Fractional Conversion from Concentration

Conversion is the currency every reactor design equation on this site is quoted in, and it is deliberately a fraction rather than an amount. Writing the performance of a vessel as $X$ instead of "kilograms per hour of product" makes it scale-free: a bench flask and a forty-cubic-metre reactor at the same conditions reach the same conversion, and the whole apparatus of Damköhler numbers and design equations follows from that.

The definition is a subtraction and a division — what went in less what came out, over what went in — but it hides three decisions. The first is WHICH species. Conversion is always quoted on the limiting reactant, the one that runs out first. A reactant fed at three times stoichiometric requirement can only ever reach 33% conversion no matter how perfect the reactor is, and quoting that number is a way of hiding a good result inside a bad-looking one, or the reverse.

The second is the BASIS. The concentration form used here assumes the volume does not change between inlet and outlet. That is a fair assumption for nearly all liquid-phase work, where the density barely moves. It is not fair for a gas-phase reaction that changes the number of moles: a reaction going from two moles to one contracts as it proceeds, so the outlet concentration reads high for reasons that have nothing to do with how much reacted. Gas-phase work uses the molar flow form, $X = (F_{A0} - F_A)/F_{A0}$, which is immune to it.

The third is what conversion does NOT tell you. It counts the reactant that disappeared and is entirely silent about where it went. A reactor at 99% conversion whose feed left as tar rather than product is a bad reactor with an excellent conversion. That is what yield and selectivity are for, and the three numbers should always be quoted together — conversion alone is the easiest reactor statistic to make look good.