A catalytic reactor is used to produce formaldehyde from methanol in the reaction CH₃OH — HCHO + H₂ A single-pass conversion of 60.0% is achieved in the reactor. The methanol in the reactor product is separated from the formaldehyde and hydrogen in a multiple unit process. The production rate of formaldehyde is 900.0 kg/h.

(a) Calculate the required feed rate of methanol to the process (k mol/h) if there is no recycle.

(b) Suppose the recovered methanol is recycled to the reactor and the single-pass conversion remains 60%. Without doing any calculations, prove that you have enough information to determine the required fresh feed rate of methanol (k mol/h) and the rates (k mol/h) at which methanol enters and leaves the reactor. Then perform the calculations.

(c) The single-pass conversion in the reactor, X_sp affects the costs of the reactor (C_τ) and the separation process and recycles line (C_s). What effect would you expect an increased X_sp would have on each of these costs for a fixed formaldehyde production rate? What would you expect a plot of (C_r + C_s) versus X, to look like? What does the design specification X_sp = 60% probably represent?