Mole Fraction
Mole fraction (χ) is a dimensionless concentration unit expressing the ratio of the moles of one component to the total moles of all components in a mixture. The sum of all mole fractions in a mixture always equals exactly 1. Mole fraction is used in Raoult's law, Dalton's law of partial pressures, and chemical thermodynamics because it is independent of temperature and pressure.
Key Formula
χ_i = n_i / (n_1 + n_2 + ... + n_j)
LaTeX: \chi_i = \dfrac{n_i}{\displaystyle\sum_{j} n_j}
| Symbol | Meaning | Unit |
|---|---|---|
| χ_i | Mole fraction of component i | dimensionless |
| n_i | Moles of component i | mol |
| Σn_j | Total moles of all components in the mixture | mol |
Worked Example
Problem
A gas mixture contains 2.0 mol of N₂ and 0.5 mol of O₂. What is the mole fraction of each gas?
Solution
Step 1: Total moles = 2.0 + 0.5 = 2.5 mol. Step 2: Mole fraction of N₂: χ(N₂) = 2.0 / 2.5 = 0.80. Step 3: Mole fraction of O₂: χ(O₂) = 0.5 / 2.5 = 0.20. Step 4: Verify: 0.80 + 0.20 = 1.00 ✓.
Answer
χ(N₂) = 0.80; χ(O₂) = 0.20
Mole Fractions in Dry Air (Approximate)
| Gas | Symbol | Mole Fraction (χ) | Percent (%) |
|---|---|---|---|
| Nitrogen | N₂ | 0.7808 | 78.08 |
| Oxygen | O₂ | 0.2095 | 20.95 |
| Argon | Ar | 0.00934 | 0.934 |
| Carbon dioxide | CO₂ | 0.000421 | 0.0421 |
| Other gases | Various | ~0.000239 | ~0.0239 |
Interactive Tools
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Related Terms
Molarity
Molarity (M) is the most common measure of solution concentration, defined as the number of moles of solute dissolved per litre of solution. It is temperature-dependent because liquid volumes change with temperature. Molarity is widely used in titrations, reaction stoichiometry involving solutions, and the preparation of standard laboratory solutions.
Molality
Molality (m) is a measure of solution concentration expressed as the number of moles of solute per kilogram of solvent (not solution). Unlike molarity, molality is independent of temperature and pressure because it is based on mass rather than volume, making it ideal for studying colligative properties such as boiling point elevation and freezing point depression. It is the preferred concentration unit in thermodynamic calculations involving solutions.
Henry's Law
Henry's Law states that the amount of a gas dissolved in a liquid at constant temperature is directly proportional to the partial pressure of that gas above the liquid. It applies to dilute solutions of gases that do not react chemically with the solvent. Henry's Law explains why carbonated beverages fizz when opened (pressure release), and is critical in understanding oxygen transport in blood, gas exchange in lungs, and environmental fate of volatile compounds.
From Latin "moles" (mass) and French "fraction" (from Latin "fractio", a breaking). The concept of dividing a mixture by mole proportion was formalised alongside Dalton's atomic theory in the early 19th century.