Question

Consider the chemical reaction:
$N_2\left(g\right)+3H_2\left(g\right)\to 2N{H}_3\left(g\right)$

The rate of this reaction can be expressed; in terms of time and of concentration of $N_2\left(g\right),H_2\left(g\right)$ $N{H}_3\left(g\right)$. Identify the correct relationship amongst the rate expressions.

• A. Rate $=-\frac{d\left[N_2\right]}{dt}=-\frac{1}{3}\frac{d\left[H_2\right]}{dt}=+\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$
• B. Rate $=-\frac{d\left[N_2\right]}{dt}=-\frac{3d\left[H_2\right]}{dt}=\frac{2d\left[N{H}_3\right]}{dt}$
• C. Rate $=-\frac{d\left[N_2\right]}{dt}=-\frac{1}{3}\frac{d\left[H_2\right]}{dt}=\frac{d\left[N{H}_3\right]}{dt}$
• D. Rate $=-\frac{d\left[N_2\right]}{dt}=\frac{d\left[H_2\right]}{dt}=\frac{d\left[N{H}_3\right]}{dt}$

Answer 1

Answer: (A)

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

As the reaction proceed, the concentration of the reactant decrease and that of the product increases.

Thus, the rate of the reaction of the reactant and product can be given as follow:

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