Methyl tert-butyl ether (MTBE) is industrially produced by the acid-catalyzed reaction of isobutene (C4H8) with methanol (CH3OH):
C4H8(g) + CH3OH(l) → C5H12O(l)
Under pilot-plant conditions (40 °C, [C4H8] = 0.60 mol L−1, [CH3OH] = 1.50 mol L−1) the rate of MTBE formation is 0.015 mol L−1 s−1. For scale-up, engineers require a rate of at least 0.050 mol L−1 s−1 while observing the following constraints:
• The reaction temperature must not exceed 60 °C to avoid excessive polymerization side reactions.
• The acid resin catalyst loading cannot be increased beyond its current level.
• The feed composition must satisfy 0.50 mol L−1 ≤ [C4H8] ≤ 1.20 mol L−1 and 1.00 mol L−1 ≤ [CH3OH] ≤ 3.00 mol L−1.
Kinetic studies show that the rate law is
rate = k[C4H8][CH3OH]
and that the uncatalyzed Arrhenius activation energy remains 55 kJ mol−1 over the temperature range 40 °C – 60 °C.
(a) Calculate the factor by which the rate must be increased relative to the pilot-plant rate to meet the production specification.
(b) Assuming the feed concentrations remain unchanged, determine the rate at 60 °C. You may treat k as obeying the Arrhenius equation with the given activation energy.
(c) If the target rate is still not achieved at 60 °C, identify permissible changes to [C4H8] and/or [CH3OH] that, together with operation at 60 °C, will reach or exceed the required rate while satisfying all composition constraints. Support your answer with quantitative calculations.
(d) Provide a concise justification, grounded in kinetic principles and the stated safety constraints, for why the set of conditions you selected in part (c) is suitable for industrial operation.