Identify the limiting reactant, calculate the theoretical yield, and find the percent yield of a reaction (MA STE HS-PS1-7(MA), quantitative reasoning in reactions).

What this topic is asking

Standard HS-PS1-7(MA) expects quantitative reasoning about real reactions, and real reactions rarely use exactly matching amounts of each reactant. This page handles two practical questions: when two reactants are mixed, which one runs out first (the limiting reactant), and how the amount you actually make compares with the amount the equation predicts (the percent yield).

The limiting reactant

A kitchen analogy makes the idea concrete: if a recipe needs 2 slices of bread and 1 slice of cheese per sandwich, then 10 slices of bread and 3 of cheese make only 3 sandwiches. The cheese runs out first, so cheese is the limiting "reactant" and 4 slices of bread are left over. In chemistry, the reactant that makes the least product is limiting, and all yield calculations must be based on it.

Finding the limiting reactant

The reliable method works in moles:

1. Convert each reactant's given amount to moles (divide mass by molar mass).
2. Use the mole ratio to find how much product each reactant could make on its own.
3. The reactant that makes the smaller amount of product is the limiting reactant; the other is in excess.

Theoretical, actual, and percent yield

The actual yield is almost always less than the theoretical because product is lost in transfers and filtration, the reaction may not go to completion, side reactions consume reactants, or the reactants are impure. A percent yield near 100% means an efficient, clean reaction; a low percent yield signals losses or competing reactions.

Percent yield matters far beyond the classroom. In industry, a chemical process that wastes a fifth of its raw material wastes money and energy, so chemical engineers work hard to push the yield up, by removing a product as it forms, recycling unreacted material, or using a catalyst. Comparing the percent yields of two routes to the same product is a standard way to judge which is more efficient.

How much excess is left over

Once you know the limiting reactant, you can also work out how much of the excess reactant remains. Use the mole ratio to find how much of the excess was actually consumed by the limiting reactant, then subtract that from the amount you started with. For example, if 4 mol of hydrogen reacts with 3 mol of oxygen in $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$, the limiting hydrogen uses only 2 mol of oxygen (the 2 to 1 ratio), so $3 - 2 = 1$ mol of oxygen is left over. Tracking the leftover is a common follow-up to a limiting-reactant question.

Try this

Q1. A reaction makes 18 g of product but the theoretical yield is 24 g. Find the percent yield. [1]

• Cue. $\dfrac{18}{24} \times 100 = 75\%$.

Q2. Why must yield calculations use the limiting reactant rather than the excess one? [1]

• Cue. Once the limiting reactant is used up the reaction stops, so it sets the maximum product; the leftover excess cannot make any more.