A batch reactor converts component A into B, which in turn decomposes into C: where k 1 = k 10 e -E 1 RT and

A batch reactor converts component A into B, which in turn decomposes into C:

where                                                 k₁ = k₁₀e^-E₁ ^ˆ•RT and k₂ = k₂₀e^-E₂ ^ˆ•RT.

The concentrations of A and B are denoted by x₁ and x₂, respectively. The reactor model is

                                                           dx₁ / dt = k₁₀x₁e^-E₁ ^/RT

                                                           dx₂ / dt = k₁₀x₁e^-E₁ ^/RT - k₂₀x₂e^-E₂ ^/RT

Thus, the ultimate values of x₁ and x₂ depend on the reactor temperature as a function of time. For

                                                            k₁₀ = 1.335 × 10¹⁰ min^-1,     k₂₀ = 1.149 × 10¹⁷ min^-1
                                                            E₁ = 75,000 Jˆ•g mol,            E₂ = 125,000 Jˆ•g mol
                                                            R = 8.31 Jˆ•(g mol K)             x₁₀ = 0.7 molˆ•L, x₂₀ = 0
Find the constant temperature that maximizes the amount of B, for 0 ‰¤ t ‰¤ 6 min.

k, k, A B C