Balances with reactions

With a reaction, the balance on each substance includes what's made and used: out = in + (coefficient × extent), where the extent, ξ (xi), is how many times the reaction "happened" in moles, and coefficients are negative for reactants. For N₂ + 3H₂ → 2NH₃ with extent ξ: N₂ out = N₂ in − ξ, H₂ out = H₂ in − 3ξ, NH₃ out = NH₃ in + 2ξ.

Conversion is the fraction of a reactant fed that reacts. Feed 100 mol/h of N₂ and 300 of H₂, with 25% of the N₂ converted: ξ = 25, so out come 75 N₂, 300 − 75 = 225 H₂ and 50 NH₃. Note the total moles fell from 400 to 350, which is fine: only mass must balance.

The limiting reactant is the one that would run out first if the reaction went all the way; the others are in excess. Percent excess compares what's fed with what the limiting reactant needs: if burning 100 mol of methane needs 200 mol of O₂ and you feed 240, the oxygen is 20% in excess. Plants feed the cheaper reactant in excess to make sure the expensive one reacts.

Often more than one reaction happens: A → B (wanted) and A → C (not). Then yield is how much of the wanted product you got compared with the most you could have; and selectivity compares wanted with unwanted product. Feed 100 mol of A, 80 react, and you get 60 mol of B and 20 of C: conversion 80%, yield of B 60% (of what the feed could give), selectivity 60 ÷ 20 = 3 mol of B per mol of C.

Definitions of yield and selectivity vary between textbooks and companies (per mol fed, per mol reacted, as a ratio or a fraction), so always write down which one you're using.