Mole Fraction Mixture

Mole fraction in a mixture

The mole fraction χᵢ of a component is just its moles divided by the total moles in the mixture: χᵢ = nᵢ / Σnⱼ. The number is dimensionless, always falls between 0 and 1, and every fraction in a mixture adds up to 1 (Σχᵢ = 1). Take 2 mol of A with 8 mol of B → χ_A = 2/10 = 0.2 and χ_B = 8/10 = 0.8. Since it counts only moles, the mole fraction is independent of temperature and volume. That is why thermodynamics reaches for it first, and why Raoult's law for ideal solutions is written in terms of it: P_solvent = χ_solvent · P°_solvent.

Applications

You meet it in thermodynamics (Gibbs free energy of mixing, chemical potential) and in fractional distillation, where vapor-liquid equilibrium and McCabe-Thiele diagrams depend on it. Oxygen therapy uses it too: FiO₂ is the mole fraction of O₂ in inspired gas, around 0.21 in room air and reaching 1.0 with pure O₂. It also shows up in gas-phase partial pressures (P_i = χ_i·P_total) and in reading phase diagrams.

FAQ

Mole fraction vs mass fraction? One counts moles, the other counts grams (mass fraction, w). When the species in a mixture have different molar weights, χ and w end up pretty far apart.

Does it depend on temperature or volume? No. Barring a reaction, the mole counts stay put as T or V change, so χ holds steady whether you heat the mixture, compress it, or dilute it by volume.

How does it connect to partial pressure? With ideal gases, P_i = χ_i · P_total. So in air at 1 atm, where χ_O₂ ≈ 0.21, you get P_O₂ ≈ 0.21 atm.