Question

For the reaction$\underset{\mathrm{dinitrogen}\mathrm{pentaoxide}}{\underbrace{2{\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)}}\to \underset{\mathrm{Nirogen}\mathrm{dioxide}}{\underbrace{4{\mathrm{NO}}_2\left(\mathrm{g}\right)}}+\underset{\mathrm{Oxygen}}{\underbrace{{\mathrm{O}}_2\left(\mathrm{g}\right)}}$, if the initial concentration of ${\mathrm{N}}_2{\mathrm{O}}_5$is $7.2{\mathrm{mol}}^{-1}$ and after $20$minutes, ${\mathrm{NO}}_2$ becomes $2.4{\mathrm{mol}}^{-1}$, then what will be the rate of decomposition of ${\mathrm{N}}_2{\mathrm{O}}_5$ in ${\mathrm{mol}}^{-1}{\min }^{-1}$$?$

Answer 1

Step 1: Given data

The initial concentration of ${\mathrm{N}}_2{\mathrm{O}}_5$ is $7.2{\mathrm{mol}}^{-1}$

Concentration after $20$minutes is $2.4{\mathrm{mol}}^{-1}$

Step 2: Applying the formula

From first-order reaction

$\mathrm{Kt}=\ln \frac{{\mathrm{A}}_{°}}{\mathrm{At}}$ where K is rate constant, ${\mathrm{A}}_{°}$ is initial concentration, $\mathrm{At}$ is the concentration after some time.

Now, substituting the values we get

$$\begin{gathered} \mathrm{K}\times 20=2.303\log \times \frac{7.2}{2.4} \\ \mathrm{K}=0.06\mathrm{mol}{\mathrm{l}}^{-1}{\min }^{-1} \end{gathered}$$

Therefore, the Rate of decomposition of ${\mathrm{N}}_2{\mathrm{O}}_5$ is $0.06\mathrm{mol}{\mathrm{l}}^{-1}{\min }^{-1}$.