Mole Fraction Calculator

Mole fraction (χ): composition of a mixture

The mole fraction χᵢ of component i is just its moles divided by the total moles in the mixture: χᵢ = nᵢ / Σnⱼ. The number is dimensionless and always sits somewhere between 0 and 1. Add up the fractions of every component and you get exactly 1 (Σχᵢ = 1). Take 1 mol of ethanol mixed with 2 mol of water: χ_ethanol works out to 1/3 ≈ 0.333 and χ_water to 2/3 ≈ 0.667. Where molarity (mol/L) shifts with temperature and volume, the mole fraction does not, which is why thermodynamics of solutions leans on it.

Applications

It underpins solution thermodynamics (Raoult's law: P = χ_solvent · P°) and Henry's law for dissolved gases. You also meet it in fractional distillation of petroleum and ethanol, in gas mixtures like medical O₂/N₂ oxygen therapy or breathable atmospheres, and across the design of separation columns in chemical engineering. By Avogadro's law, mole fraction matches volume fraction for ideal gases.

FAQ

Mole fraction vs molarity? Molarity is tied to volume, and volume drifts as temperature changes. Mole fraction belongs to the composition itself, so it suits thermodynamic work better.

Can χ exceed 1? No. By definition χ ∈ [0, 1]. A value of 1 means you have the pure substance, and 0 means it isn't there at all.

Mole percent? Multiply χ by 100%. So χ = 0.25 reads as 25 mol%.