Mole Fraction Formula

Mole fraction (χ, Greek letter chi) expresses the ratio of moles of one component to total moles in a mixture. It's a dimensionless concentration unit essential for Raoult's Law, Dalton's Law, and colligative properties.

Mole Fraction Formula

χi = ni / ntotal

Mole fraction of component i = moles of i / total moles

Key Properties of Mole Fraction

  • Dimensionless: No units! Pure number between 0 and 1
  • Sum equals 1: χ₁ + χ₂ + χ₃ + ... = 1.00
  • Independent of temperature: Unlike molarity, mole fraction doesn't change with temperature
  • Symbol: χ (chi) or X, with subscript for component

Variable Definitions

χi = Mole Fraction of Component i

Units: Dimensionless (no units)

Range: 0 to 1 (or 0% to 100%)

💡 Pure substance: χ = 1.00

ni = Moles of Component i

Units: mol

Number of moles of the specific component

ntotal = Total Moles

Formula: ntotal = n₁ + n₂ + n₃ + ...

Sum of moles of all components in the mixture

For binary solution: ntotal = nsolute + nsolvent

Binary Mixture (Two Components)

Component A:

χA = nA / (nA + nB)

Component B:

χB = nB / (nA + nB)

Sum Property:

χA + χB = 1.00

Therefore: χB = 1 - χA

Step-by-Step Example

Problem: A solution contains 2.0 mol ethanol and 8.0 mol water. Calculate the mole fractions of each.

Given:

  • nethanol = 2.0 mol
  • nwater = 8.0 mol
  • Find: χethanol and χwater

Step 1: Calculate total moles

ntotal = nethanol + nwater
ntotal = 2.0 mol + 8.0 mol = 10.0 mol

Step 2: Calculate χethanol

χethanol = nethanol / ntotal
χethanol = 2.0 mol / 10.0 mol = 0.20

Step 3: Calculate χwater

χwater = nwater / ntotal
χwater = 8.0 mol / 10.0 mol = 0.80

Step 4: Verify sum = 1

χethanol + χwater = 0.20 + 0.80 = 1.00 ✓

Answers: χethanol = 0.20 (or 20%), χwater = 0.80 (or 80%)

Applications of Mole Fraction

📊 Dalton's Law

Partial pressure: Pi = χi × Ptotal

Mole fraction determines each gas's contribution to total pressure

💧 Raoult's Law

Vapor pressure: P = χsolvent × P°

Vapor pressure lowering depends on solvent mole fraction

🧪 Colligative Properties

ΔTf = Kf × m × i, where mole fraction relates to molality

🔬 Phase Diagrams

Composition axis in binary phase diagrams uses mole fraction

Common Mistakes

❌ Using mass instead of moles

Mole fraction uses MOLES, not grams! Must convert mass to moles using molar mass first.

❌ Forgetting to include all components

ntotal must include ALL components in the mixture, including the solvent!

❌ Mole fractions not summing to 1

If χ₁ + χ₂ + ... ≠ 1.00, you made a calculation error. Always check this!

❌ Confusing with mass fraction

Mole fraction = moles/moles. Mass fraction = mass/mass. Different concepts!

Related Calculators

Mole Fraction Calculator

Calculate χ from moles or masses

Dalton's Law

Partial pressures from mole fractions

Raoult's Law

Vapor pressure calculations

Concentration Converter

Convert χ to other units

Concentration & Solution Calculators

All concentration tools

Mass Percent vs Mole Fraction

Compare composition methods

Frequently Asked Questions

What is mole fraction?

χ = ni / ntotal. It's the ratio of moles of one component to total moles in a mixture. Dimensionless, always between 0 and 1.

Why is mole fraction dimensionless?

It's moles divided by moles - the units cancel! This makes it independent of amount and temperature, unlike molarity.

How do I convert mass to mole fraction?

First convert each mass to moles (n = mass / molar mass), then calculate χ = ni / (n₁ + n₂ + ...).

Can mole fraction be expressed as a percent?

Yes! Multiply by 100. χ = 0.25 means 25 mol% (or 25 mole percent). Both forms are used.

When should I use mole fraction vs molarity?

Use mole fraction for: gas mixtures, vapor pressure, colligative properties. Use molarity for: aqueous solutions, reaction stoichiometry, titrations.

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