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Q. In a catalytic experiment involving the Haber process,
$N_{2(g)}+3 H_{2(g)} \rightarrow 2 N H_{3(g)}$
the rate of reaction was measured as
Rate $=\left[ NH _{3}\right]=2.0 \times 10^{-4} Ms ^{-1}$ .If there were no side reactions what was the rate of reaction expressed in terms of $N_{2}$ ?

J & K CETJ & K CET 2010Chemical Kinetics

Solution:

Given, rate $=2.0 \times 10^{-4} Ms ^{-1}$
For the reaction, $N _{2}(g)+3 H _{2}(g) \rightarrow 2 NH _{3}(g)$
$-\frac{d\left[N_{2}\right]}{d t}=-\frac{d\left[H_{2}\right]}{3 d t}=+\frac{d\left[ NH _{3}\right]}{2 d t}$
$\frac{-d\left[N_{2}\right]}{d t}=\frac{d\left[N H_{3}\right]}{2 d t}$
$=\frac{2.0 \times 10^{-4}}{2}=1.0 \times 10^{-4} Ms ^{-1}$