A batch reactor converts component A into B, which ill in

Chapter 22, Problem 22.10

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A batch reactor converts component A into B, which ill in turn decomposes into C: k1 kz A~ B ~c where k1 = klOe-EtiRT and k 2 = k 20e-EziRT. The concentrations of A and B are denoted by x1 and x2, respectively. The reactor model is dx1 I dt =- k1QX1e-Et RT dxz I - = k10x1e-Et RT - kzoxze-EziRT dt Thus, the ultimate values of x1 and x2 depend on the reactor temperature as a function of time. For k10 = 1.335 X 1010 min-I, E1 = 75,000 Jig mol, R = 8.31 J/(gmol K) k 20 = 1.149 X 1017 min-1 E2 = 125,000 J/gmol x 10 = 0.7 moVL, xzo = 0 Find the constant temperature that maximizes the amount of B, for 0 ~ t ~ 8 min. Next allow the temperature to change as a cubic function of time Find the values of a0, a1, a2, a3 that maximize x 2 by integrating the model and using a suitable optimization method.

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