• # question_answer Consider the following case of completing 1st order reactions.             After the start of the reaction at t = 0 with only A, the [C] is equal to the [D] at all times. The time in which all three concentrations will be equal is given by - A) $t=\frac{1}{2{{k}_{1}}}\ell n3$                        B) $t=\frac{1}{2{{k}_{2}}}\ell n\,3$ C) $t=\frac{1}{3{{k}_{1}}}\ell n2$                        D) $t=\frac{1}{3{{k}_{1}}}\ell n2$

${{k}_{1}}={{k}_{2}}\Rightarrow \frac{2}{3}rd$ of A has r exacted for $\left[ A \right]=\left[ C \right]=\left[ D \right]$ $\therefore$      ${{k}_{1}}+{{k}_{2}}=\frac{1}{t}\text{ }\ln \text{ }\frac{{{\left[ A \right]}_{0}}}{\frac{1}{3}{{\left[ A \right]}_{0}}}$ $\Rightarrow$   $t=\frac{1}{{{k}_{1}}+{{k}_{2}}}\ln \text{ }3=\frac{1}{2{{k}_{1}}}\ln \text{ }3=\frac{1}{2{{k}_{2}}}\ln \text{ }3$