Chemistry › Chemical Kinetics › Integrated rate laws
For the reaction \(\mathrm{N}_2 \mathrm{O}_5(\mathrm{g}) \rightarrow 2 \mathrm{NO}_2(\mathrm{g})+(1 / 2)…
For the reaction \(\mathrm{N}_2 \mathrm{O}_5(\mathrm{g}) \rightarrow 2 \mathrm{NO}_2(\mathrm{g})+(1 / 2) \mathrm{O}_2(\mathrm{g})\) the value of rate of disappearance of \(\mathrm{N}_2 \mathrm{O}_5\) is given as \(6.25 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\). The rate of formation of \(\mathrm{NO}_2\) and \(\mathrm{O}_2\) is given respectively as
$6.25 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ and $6.25 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ $1.25 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ and $3.125 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ $6.25 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ and $3.125 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ $1.25 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ and $6.25 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ Solution
Rate of disappearance of reactant $=$ rate of appearance of product
$\begin{aligned}
& \text { or }-\frac{1}{\text { stoichiometric coefficient }} \frac{\mathrm{d} \text { [reactant }]}{\mathrm{dt}} \\
& \text { of reactant } \\
& =+\frac{1}{\text { stoichiometric }} \frac{\mathrm{d} \text { [product }]}{\mathrm{dt}} \\
& \text { coefficient of product } \\
&
\end{aligned}$
For the reaction,
$\begin{aligned} & \mathrm{N}_2 \mathrm{O}_5(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \\ & \frac{-\mathrm{d}\left[\mathrm{N}_2 \mathrm{O}_5\right]}{\mathrm{dt}}=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}} \\ & =+\frac{2 \mathrm{~d}\left[\mathrm{O}_2\right]}{\mathrm{dt}} \\ & \therefore \quad \frac{\mathrm{d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}}=-2 \frac{\mathrm{d}\left[\mathrm{N}_2 \mathrm{O}_5\right]}{\mathrm{dt}} \\ & =2 \times 6.25 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} \\ & =12.5 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} \\ & =1.25 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} \\ & \end{aligned}$
$\begin{aligned}
\frac{\mathrm{d}\left[\mathrm{O}_2\right]}{\mathrm{dt}} & =-\frac{\mathrm{d}\left[\mathrm{N}_2 \mathrm{O}_5\right]}{\mathrm{dt}} \times \frac{1}{2} \\
& =\frac{6.25 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}}{2} \\
& =3.125 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}
\end{aligned}$
Asked in: NEET 2010 (Screening)
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