Journal of Physical Chemistry, Vol.100, No.21, 8843-8853, 1996
Finite-Time Optimization of Chemical-Reactions - Na-Reversible-Arrow-MB
We investigate the optimization of chemical reactions of the type nA reversible arrow mB in a closed container. The goal is to produce a maximal amount of A or B within a given finite time. The controls are taken to be volume and temperature, restricted to allowed regions in (V,beta)-space with beta = 1/kT. We show that the optimal path is achieved by choosing V and beta such that, for the current amounts of reaction products N-A and N-B, the reaction rate f(N-B,N-A,V,beta) = dN(B)/dt is at all times maximal or minimal. For different combinations of endo/exothermicity exothermicity and activation energies switches between extremal values of V and/or beta may be included in the optimal path. The resulting paths are described qualitatively for general values of n and m, while the reactions 2NH(3) reversible arrow N-2 + 3H(2), N2O4 reversible arrow 2NO(2), and 2NO(2) reversible arrow N-2 + 2O(2) are used as concrete examples. that the optimal and equilibrium paths differ by a constant Delta beta; a possible connection with a constant thermodynamic speed path is discussed.