How to Do Stoichiometry

The Mole Concept Foundation

Stoichiometry is built on the mole, the chemist's counting unit. One mole equals 6.022 x 10^23 particles (Avogadro's number), which is the number of atoms in exactly 12 grams of carbon-12. The molar mass of any element equals its atomic mass in grams per mole, read directly from the periodic table. For compounds, the molar mass is the sum of the molar masses of all atoms in the formula. Water (H2O) has a molar mass of 2(1.008) + 16.00 = 18.02 g/mol.

The mole bridges the gap between the atomic scale (where reactions occur between individual atoms and molecules) and the laboratory scale (where chemists measure grams and liters). A balanced equation tells us the ratio of moles that react and form: 2H2 + O2 -> 2H2O means 2 moles of hydrogen react with 1 mole of oxygen to produce 2 moles of water. These mole ratios are the conversion factors that make all stoichiometric calculations possible.

Step-by-Step Stoichiometry Method

Mole Ratios in Practice

The mole ratio is the central concept in stoichiometry. It comes directly from the balanced equation coefficients and serves as the conversion factor between any two substances in the reaction. For the equation 2Al + 3Cl2 -> 2AlCl3, the available mole ratios are: 2 mol Al : 3 mol Cl2, 2 mol Al : 2 mol AlCl3, 3 mol Cl2 : 2 mol AlCl3, and the inverses of each. Choose the ratio that converts from the substance you know to the substance you want.

Mole ratios work because chemical equations describe molecular-level events. The equation 2Al + 3Cl2 -> 2AlCl3 means that every 2 atoms of aluminum react with exactly 3 molecules of chlorine to form 2 formula units of aluminum chloride. Scaling this up by Avogadro's number gives the mole-level statement: 2 moles of aluminum react with 3 moles of chlorine. Because the mole is just a counting unit, the ratio holds at any scale.

A common mistake is using mass ratios instead of mole ratios. The balanced equation 2H2 + O2 -> 2H2O does NOT mean that 2 grams of hydrogen react with 1 gram of oxygen. It means 2 moles (4.032 g) of hydrogen react with 1 mole (32.00 g) of oxygen. The mass ratio is 4.032:32.00, or approximately 1:8. This is why the conversion to moles is essential: mole ratios from the equation apply only to moles, never directly to grams.

Solution Stoichiometry

For reactions in solution, molarity (moles per liter, abbreviated M) provides the link between solution volume and moles: moles = molarity x volume (in liters). If 25.0 mL of 0.100 M NaOH is needed for a titration, the moles of NaOH are: 0.100 mol/L x 0.0250 L = 0.00250 mol. This conversion replaces the grams-to-moles step when working with solutions rather than pure substances.

The dilution equation M1V1 = M2V2 follows directly from the conservation of moles during dilution. Adding solvent changes the volume and concentration but not the number of moles of solute. If 10.0 mL of 6.00 M HCl is diluted to 100.0 mL, the new concentration is (6.00)(0.0100)/(0.1000) = 0.600 M. Dilution is a physical change, not a chemical reaction, so no balanced equation or mole ratio is needed.

Titration problems combine solution stoichiometry with mole ratios. At the equivalence point of a titration, the moles of acid equal the moles of base (for monoprotic acid with monobasic base). If 35.0 mL of 0.150 M HCl neutralizes 25.0 mL of NaOH of unknown concentration: moles HCl = 0.150 x 0.0350 = 0.00525 mol. Since the mole ratio is 1:1, moles NaOH = 0.00525 mol, and the NaOH concentration is 0.00525/0.0250 = 0.210 M.

Gas Stoichiometry

When reactions involve gases, the ideal gas law provides an additional conversion pathway between volume and moles. At standard temperature and pressure (STP: 0 degrees C and 1 atm), one mole of any ideal gas occupies exactly 22.4 liters. This molar volume serves as a convenient conversion factor: 22.4 L of any gas at STP contains one mole of that gas, regardless of its identity. For conditions other than STP, the ideal gas law (PV = nRT) converts between volume and moles using the actual temperature and pressure.

For the decomposition of potassium chlorate, 2KClO3(s) -> 2KCl(s) + 3O2(g), if 24.5 g of KClO3 (molar mass 122.55 g/mol) decomposes completely: moles KClO3 = 24.5/122.55 = 0.200 mol. Using the mole ratio, moles O2 = 0.200 x (3/2) = 0.300 mol. At STP, volume = 0.300 x 22.4 = 6.72 L of oxygen gas. At 25 degrees C and 1.00 atm instead, V = nRT/P = 0.300 x 0.0821 x 298.15 / 1.00 = 7.34 L. The extra step of applying gas laws adds flexibility but follows the same logical framework.

Gas stoichiometry problems frequently require collecting gas over water. When a gas is collected by water displacement, the total pressure in the collection vessel equals the partial pressure of the collected gas plus the vapor pressure of water at the collection temperature. The actual pressure of the collected gas must be corrected by subtracting water vapor pressure before using PV = nRT to calculate moles. At 25 degrees C, water vapor pressure is 23.8 mmHg, which is a small but significant correction for precise calculations.

Volume ratios provide a shortcut for gas-phase reactions when all species are gases at the same temperature and pressure. Under these conditions, volume ratios equal mole ratios because V = nRT/P makes volume directly proportional to moles when T and P are constant. For the reaction N2(g) + 3H2(g) -> 2NH3(g), one liter of nitrogen reacts with three liters of hydrogen to produce two liters of ammonia, all at the same temperature and pressure. This principle, known as Gay-Lussac's law of combining volumes, was historically important in establishing the relationship between gas volumes and molecular formulas.

Stoichiometry and the Law of Conservation of Mass

Stoichiometry is fundamentally grounded in the law of conservation of mass: atoms are neither created nor destroyed in chemical reactions. The balanced equation enforces this law by ensuring equal numbers of each type of atom on both sides. Every stoichiometric calculation is essentially a bookkeeping exercise that tracks atoms from reactants to products. The total mass of products always equals the total mass of reactants, providing a built-in check on calculations. If your calculated product mass exceeds the total reactant mass, an error has occurred somewhere in the calculation.