Chemistry - Chemical Kinetics Question with Solution | TestHub

For the given reaction:

$2{\mathrm{NO}}_{(\mathrm{g})}+2{\mathrm{H}}_{2(\mathrm{g})}\to {\mathrm{N}}_{2(\mathrm{g})}+2{\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{g})}$

The rate of reaction is expressed in terms of the rate of consumption of reactants and the rate of formation of products as:

$\text{Rate}=-\frac{1}{2}\frac{\mathrm{d}[\mathrm{NO}]}{\mathrm{dt}}=-\frac{1}{2}\frac{\mathrm{d}[{\mathrm{H}}_2]}{\mathrm{dt}}=\frac{\mathrm{d}[{\mathrm{N}}_2]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}[{\mathrm{H}}_2\mathrm{O}]}{\mathrm{dt}}$

Equating the rate of formation of ${\mathrm{N}}_2$ and the rate of consumption of ${\mathrm{H}}_2$, we get:

$\frac{\mathrm{d}[{\mathrm{N}}_2]}{\mathrm{dt}}=-\frac{1}{2}\frac{\mathrm{d}[{\mathrm{H}}_2]}{\mathrm{dt}}$

Answer: $\frac{\mathrm{d}\left[{\mathrm{N}}_2\right]}{\mathrm{dt}}=-\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{H}}_2\right]}{\mathrm{dt}}$