Mole Fraction

Xi = ni ÷ n(total): the fraction of all moles in a mixture that belong to one component — always unitless.

X_i = \frac{n_i}{n_{\text{total}}}

X(i) = moles of component i / total moles

What it means

Mole fraction is each component's share of the total moles in a mixture. Because it counts particles rather than mass or volume, it is the natural concentration for gas mixtures — each gas's partial pressure is its mole fraction times the total pressure — and for Raoult's-law vapor pressure problems over liquid solutions.

Variables

Symbol	Name	Unit	Meaning
$Xi$	Mole fraction of component i	unitless	The share of the mixture's moles belonging to component i; a number between 0 and 1.
$ni$	Moles of component i	mol	The moles of the single component of interest.
$n_total$	Total moles	mol	The sum of the moles of every component in the mixture.

Assumptions

Every component's moles are included in the total — none are left out.
The mole fractions of all components sum to exactly 1.
Mole fraction is unitless, since moles cancel.
The mixture is uniform at the molecular level.

Worked example

Problem

A gas mixture contains 1.00 mol H2, 2.00 mol N2, and 3.00 mol Ar. Calculate the mole fraction of H2.

Given:

n(H2) = 1.00 mol
n(N2) = 2.00 mol
n(Ar) = 3.00 mol

Total the moles: n(total) = 1.00 + 2.00 + 3.00 = 6.00 mol.
Write X(H2) = n(H2) / n(total).
Substitute: X(H2) = 1.00 / 6.00 = 0.167.
Cross-check the others: X(N2) = 2.00/6.00 = 0.333 and X(Ar) = 3.00/6.00 = 0.500.
Sum check: 0.167 + 0.333 + 0.500 = 1.000.

X(H2) = 0.167

About one-sixth of the gas molecules are H2 — in a 600 kPa mixture, hydrogen's partial pressure would be 0.167 × 600 kPa = 100 kPa.