χᵢ = nᵢ / (n₁ + n₂ + …)
Mole fraction (χ) is a dimensionless quantity: χᵢ = nᵢ/n_total. The sum of all mole fractions in a mixture always equals 1. Mole fraction is used in: Raoult's law (Pᵢ = χᵢP°ᵢ — vapor pressure of ideal solutions), Dalton's law (Pᵢ = χᵢP_total — partial pressures of gas mixtures), and calculating activity in non-ideal mixtures. For binary solutions, χ_solvent + χ_solute = 1. Mole fraction is temperature and pressure independent (unlike molarity). Converting to molality: m = χ_solute/(χ_solvent × M_solvent/1000). In thermodynamics, chemical potential depends on mole fraction: μᵢ = μ°ᵢ + RT ln(χᵢ). Mole fraction is particularly important in phase diagrams, distillation calculations, and gas mixture analysis.