Question

Dinitrogen pentaoxide decomposes as $2N_2{O}_5\to 4N{O}_2+O_2.$ the rate can be given in three ways
$\frac{-d\left[N_2{O}_5\right]}{dt}=k_1\left[N_2{O}_5\right],\frac{d\left[N{O}_2\right]}{dt}=k_2\left[N_2{O}_5\right],\frac{d\left[O_2\right]}{dt}=k_3\left[N_2{O}_5\right]$
The relation between the rate constants $k_1,k_{2}and{k}_3$is:

• A. (A)$k_2=2k_{1}and{k}_3=1/2k_1$
• B. (B)$k_1=2k_{2}and{k}_3=2k_1$
• C. (C)$k_1=k_2=k_3$
• D. (D)$k_1=2k_2=3k_3$

Answer 1

The correct option is A (A)$k_2=2k_{1}and{k}_3=1/2k_1$

$r=-\frac{1}{2}\frac{d\left[N_2{O}_5\right]}{dt}=\frac{1}{4}\frac{d\left[N{O}_2\right]}{dt}=\frac{d\left[O_2\right]}{dt}=k\left[N_2{O}_5\right]$
$k_1=2k$
$k_2=4k=2k_1$
$k_3=k=k_1/2$