Question

The rate of the reaction $2N_2{O}_5⟶4N{O}_2+O_2$ can be written in three ways:
$\frac{-d\left[N_2{O}_5\right]}{dt}=k\left[N_2{O}_5\right]$
$\frac{d\left[N{O}_2\right]}{dt}=k^{\prime }\left[N_2{O}_5\right]$
$\frac{d\left[O_2\right]}{dt}=k^{\prime \prime }\left[N_2{O}_5\right]$
The relationship between $k$ and $k^{\prime }$ and between $k$ and $k^{\prime \prime }$ are :

• A. $k^{\prime }=2k;k^{\prime \prime }=k$
• B. $k^{\prime }=2k;k^{\prime \prime }=k/2$
• C. $k^{\prime }=2k;k^{\prime \prime }=2k$
• D. $k^{\prime }=k;k^{\prime \prime }=k$

Answer 1

The correct option is B $k^{\prime }=2k;k^{\prime \prime }=k/2$

The expression for the rate of the reaction can be written as :

$-\frac{1}{2}\frac{d\left(N_2{O}_5\right)}{dt}=-\frac{1}{4}\frac{d\left(N{O}_2\right)}{dt}=\frac{d\left(O_2\right)}{dt}$

$\frac{1}{2}k\left(N_2{O}_5\right)=\frac{1}{4}{k}^{\prime }\left(N_2{O}_5\right)=k^{\prime \prime }\left(N_2{O}_5\right)$

$\frac{k}{2}=\frac{k^{\prime }}{4}=k^{\prime \prime }$

$k^{\prime }=2k,k^{\prime \prime }=\frac{k}{2}$

Thus, the relationship between $k$ and $k^{\prime }$ and between $k$ and $k^{\prime \prime }$ are $k^{\prime }=2k;k^{\prime \prime }=k/2$.

Hence, the correct option is B.