The reaction given below \(2 \mathrm{NH}_{3(\mathrm{~g})} \xrightarrow{\mathrm{Pt}} \mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})}\) has rate of reaction \(2.5 \times 10^{-6} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{sec}^{-1}\) formation of \(\mathrm{H}_{2(\mathrm{~g})}\) ?

\(\text {For the reaction, } 2 \mathrm{NH}_{3(\mathrm{~g})} \xrightarrow{\mathrm{Pt}} \mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \)
\( \text {Rate of reaction }=-\frac{1}{2} \frac{\mathrm{~d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}\)\(=\frac{1 \mathrm{~d}\left[\mathrm{H}_2\right]}{3} \)
\( \therefore 2.5 \times 10^{-6}=\frac{1}{3} \frac{\mathrm{~d}\left[\mathrm{H}_2\right]}{\mathrm{dt}} \)
\( \therefore \frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=3 \times 2.5 \times 10^{-6}=7.5 \times 10^{-6}\)\(\mathrm{~mol} \mathrm{dm}^{-3} \mathrm{sec}^{-1}\)