Limiting & Excess Reagents

Convert every reactant's given amount to moles, then divide each by its own coefficient in the balanced equation. Whichever reactant gives the smaller result is the limiting reagent — it doesn't have enough moles, relative to what the equation demands, to keep up with the other reactant. The division has a concrete meaning: $n÷\text{coefficient}$ is the number of times (in moles) that reactant could run the equation's "recipe". In the sandwich analogy, 10 slices of bread $÷$ 2 per sandwich allows 5 sandwiches, and 2 slices of cheese $÷$ 1 allows 2, so the cheese is limiting. Whichever ingredient allows fewer batches decides how many batches actually happen.

Two other methods give the same answer, and it is worth knowing them because some questions are set up for one or the other. You can pick one reactant and use the mole ratio to find how much of the other it would need: if more is needed than is available, the second reactant is limiting. Or you can calculate the amount of product each reactant could make on its own; the reactant giving the smaller amount of product is limiting, and that smaller amount is the answer for the product.

Masses are even more misleading than raw moles. Mix $6.0\text{ g}$ of ${\text{H}}_2$ with $40.0\text{ g}$ of ${\text{O}}_2$ for $2{\text{H}}_2+{\text{O}}_2\to 2{\text{H}}_2\text{O}$. Oxygen has almost seven times the mass, so it looks plentiful, but hydrogen molecules are so light that $6.0\text{ g}$ is $2.970\text{ mol}$, enough for $2.970÷2=1.485$ batches, while $40.0\text{ g}$ of oxygen is only $1.250\text{ mol}$, enough for $1.250$ batches. Oxygen, the heavier reactant, is the limiting one, and only $2.500\text{ mol}$ ($45.1\text{ g}$) of water can form. Always convert to moles before comparing anything.

• All yield calculations (mass of product, moles of product) must be based on the limiting reagent — never the excess reagent.
• Excess remaining = starting moles of the excess reagent $-$ moles of it actually consumed (found using the mole ratio with the limiting reagent).

A before–change–after table keeps the bookkeeping straight. The "change" row comes entirely from the limiting reagent through the mole ratios; reactants decrease and products increase. At the end, the limiting reagent is at exactly zero, the excess reagent has something left, and the product has what formed. Here it is for $4.0\text{ mol}$ of ${\text{N}}_2$ with $9.0\text{ mol}$ of ${\text{H}}_2$ (hydrogen limiting, since $9.0÷3=3.0$ is less than $4.0÷1=4.0$):

Reactants mixed in exactly the equation's ratio are called stoichiometric amounts, and then nothing is left over. In practice chemists often add one reactant in deliberate excess. If one reactant is expensive or hazardous, an excess of the cheap one makes sure every bit of the valuable one reacts. Engines and furnaces burn fuel with excess air so the fuel is the limiting reagent and burns completely to ${\text{CO}}_2$ rather than toxic CO. In a precipitation lab, an excess of the precipitating solution guarantees that all of the ion being measured leaves the solution. In each case the choice of limiting reagent is a design decision.