Chemistry - Chemical Kinetics Question with Solution | TestHub

The unit of rate constant $k$ is ${\text{s}}^{-1}$, indicating that the reaction is of first order.

For a first-order reaction, the integrated rate equation is:

$k=\frac{2.303}{t}\log \frac{[A{]}_0}{[A{]}_t}$

Substituting the given values $k=2\times 10^{-2}{\text{s}}^{-1}$, $t=100\text{s}$, and $[A{]}_0=1.0{\text{mol dm}}^{-3}$:

$2\times 10^{-2}=\frac{2.303}{100}\log \frac{1.0}{[A{]}_t}$

$2\times 10^{-2}\times 100=2.303\log \frac{1}{[A{]}_t}$

$2=2.303\log \frac{1}{[A{]}_t}$

$\log \frac{1}{[A{]}_t}=\frac{2}{2.303}=0.868$

Answer: $0.868$