Limiting Reactant: Sandwiches, Then Hydrogen and Oxygen

Medium

Problem

Sandwich analogy: one sandwich needs 2 slices of bread and 1 slice of cheese (2 bread + 1 cheese -> 1 sandwich). You have 20 slices of bread and 8 slices of cheese. How many sandwiches can you make, and what limits you? Then do the chemistry: 10.0 g of H2 reacts with 80.0 g of O2 (2H2 + O2 -> 2H2O). Which reactant is limiting, and what mass of water forms?

Given

Sandwich recipe: 2 bread slices + 1 cheese slice -> 1 sandwich
Bread available: 20 slices; cheese available: 8 slices
Reaction: 2H2 + O2 -> 2H2O
Reactants: 10.0 g H2 and 80.0 g O2

Find

Which reactant limits each reaction and how much product can form.

Principle

A limiting reactant is the ingredient that runs out first according to the balanced equation's ratio, and it alone determines how much product can form. Finding it is a two-part job: convert each reactant to moles, then divide each by its coefficient and compare — the smallest result limits. Excess reactants are partly consumed but left over.

Formula

n_{\mathrm{product}} = \min_i\left(\frac{n_i}{\nu_i}\right) \times \nu_{\mathrm{product}}

product moles limited by min(reactant moles / reactant coefficient)

Solution

Sandwiches from bread: 20 slices / 2 = 10 possible sandwiches. Sandwiches from cheese: 8 slices / 1 = 8 possible sandwiches. Cheese gives the smaller number, so cheese limits and 8 sandwiches form (4 bread slices left over).
Convert H2 to moles: M(H2) = 2 x 1.008 = 2.016 g/mol. n(H2) = 10.0 g / 2.016 g/mol = 4.960 mol.
Convert O2 to moles: M(O2) = 2 x 15.999 = 31.998 g/mol. n(O2) = 80.0 g / 31.998 g/mol = 2.500 mol.
Divide by coefficients. For H2: 4.960 / 2 = 2.480. For O2: 2.500 / 1 = 2.500. The smaller value (2.480) belongs to H2, so hydrogen is limiting — even though oxygen has fewer moles, the recipe demands less of it.
Oxygen needed for all the H2: 4.960 mol H2 x (1 mol O2 / 2 mol H2) = 2.480 mol O2, which is less than the 2.500 mol available. Confirms H2 limits.
Water formed: 4.960 mol H2 x (2 mol H2O / 2 mol H2) = 4.960 mol H2O. Mass = 4.960 mol x 18.015 g/mol = 89.4 g H2O.

Cheese limits the sandwiches: 8 sandwiches. H2 limits the water: 89.4 g of H2O.

Unit check

Moles divided by unitless coefficients stay in moles; comparing the quotients is valid because both represent how many full reaction 'recipes' each reactant can support. Grams re-enter only at the final product step via g/mol, giving a clean gram answer.

What this means physically

The limiting reactant sets the ceiling on everything downstream: no matter how much excess oxygen surrounds it, 10.0 g of hydrogen can only make 89.4 g of water, and the leftover oxygen simply has nothing to react with. In industry, spotting the limiting reagent is how feed ratios and costs are planned.

Common mistake

Students compare masses directly (80.0 g O2 > 10.0 g H2, so O2 must run out first) or compare moles directly (2.50 mol O2 < 4.96 mol H2, so O2 limits). Both skip the equation ratio: a reactant only runs out relative to what the recipe demands.