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

For the reaction $\mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NH}_{3(\mathrm{~g})}$ rate of disappearance of $\mathrm{N}_{2(\mathrm{~g})}$ is $2.22 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3}$. What is the rate of appearance of $\mathrm{NH}_{3(\mathrm{~g})}$ ?
  1. $4.44 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3}$
  2. $1.11 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3}$
  3. $2.22 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3}$
  4. $3.33 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3}$

Solution

$\begin{aligned} & -\frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}=-\frac{1}{5} \frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=+\frac{1}{5} \frac{\mathrm{d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}} \\ & 2.22 \times 10^{-3}=\frac{1}{2} \frac{\mathrm{d}\left(\mathrm{NH}_3\right)}{\mathrm{dt}} \\ & \frac{\mathrm{d}\left(\mathrm{NH}_3\right)}{\mathrm{dt}}=4.44 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3}\end{aligned}$

Asked in: MHT CET 2022 (10 Aug Shift 2)

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