Q82 / 200 · NEET 2009 (Screening) · Chemistry

For the reaction, $\mathrm{N}_2+3 \mathrm{H}_2 \longrightarrow 2 \mathrm{NH}_3$, if $\frac{\mathrm{d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}}=2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$, the value of $\frac{-\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}$ would be

  • Correct answer
    A
    $3 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
  • B
    $4 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
  • C
    $6 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
  • D
    $1 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$

Solution

Key Idea Rate of disappearance of reactant $=-\frac{1}{\text { stoichiometry }} \times \frac{\text { change in conc of reactant }}{\text { time taken }}$ coefficient of the reactant Rate of appearance of product change in conc $=\frac{1}{\text { stoichiometry coefficient }} \times \frac{\text { of product }}{\text { time taken }}$ For the reaction, $$ \begin{aligned} & \mathrm{N}_2+3 \mathrm{H}_2 \longrightarrow 2 \mathrm{NH}_3 \\ & \begin{aligned} & \text { Rate }=-\frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}=-\frac{1}{3} \frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}} \\ & \text { or } \quad-\frac{1}{3} \frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}} \\ &-\frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=\frac{3}{2} \times 2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} \\ &=3 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} \end{aligned} \end{aligned} $$

Hence, the correct answer is option: 'A'.

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