(3)

For a first order reaction, A $\to$ Products and for concentration of the reactant at two different times,

          $k=\frac{2.303}{t_2-t_1}\log \frac{{\left[A\right]}_1}{{\left[A\right]}_2}$

$\therefore$    $k=\frac{2.303}{t_2-t_1}\log \frac{{\left(\mathrm{rate}\right)}_1}{{\left(\mathrm{rate}\right)}_2}$      $(\because \text{rate}\propto [A\left]\right)$

$k=\frac{2.303}{(20-10)}\log \left(\frac{{\displaystyle 0.04}}{{\displaystyle 0.03}}\right)=0.0287$ ${\text{sec}}^{-1}$

$t_{1/2}=\frac{0.693}{k} =\frac{0.693}{0.0287 {\text{sec}}^{-1}}=24.14$ $\text{sec}$

(4)

Half-life period of a first order reaction is independent of initial concentration,

$t_{1/2}=\frac{0.693}{k}$