(a) A reaction is second order in A and first order in $\mathit{B}$.
(i) Write the differential rate equation.
(ii) How is the rate affected on increasing the concentration of A three times?
(iii) How is the rate affected when the concentrations of both A and B are doubled?
(b) A first order reaction takes $40$ minutes for $30\%$ decomposition. Calculate ${\mathit{t}}_{1∕2}$ this reaction.
$($ Given $\log 1.428=0.1548)$
OR
(a) For a first order reaction, show that time required for $99\%$ completion is twice the time required for the completion of $90\%$ of reaction.
(b) Rate constant ' $\mathit{k}$ ' of a reaction varies with temperature ' $\mathit{T}$ ' according to the equation:
$\log \mathit{k}=\log \mathit{A}-\frac{{\mathit{E}}_{\mathit{a}}}{2.303\mathit{R}}\left(\frac{1}{\mathit{T}}\right)$
Where ${\mathit{E}}_{\mathit{a}}$ is the activation energy. When a graph is plotted for $\log \mathit{k}$ Vs. $\frac{1}{\mathit{T}}$, a straight line with a slope of $-4250\mathit{K}$ is obtained. Calculate ' ${\mathit{E}}_{\mathit{a}}$ ' for the reaction. $\left(\mathit{R}=8.314{\mathit{J}\mathit{K}}^{-1}{\mathit{m}\mathit{o}\mathit{l}}^{-1}\right)$