Question

Which of the following equations is correct regarding rate of disappearance of reactant and appearance of product for

N_2(g) + 3H_2(g) → 2NH_3(g)

Options

• \[3\frac{\mathrm{d}[\mathrm{N}_{2}]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}[\mathrm{N}_{2}]}{\mathrm{dt}}\]

• \[\frac{1}{2}\frac{\mathrm{d}\left[\mathrm{N}_{2}\right]}{\mathrm{dt}}=\frac{1}{3}\frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{dt}}\]

• \[2\frac{\mathrm{d}\left[\mathrm{NH}_{3}\right]}{\mathrm{dt}}=3\frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{dt}}\]

• \[3\frac{\mathrm{d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}}=-2\frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}\]

Answer 1

\[3\frac{\mathrm{d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}}=-2\frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}\]

Explanation:

\[\mathrm{N_{2(g)}+3H_{2(g)}\longrightarrow2NH_{3(g)}}\]

For the above reaction we can write,

\[-\frac{\mathrm{d}\left[\mathrm{N}_{2}\right]}{\mathrm{dt}}=-\frac{1}{3}\frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}\left[\mathrm{NH}_{3}\right]}{\mathrm{dt}}\]

∴ \[3\frac{\mathrm{d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}}=-2\frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}\]