A chemist carried out an auto-catalytic reaction in a batch reactor and collected data on reaction rates at different concentrations of the reactant during the reaction. The following figure shows the graph of 1/rA versus CA obtained by plotting these data, where rA and CA are the rate of reaction and concentration of the reactant, A, respectively. (a) Explain in detail, without referring to any equations or doing any calculations, why the rate of reaction varied with concentration in the way depicted in the figure and why a minimum point exists in the graph. (10 marks) (b) Derive a general expression for the reaction time, tmax, at which the rate of an autocatalytic reaction is maximum. Define all symbols used in your derivation clearly. (15 marks)