Question

For a certain first order reaction $32\%$ of the reactant is left after $570\mathrm{s}.$ The rate constant of this reaction is _______$\times {10}^{-3}{\mathrm{s}}^{-1}.$

(Round off the nearest integer).

[Given : ${\log }_{10}2=0.301,\ln 10=2.303]$

Answer 1

Answer: $2\times {10}^{-3}{\sec }^{-1}$

For $1^{\mathrm{st}}$ order reaction,

$$\begin{gathered} \mathrm{K}=\frac{2.303}{\mathrm{t}}.\log \frac{\left[{\mathrm{A}}_{\circ }\right]}{\left[{\mathrm{A}}_t\right]} \\ \mathrm{t}=570\sec \\ {\mathrm{A}}_{\circ }=100 \\ {\mathrm{A}}_t=32 \\ =\frac{2.303}{570\sec }.\log \left(\frac{100}{32}\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{999}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}{\mathbf{sec}}^{\mathbf{-}\mathbf{1}}\mathbf{\approx }\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}{\mathbf{sec}}^{\mathbf{-}\mathbf{1}} \end{gathered}$$

For a certain first order reaction $32\%$ of the reactant is left after $570\mathrm{s}.$ The rate constant of this reaction is 2$\times {10}^{-3}{\mathrm{s}}^{-1}.$