Question

Consider the chemical reaction:
$N_2\left(g\right)+3H_2\left(g\right)\to 2N{H}_3\left(g\right)$.
The overall rate of this reaction can be expressed in terms of time derivative of concentration of $N_2\left(g\right)$, $H_2$, or $N{H}_3\left(g\right)$.
Identify the correct relationship among the given 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. $$Rate=\frac{-d\left[N_2\right]}{dt}=-3\frac{d\left[H_2\right]}{dt}=+2\frac{d\left[N{H}_3\right]}{dt}$$
• C. $$Rate=\frac{-d\left[N_2\right]}{dt}=\frac{1}{3}\frac{d\left[H_2\right]}{dt}=+\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$$
• 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

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

$N_2\left(g\right)+3H_2\left(g\right)⟶2N{H}_3\left(g\right)$

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

The concentrations of the reactants decrease and the concentrations of the products increase with the progress of the reaction. To equalize the rates with respect to various components, suitable coefficients are used.