(b) The alkylation of toluene with acetylene in the presence of sulphuric acid is carried out in a batch reactor. 6000kg of toluene is charged in each batch, together with the required amount of sulphuric acid and the acetylene is fed continuously to the reactor under pressure. Under circumstances of intense agitation, it may be assumed that the liquid is always saturated with acetylene, and that the toluene is consumed in a simple pseudo first-order reaction with a rate constant of 0.0011s1. If the reactor is shut down for a period of 900s ( 15min) between batches, use a graphical method to determine the optimum reaction time for the maximum rate of production of alkylate, and calculate this maximum rate in terms of mass P toluene consumed per unit time