Counting atomsby weighing them.

What stoichiometry is

Stoichiometry is the quantitative relationship between the substances in a chemical reaction. A balanced equation tells you how many particles react with how many; the mole turns those particle counts into masses you can put on a balance.

One mole contains exactly 6.02214076 × 10²³ entities. You never count them directly. Instead you use the molar mass M, in g/mol, which links mass m and amount n through n = m / M. Almost every stoichiometry problem is a chain of three steps: mass to moles, moles to moles using the coefficients, and moles back to mass.

Step 1: balance the equation and find molar masses

Take the classic teaching synthesis of aspirin: salicylic acid (C7H6O3) reacts with acetic anhydride (C4H6O3) to give acetylsalicylic acid (C9H8O4) and acetic acid (C2H4O2). The equation is already balanced 1 : 1 → 1 : 1. Check it by counting: 11 C, 12 H and 6 O on each side.

From standard atomic weights the molar masses are 138.12 g/mol for salicylic acid, 102.09 g/mol for acetic anhydride, 180.16 g/mol for aspirin and 60.05 g/mol for acetic acid. The free molecular weight tool gives the same values from a SMILES string.

Step 2: find the limiting reagent

Suppose you use 2.00 g of salicylic acid and 5.00 mL of acetic anhydride (density 1.08 g/mL, so 5.40 g). Convert both to moles: 2.00 / 138.12 = 0.01448 mol of salicylic acid and 5.40 / 102.09 = 0.0529 mol of anhydride.

Divide each amount by its coefficient. Both coefficients are 1, so the smaller number, 0.01448 mol, belongs to salicylic acid: it is the limiting reagent. The anhydride is in excess on purpose, because it is cheap and its excess is easy to destroy with water at the end. A common mistake is to compare masses instead of moles; 2.00 g is less than 5.40 g, but that only matters after conversion.

Step 3: theoretical yield, percent yield and atom economy

The theoretical yield follows from the limiting reagent: 0.01448 mol of salicylic acid can give at most 0.01448 mol of aspirin, which is 0.01448 × 180.16 = 2.61 g.

If you isolate 2.10 g of dry product, the percent yield is 2.10 / 2.61 × 100 = 80.5%. Percent yield says nothing about purity: a wet or contaminated product can even exceed 100%, which is a sign to dry it or check it, not a success.

Atom economy asks a different question: how much of the reactants' mass could end up in the product at all? Here it is 180.16 / (138.12 + 102.09) × 100 = 75.0%. The other quarter leaves as acetic acid, however well the reaction runs. Green chemistry metrics such as the E-factor go further and count solvents and work-up waste too.

Formulas from composition

Stoichiometry also runs backwards, from measured composition to a formula. A compound containing 40.0% C, 6.7% H and 53.3% O by mass gives, per 100 g, 3.33 mol C, 6.65 mol H and 3.33 mol O. Dividing by the smallest value gives a 1 : 2 : 1 ratio, so the empirical formula is CH2O. Only a molar mass measurement tells you whether the molecule is CH2O itself, or a multiple such as C6H12O6.

Solutions and titrations

In solution, amount comes from concentration and volume: n = c × V. To make 250 mL of 0.100 M sodium chloride you need 0.100 × 0.250 = 0.0250 mol, which is 0.0250 × 58.44 = 1.461 g, dissolved and made up to the mark in a volumetric flask. A dilution keeps the amount of solute constant, so C₁V₁ = C₂V₂.

Titrations use the same logic in reverse. If 21.40 mL of 0.1000 M NaOH neutralises 25.00 mL of hydrochloric acid, the acid contained 0.1000 × 0.02140 = 0.002140 mol, and its concentration is 0.002140 / 0.02500 = 0.08560 M. With a 1 : 1 reaction the moles match directly; for sulfuric acid, which needs two hydroxides per molecule, you would halve the acid amount.

A checklist that catches most mistakes

Balance the equation before anything else. Convert every given quantity to moles. Divide by coefficients to find the limiting reagent. Carry units through every line, and keep one or two extra digits until the final answer. Finally, check that the answer is plausible: a yield above 100% or a concentration higher than the stock means something upstream is wrong.