c
order of reaction \(=1\)

Rate of reaction at \(10\, \mathrm{s}=-0.04 \,\mathrm{mol} \,\mathrm{L}^{-1} \,\mathrm{s}^{-1}\)

Rate of reaction at \(20\, \mathrm{s}=\mathrm{s}=0.03\, \mathrm{mol} \,\mathrm{L}^{-1} \mathrm{s}^{-1}\)

\(\therefore\) Half - life period \(\left(\mathrm{t}_{1 / 2}\right)=?\)

We have the equation for rate \(-\) constant \(k\) in first order reaction

\(\mathrm{k}=\frac{2.303}{\mathrm{t}} \log \frac{\mathrm{A}_{\mathrm{t}}}{\mathrm{A}_{0}}\)

\(=\frac{2.303}{105} \log \frac{0.04}{0.03}\)

\(=\frac{2.303}{105} \times 0.124\)

\(\mathrm{k}=0.028\, \mathrm{s}^{-1}\)

We know that, \(t_{1 / 2}=\frac{0.693}{k}\)

\(=\frac{0.693}{0.028773391}=24.14\, \mathrm{s}=24.1\, \mathrm{s}\)