Mole Fraction Calculator

Calculate mole fraction of each component in a mixture. Mole fractions sum to 1.000 and are used in Raoult's Law, ideal gas mixtures, and thermodynamic calculations.

⚗️ Solutions📐 xᵢ = nᵢ/nᵀᵒᵗₐₗ🧪 Chemistry
Moles of component 1 n1
Moles of component 2 n2
Moles of component 3 n3 (optional)
Component names (optional)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Mole Fraction Calculator—xᵢ = nᵢ/nᵀᵒᵗₐₗdimensionless

Step-by-Step Examples

Example 1
Binary Mixture

2.00 mol ethanol + 8.00 mol water.

  • n_total = 10.00 mol
  • x(ethanol) = 2.00/10.00 = 0.200
  • x(water) = 8.00/10.00 = 0.800
  • Sum = 1.000
✓ x(ethanol)=0.200, x(water)=0.800
Example 2
Air Composition

N2: 0.78 mol, O2: 0.21 mol, Ar: 0.01 mol.

  • Total = 1.00 mol
  • x(N2)=0.78, x(O2)=0.21, x(Ar)=0.01
  • Sum = 1.00 (by design for normalized mixture)
✓ x(N2)=0.780, x(O2)=0.210, x(Ar)=0.010
Example 3
From Masses

10.0 g ethanol (M=46.07) + 90.0 g water (M=18.02).

  • n(ethanol)=10.0/46.07=0.217 mol
  • n(water)=90.0/18.02=4.994 mol
  • x(ethanol)=0.217/5.211=0.0416
✓ x(ethanol)=0.0416 (4.16 mol%)

Real-World Applications

💧
Raoult Law
P_solution = x_solvent x P0. Mole fraction used directly in vapor pressure calculation.
💨
Gas Mixtures
For ideal gases: x_i = P_i/P_total. Mole fraction equals pressure fraction.
🧪
Thermodynamics
Activity in ideal solutions equals mole fraction. Chemical potential: mu = mu0 + RT*ln(x).
🍺
Beer/Wine Production
Alcohol content expressed as mole fraction and volume fraction for thermodynamic calculations.

Common Mistakes to Avoid

⚠️
Mole fractions sum to exactly 1

x1 + x2 + x3 = 1.000. If not, recheck. Each mole fraction must be between 0 and 1.

⚠️
Use moles, not grams

Mole fraction uses n (moles), not mass (grams). Convert mass to moles first using molar mass.

⚠️
Mole fraction is dimensionless

x has no units. It is a pure number between 0 and 1.

Frequently Asked Questions

What is mole fraction? ▾
x_i = n_i / n_total. Fraction of total moles contributed by component i. Dimensionless, range 0-1. All components sum to 1.
How does mole fraction relate to mass fraction? ▾
Mass fraction = x_i * M_i / (sum of x_j * M_j). They differ for components with different molar masses.
What is mole percent? ▾
mol% = mole fraction x 100%. Air: 78% N2 means x(N2)=0.78. Simpler communication of composition.
How is mole fraction used in Dalton law? ▾
For ideal gas: P_i = x_i * P_total. Mole fraction equals partial pressure fraction. Very useful for gas mixture calculations.
What is molality in terms of mole fraction? ▾
m = 1000 * x_solute / (M_solvent * x_solvent). Related but different: molality uses solvent mass, mole fraction uses total moles.

Related Chemistry Calculators

💧 Raoult Law💨 Dalton Law🧪 Molality🧪 Molarity🧪 Solution Prep

Formula Explorer connections

Interpretation: This formula connects solute amount and solution volume, mass or particle count to concentration and colligative behavior. Assumption: Distinguish solution volume from solvent volume, use the stated temperature, and account for dissociation or nonideal activity when required.

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