The rate of a chemical reaction is expressed in terms of the rate of change in concentration of any reactant or product, divided by its stoichiometric coefficient in the balanced chemical equation. For reactants, the rate is negative (disappearance), and for products, it is positive (appearance).

For the general reaction $aA + bB \rightarrow cC + dD$, the rate is: $\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = +\frac{1}{c}\frac{d[C]}{dt} = +\frac{1}{d}\frac{d[D]}{dt}$

Applying this to the given reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$: $\text{Rate} = -\frac{d[N_2]}{dt} = -\frac{1}{3}\frac{d[H_2]}{dt} = +\frac{1}{2}\frac{d[NH_3]}{dt}$

Comparing the terms for $N_2$ and $NH_3$: $-\frac{d[N_2]}{dt} = +\frac{1}{2}\frac{d[NH_3]}{dt}$

This relationship indicates that the rate of consumption of nitrogen is half the rate of formation of ammonia .