Stoichiometry is the quantitative bookkeeping of a chemical reaction: given a balanced equation, it tells you how much product forms from a given amount of reactant, and which reactant runs out first. Everything flows from the mole ratio encoded in the balanced coefficients.
1 — Balancing and the mole ratio. A balanced equation conserves atoms, so its coefficients give the ratio of moles in which species react and form. In N₂ + 3 H₂ → 2 NH₃, 1 mole of N₂ reacts with 3 moles of H₂ to give 2 moles of NH₃. This ratio — read straight off the coefficients — is the engine of every calculation here. (Coefficients are mole/volume ratios, not mass ratios.)
2 — The master plan (mass–mass). To go from a mass of one species to a mass of another:
mass given → moles (÷ M) → ×(coefficient ratio) → moles wanted → mass (× M).
Convert to moles, apply the balanced-equation ratio, convert back to mass. Skipping the mole step and using a mass ratio directly is the single most common mistake.
3 — Mass–volume and volume–volume (gases). For a gaseous product, convert moles to volume with the molar volume (22.4 L per mole at STP). For two gases at the same temperature and pressure, volumes are in the same ratio as moles (Avogadro's law), so you can use the volume ratio directly without converting to moles — e.g. 10 L of N₂ needs 30 L of H₂ and gives 20 L of NH₃.
4 — Limiting reagent. When the amounts of two reactants are both given, one usually runs out first and caps the amount of product — that is the limiting reagent; the other is in excess. To find it: convert each reactant to moles, divide each by its own coefficient, and the smallest result is the limiting reagent. All product amounts must be computed from the limiting reagent, never from the excess one. This is the highest-value idea in the concept.
5 — Excess left over. The excess reactant is only partly consumed. Moles of excess used = moles of limiting reagent × (excess coefficient / limiting coefficient); excess left = initial excess − used. Convert back to mass if asked. A frequent slip is reporting the amount reacted when the question wants the amount remaining.
6 — Percentage yield. Real reactions rarely give the full theoretical amount. The theoretical yield is what stoichiometry predicts (from the limiting reagent); the actual yield is what is obtained.
percent yield = (actual yield / theoretical yield) × 100.
Rearrange to get actual yield from a stated percent, or to back-out the theoretical yield. Yield is computed on the same species (mass-to-mass or mole-to-mole), not across different products. …