Mole Fraction (x) | Basic Concepts of Chemistry Class 11

Mole Fraction ($\chi$)

Dimensionless Concentration Term | Basic Concepts of Chemistry

1. Definition & Formula

Mole Fraction ($\chi$ or $x$) is the ratio of the number of moles of a specific component to the total number of moles of all components in the solution.

For a binary solution containing component A (Solvent) and component B (Solute):

$$ \chi_A = \frac{n_A}{n_A + n_B} \quad \text{and} \quad \chi_B = \frac{n_B}{n_A + n_B} $$

Property: The sum of mole fractions of all components is always unity (1).

$$ \chi_A + \chi_B = 1 $$

2. Key Characteristics

• Unitless: Since it is a ratio of moles to moles, it has no units.
• Temperature Independent: Mole fraction involves only masses (via moles) and not volume. Therefore, unlike Molarity, it does not change with temperature.
• Maximum Value: 1 (Pure component).
• Minimum Value: 0 (Component not present).

3. Important Relations

A. Relation with Molality ($m$)

If $\chi_B$ is the mole fraction of solute and $M_A$ is the molar mass of solvent (g/mol):

$$ m = \frac{\chi_B \times 1000}{(1 - \chi_B) \times M_A} $$

B. Relation with Vapor Pressure (Raoult's Law)

For a solution of volatile liquids:

$$ p_A = p_A^\circ \chi_A $$

C. Relation with Partial Pressure (Dalton's Law)

In a gaseous mixture:

$$ p_i = \chi_i \times P_{total} $$

4. Worked Example

Question: A solution is prepared by mixing 46g of Ethanol ($C_2H_5OH$) and 36g of Water ($H_2O$). Calculate the mole fraction of each.

Solution:

• Molar Mass: Ethanol = 46 g/mol, Water = 18 g/mol.
• Moles of Ethanol ($n_E$) = $46/46 = 1$ mol.
• Moles of Water ($n_W$) = $36/18 = 2$ mol.
• Total Moles = $1 + 2 = 3$.
• $\chi_{Ethanol} = 1/3 = 0.33$.
• $\chi_{Water} = 2/3 = 0.67$.
• Check: $0.33 + 0.67 = 1$.

Practice Quiz

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