Mole Fraction Calculator (from moles or from grams and molar masses)

Understanding the mole fraction calculator — concept and principle

This calculator finds the mole fraction and mole percent of each component in a mixture, from amounts in moles or from masses and molar masses. With a total pressure it also gives partial pressures by Dalton's law. It is used in chemistry, chemical engineering and for gas-mixture and vapour-pressure calculations.

How it is calculated

X_i = n_i ÷ Σn

Mole percent = X_i × 100

If masses are given: n_i = mass ÷ molar mass

Partial pressure (ideal gas) = X_i × P_total

• Up to 10 components, one per line; pressure in any unit.

The principle

Mole fraction counts what share of all the particles in a mixture belong to one component. Because it is a ratio of amounts, it has no unit and the fractions always add up to 1. Many physical laws work naturally with mole fractions: in an ideal gas mixture each gas contributes to the total pressure in proportion to its share of the molecules, and Raoult's law gives a solvent's vapour pressure in proportion to its mole fraction.

Worked example

Default inputs: masses and molar masses, 46.07 g of ethanol (46.07 g/mol) and 36.03 g of water (18.015 g/mol); total pressure 101.325.

1. Ethanol: 46.07 ÷ 46.07 = 1 mol; water: 36.03 ÷ 18.015 = 2 mol.
2. Total amount = 3 mol; 2 components.
3. X₁ = 1 ÷ 3 = 0.3333, or 33.33%; all fractions 0.3333, 0.6667.
4. Partial pressure of component 1 = 0.3333 × 101.325 = 33.77.

How to read the result

The fractions must sum to 1; if they do not, an input is wrong. Mole fraction differs from mass fraction: here ethanol is 56% of the mass but only a third of the molecules. Partial pressures from Dalton's law apply to ideal gas mixtures; for liquids, use Raoult's law with vapour pressures.

Common mistakes

• Mixing mole fractions with mass fractions.
• Forgetting to convert masses with the correct molar masses.
• Applying the partial-pressure result to a liquid mixture.
• Leaving out a component, such as the solvent.

Frequently asked questions

Do mole fractions have units?

No. They are ratios and always add up to 1.

How is mole fraction different from molarity?

Molarity is moles per litre of solution; mole fraction is moles over total moles.

What is the mole fraction of oxygen in dry air?

About 0.21.

Can I enter more than two components?

Yes, up to ten, one per line.

Sources: OpenStax, Chemistry: Atoms First 2e, section 11.4 "Colligative Properties"