Why one reactant runs out first
Reactions use reactants in fixed proportions given by the balanced equation. In practice, the amounts mixed rarely match those proportions exactly. The reactant that is used up first is the limiting reactant: once it is gone, the reaction stops, and the other reactant is left in excess. The limiting reactant sets the maximum amount of product, the theoretical yield.
The method
For a reaction aA + bB → cC:
- Convert each mass to moles: n = mass ÷ molar mass.
- Divide each by its coefficient: n_A ÷ a and n_B ÷ b.
- The smaller value is the extent of reaction ξ, and that reactant is limiting.
- Moles of product = c × ξ; theoretical yield = c × ξ × molar mass of C.
- Excess left = (n − coefficient × ξ) × molar mass for the other reactant.
Worked example
Burn 10 g of hydrogen in 64 g of oxygen: 2 H₂ + O₂ → 2 H₂O.
- n(H₂) = 10 ÷ 2.016 = 4.960 mol; n(O₂) = 64 ÷ 31.998 = 2.000 mol.
- 4.960 ÷ 2 = 2.480 and 2.000 ÷ 1 = 2.000.
- Oxygen gives the smaller value: O₂ is limiting, ξ = 2.000 mol.
- Water formed = 2 × 2.000 = 4.000 mol, or 4.000 × 18.015 = 72.06 g.
- Hydrogen used = 4.000 mol; left over = 0.960 mol, or 1.94 g.
Mass is conserved: 10 + 64 = 74 g of reactants give 72.06 g of water plus 1.94 g of unreacted hydrogen.
A common mistake
Comparing raw masses or raw moles without dividing by the coefficients gives the wrong answer. In the example, there are fewer moles of O₂ than of H₂, but that alone proves nothing: the equation needs twice as much H₂ as O₂, which is why the division matters.
Excess on purpose
Chemists often use one reactant in excess deliberately:
- to make sure an expensive or toxic reactant is fully consumed;
- to push an equilibrium toward the products, as in esterification with excess alcohol;
- because a gas such as air or oxygen is cheap and easy to supply.
From theoretical to actual yield
Real reactions rarely give 100%: side reactions, incomplete conversion and losses during purification reduce the mass recovered. Percent yield = actual mass ÷ theoretical yield × 100, which our percent yield calculator computes once you have the theoretical value from here.
Several reactants
With three or more reactants, the method is the same: divide each amount by its coefficient and take the smallest. Run the calculator on pairs, or repeat the division by hand for each reactant.