For the reaction $2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \longrightarrow 4…
For the reaction $2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \longrightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})}$ rate and rate constant are $1.02 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ and $3.4 \times 10^{-5} \mathrm{~s}^{-1}$.
What is the conc. of $\mathrm{N}_2 \mathrm{O}_5$ ?
$1.7 \mathrm{~mol} \mathrm{~L}^{-1}$
$3.0 \mathrm{~mol} \mathrm{~L}^{-1}$
$3.4 \mathrm{~mol} \mathrm{~L}^{-1}$
$5.1 \mathrm{~mol} \mathrm{~L}^{-1}$
Solution
$2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})}$
$\because \quad$ It is a first order reaction,
$\begin{array}{ll}
& \text { Rate }=\mathrm{k}\left[\mathrm{~N}_2 \mathrm{O}_5\right] \\
\therefore \quad & 1.02 \times 10^{-4}=3.4 \times 10^{-5}\left[\mathrm{~N}_2 \mathrm{O}_5\right] \\
\therefore & {\left[\mathrm{N}_2 \mathrm{O}_5\right]=\frac{1.02 \times 10^{-4}}{3.4 \times 10^{-5}}=3.0 \mathrm{~mol} \mathrm{~L}^{-1}}
\end{array}$