By Chris Deziel | Updated March 24, 2022

In the realm of stoichiometry—where chemists compare the relative amounts of substances in reactions—knowing how to determine the mole ratio is essential. Whether you’re working out the empirical formula of an unknown compound or calculating the precise amounts of reactants and products in a reaction, the principles are the same: identify the simplest whole‑number relationship between the species involved.

Determining an Empirical Formula

When a mystery compound is analyzed for its elemental composition, you’ll usually measure the mass of each element present. Converting those masses to moles (mass ÷ atomic weight) reveals how many moles of each element exist. From there, you can deduce the simplest whole‑number ratio—the empirical formula.

1. Calculate moles of each element. Divide the measured mass by the element’s atomic weight. For example, a compound containing 0.675 g H, 10.8 g O, and 13.5 g Ca yields:
   • H: 0.675 g ÷ 1.01 g mol⁻¹ = 0.675 mol
   • O: 10.8 g ÷ 16.00 g mol⁻¹ = 0.675 mol
   • Ca: 13.5 g ÷ 40.08 g mol⁻¹ = 0.337 mol
2. Divide by the smallest mole value. Here, Ca (0.337 mol) is the smallest. Dividing each mole value by 0.337 gives:
   • H: 0.675 ÷ 0.337 ≈ 2
   • O: 0.675 ÷ 0.337 ≈ 2
   • Ca: 0.337 ÷ 0.337 = 1
3. Write the empirical formula. The resulting whole‑number ratios become subscripts: CaO₂H₂, typically expressed as Ca(OH)₂.

Balancing a Reaction Equation

When the reactants and products of a reaction are known, you can write an unbalanced equation and then balance it by adjusting stoichiometric coefficients. These coefficients are, in fact, the mole ratios that satisfy the law of conservation of mass.

1. Start with the unbalanced equation. For example: H₂ + O₂ → H₂O.
2. Balance the atoms. Multiply each side by the smallest set of integers that equalizes the number of atoms for every element. The balanced equation becomes: 2 H₂ + O₂ → 2 H₂O.
3. Interpret the mole ratios. From the coefficients:
   • Hydrogen to oxygen: 2 mol H₂ : 1 mol O₂ → 2:1
   • Oxygen to water: 1 mol O₂ : 2 mol H₂O → 1:2
   • Water to hydrogen: 2 mol H₂O : 4 mol H₂ → 1:2 (simplified)

These coefficients not only balance the equation but also tell you how many moles of each species participate in the reaction. Mastering this technique ensures accurate stoichiometric calculations for any chemical process.