Chemistry - Chemical Kinetics Question with Solution | TestHub

For the reaction $2N{H}_3\to N_2+3H_2$, the rate is:

$$-\frac{1}{2}\frac{d[N{H}_3]}{dt}=\frac{d[N_2]}{dt}=\frac{1}{3}\frac{d[H_2]}{dt}$$

Given:

$$-\frac{d[N{H}_3]}{dt}=k_1[N{H}_3]$$

$$\frac{d[N_2]}{dt}=k_2[N{H}_3]$$

$$\frac{d[H_2]}{dt}=k_3[N{H}_3]$$

Comparing with the stoichiometric rate relation:

$$\frac{k_1}{2}=k_2=\frac{k_3}{3}$$

Multiplying throughout by 6:

$$3k_1=6k_2=2k_3$$

This matches Option (C).