For the reaction $\mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \rightarrow 2…

For the reaction $\mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NH}_{3(\mathrm{~g})}$, what is the relation between $\frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}$ and $\frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}$ ?
  1. $3 \frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}$
  2. $\frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=3 \frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}$
  3. $3 \frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=2 \frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}$
  4. $\frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}$

Solution

$\begin{aligned} & \mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \longrightarrow 2 \mathrm{NH}_3(\mathrm{~g}) \\ & \frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{H}_2\right]}{3 \mathrm{dt}} \\ & \frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=3 \cdot \frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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