Why is the optimal space time for the production of the intermediate product B in a consecutive reaction shorter in not-back-mixed reactors in comparison to the back-mixed CSTRs ?

Let's try a very short qualitative explanation: The reaction kinetic demands an exact reaction time tau_opt corresponding to B_max. In a not-back-mixed reactor the reaction time is not shorter and not longer than the residence time, and therefore it is optimal when residence time = tau_opt.

In a CSTR we have a residence time distribution, i.e. there are 'portions' of the reaction mass that 'reside' longer and portions that reside shorter than tau_opt in the reaction vessel. Therefore we don't operate for the whole reaction mixture at exact the optimum reaction time.

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