Mole Fraction Calculator

Mole Fraction

Mole fraction (denoted χ or x) is the ratio of moles of one component to total moles in a mixture. Unlike mass percent, it is dimensionless and scales perfectly with the gas laws and Raoult’s law.

Formula

χᵢ = nᵢ / Σnⱼ

The sum of all mole fractions in any mixture equals exactly 1.

Worked Example: 50 g Water + 30 g Ethanol

• Water: 50 g ÷ 18.015 g/mol = 2.776 mol
• Ethanol: 30 g ÷ 46.07 g/mol = 0.651 mol
• Total: 3.427 mol
• χ_water = 2.776 / 3.427 = 0.810
• χ_ethanol = 0.651 / 3.427 = 0.190

The sum 0.810 + 0.190 = 1.000 ✓.

Why Use Mole Fraction Instead of Mass %?

Dalton’s Law Connection

For an ideal gas mixture:

P_i = χᵢ × P_total

Each component’s partial pressure equals its mole fraction times the total pressure. This is why mole fractions are the natural variable for atmospheric chemistry, scuba mixes, and chemical reactor design.

Raoult’s Law Connection

For an ideal liquid mixture:

P_i = χᵢ × P*ᵢ

where P*ᵢ is the pure-component vapor pressure. Real mixtures deviate from Raoult’s law, but the mole fraction is still the right axis to plot vapor-liquid diagrams against.

Common Conversions

mole fraction → molality (m): m = χ_solute / (χ_solvent × M_solvent) mole fraction → ppm: ppm ≈ χ × 10⁶ (for dilute mixtures)

Caveats

When mixing components by mass or volume, you cannot just average mole fractions — you must convert each component to moles first. For non-ideal solutions, especially near phase boundaries or high concentrations, activities replace simple mole fractions in the equilibrium equations.