For the reaction, N_2+3 H_2 2 NH_3 , if d[NH_3] dt =2 × 10^ -4 ~mol...

Key Idea Rate of disappearance of reactant $=-\frac{1}{\text{ stoichiometry }} \times \frac{\text{ change in conc of reactant }}{\text{ time taken }}$ coefficient of the reactant Rate of appearance of product change in conc $=\frac{1}{\text{ stoichiometry coefficient }} \times \frac{\text{ of product }}{\text{ time taken }}$ For the reaction, \begin{aligned} & \mathrm{N}_2+3 \mathrm{H}_2 \longrightarrow 2 \mathrm{NH}_3 \\ & \begin{aligned} & \text{ Rate }=-\frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}=-\frac{1}{3} \frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}} \\ & \text{ or } \quad-\frac{1}{3} \frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}} \\ &-\frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=\frac{3}{2} \times 2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} \\ &=3 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} \end{aligned}\end{aligned}