Instantaneous Selectivity

Conversion asks how much of the feed reacted. Selectivity asks whether it reacted into the right thing. When a desired and an undesired reaction compete for the same reactant, the instantaneous selectivity $S_{D/U} = r_D/r_U$ is the ratio of their rates at the conditions inside the vessel at that moment — and the striking thing is how much of reactor design falls out of comparing their ORDERS.

Write both as power laws and the ratio becomes $S = (k_D/k_U) C_A^{\,n_D - n_U}$. The exponent is the difference of the two orders, and its sign is a design instruction. If the desired reaction has the HIGHER order, selectivity improves with concentration: keep the reactant concentrated, which means a tube, or a batch reactor charged all at once, and a high feed concentration with no dilution. If the desired reaction has the LOWER order, selectivity improves as concentration falls: a stirred tank, whose entire volume sits at the low outlet concentration, is now the right vessel, and a semi-batch reactor dripping the reactant into a large volume is better still.

That is a genuinely counter-intuitive result and it is worth stating plainly: the reactor that gives the WORST conversion for a given volume can be the one that gives the best selectivity, and on a plant where separation is the expensive step, selectivity usually wins the argument. Temperature is the other lever, and it works through the activation energies rather than the orders — raising temperature always favours whichever reaction has the larger $E_a$, so if the by-product route is the more activated one, running cooler and larger is the correct trade.

The word INSTANTANEOUS carries a warning. This is a snapshot at one concentration, and in any real reactor the concentration falls as conversion proceeds — down the length of a tube, or through the course of a batch — so the selectivity changes as it goes. What ends up in the product drum is the OVERALL selectivity, the ratio of the total moles of each product, which is an average of the instantaneous value weighted over the whole reactor. Those two numbers can differ substantially, and a process quoted on an inlet selectivity is quoted on its best moment rather than its result.