Chemistry › Chemical Kinetics › Rate of reaction
For the reaction, $\mathrm{N}_2+3 \mathrm{H}_2 \longrightarrow 2 \mathrm{NH}_3$, if…
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
$3 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ $4 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ $6 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ $1 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ 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,
$\begin{aligned}
& \mathrm{N}_2+3 \mathrm{H}_2 \longrightarrow 2 \mathrm{NH}_3 \\
& \begin{aligned}
& \text { Rate }=-\frac{\mathrm{d}\left[\mathrm{N}_2\right]}{\mathrm{dt}}=-\frac{1}{3} \frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}} \\
& \text { or } \quad-\frac{1}{3} \frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NH}_3\right]}{\mathrm{dt}} \\
&-\frac{\mathrm{d}\left[\mathrm{H}_2\right]}{\mathrm{dt}}=\frac{3}{2} \times 2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} \\
&=3 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}
\end{aligned}
\end{aligned}$
Asked in: NEET 2009 (Screening)
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