Question

If rate constants for decomposition of $N_2{O}_5$, formation of $N{O}_2$ and formation of $O_2$ are $K_1,K_2$ and $K_3$ respectively, then:

• A. $K_1=K_2=K_3$
• B. $2K_1=K_2=4K_3$
• C. $K_1=2K_2=K_3$
• D. $K_1=K_2=2K_3$

Answer 1

Answer: (B)

$2K_1=K_2=4K_3$

Rate of reaction $=-\frac{1}{2}\frac{d\left[N_2{O}_5\right]}{dt}=\frac{1}{4}\frac{d\left[N{O}_2\right]}{dt}=\frac{d\left[O_2\right]}{dt}$

$-\frac{d\left[N_2{O}_5\right]}{dt}=K_1\left[N_2{O}_5\right];+\frac{d\left[N{O}_2\right]}{dt}=K_2\left[N_2{O}_5\right]$

and $\frac{d\left[O_2\right]}{dt}=K_3\left[N_2{O}_5\right]$

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

$\therefore K_1=\frac{K_2}{2}=2K_3$

$\therefore 2K_1=K_2=4K_3$.