Question

For the first order decomposition reaction of $N_2{O}_5$, it is observed that
$\left(i\right)N_2{O}_5\left(g\right)\to 2N{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right);\frac{-d\left[N_2{O}_5\right]}{dt}=k\left[N_2{O}_5\right]\left(ii\right)2N_2{O}_5\left(g\right)\to 4N{O}_2\left(g\right)+O_2\left(g\right);\frac{-d\left[N_2{O}_5\right]}{dt}=k^{\prime }\left[N_2{O}_5\right]$
Which of the following is true?

• A. $k=k^{\prime }$
• B. $k=2k^{\prime }$
• C. $k=\frac{k^{\prime }}{2}$
• D. $k=k^{\prime \frac{1}{2}}$

Answer 1

The correct option is D $k=k^{\prime \frac{1}{2}}$

Take ratio of both equations