Question

$N_2{O}_2\left(g\right)\to 2NO$ is a first-order reaction interms of the concentration of $N_2{O}_2\left(g\right)$ .Which of the following is valid, $\left[N_2{O}_2\right]$ being constant?

• A. $\left[NO\right]=[N_2{O}_2{]}_0{e}^{-kt}$
• B. $\left[NO\right]=\left[N_2{O}_2{]}_0\right(1-e^{kt})$
• C. $\left[NO\right]=\left[N_2{O}_2{]}_0\right(e^{-kt}-1)$
• D. $\left[NO\right]=\left[N_2{O}_2{]}_0\right(1-e^{-kt})$

Answer 1

Answer: (D)

$\left[NO\right]=\left[N_2{O}_2{]}_0\right(1-e^{-kt})$

The reaction is $N_2{O}_2\left(g\right)\to 2NO$
The initial concentration of $N_2{O}_2$ is $[N_2{O}_2{]}_0$.. Assuming initially only $N_2{O}_2$ is present and no $NO$ is formed.
At time t, the concentrtion of $N_2{O}_2$ and NO are $\left[N_2{O}_2\right]$ and $\left[NO\right]$ respectively.
The total concentration is equal to $\left[N_2{O}_2\right]+\left[NO\right]=[N_2{O}_2{]}_0$ ......(1)
But from integrated rate law equation fo first order reaction , $\left[N_2{O}_2\right]=[N_2{O}_2{]}_0{e}^{-kt}$......(2)
Substituting equation (2) in equation (1)
$[N_2{O}_2{]}_0{e}^{-kt}+[NO]=[N_2{O}_2{]}_0$
$\left[NO\right]=[N_2{O}_2{]}_0-[N_2{O}_2{]}_0{e}^{-kt}=\left[N_2{O}_2{]}_0\right(1-e^{-kt})$