The rate of first order reaction is 0 . 04mol L ^ - 1 s ^ - 1 at 10...

 Rater = k\left[A\right]0 . 04 = k{\left[{A}_{0}\right]}_{10}0 . 03 = k{\left[{A}_{}\right]}_{20}$</p><p>$⇒ \dfrac{{\left[{A}_{0}\right]}_{10}}{{\left[A\right]}_{20}} = \dfrac{0 . 04}{0 . 03} = \dfrac{4}{3}$</p><p>Fromt = \dfrac{2 . 303}{k}log\dfrac{{\left[A\right]}_{10}}{{\left[A\right]}_{20}}10 = \dfrac{2 . 303}{k}log\dfrac{4}{3}10 = \dfrac{2 . 303}{k} ( 0 . 6020 - 0 . 4771 ) k = \dfrac{2 . 303}{10} \times 0 . 1249 = 2 . 876 \times {10}^{- 2}\min^{- 1}$

${t}_{1/2} = \dfrac{0 . 693}{k} = \dfrac{0 . 693}{2 . 876 \times {10}^{- 2}} = 0 . 24 \times {10}^{2}min = 24min .$