\left[N_2{O}_5\right]}_0-kt$

${\left[N_2{O}_5\right]}_t={\left[N_2{O}_5\right]}_0{e}^{-kt}{\left[N_2{O}_5\right]}_0={\left[N_2{O}_5\right]}_t{e}^{kt}\ln \left(\frac{{\left[N_2{O}_5\right]}_0}{{\left[N_2{O}_5\right]}_t}\right)=e^{kt}\ln {\left[N_2{O}_5\right]}_t=\ln {\left[N_2{O}_5\right]}_0-kt$