Mole Fraction Formula: Definition, Properties, Examples

Mole Fraction Formula: Mole Fraction is a fundamental concept in chemistry that quantifies the proportion of molecules of a specific component in a mixture relative to the total number of molecules in that mixture. It holds significant importance in a range of competitive examinations such as IIT, JEE Mains, and NEET, and also aids in understanding advanced principles of chemistry.

Significance of Mole Fraction

Understanding Mole Fraction is essential for grasping advanced chemistry concepts. By working through solved examples, you can see how this concept is applied and learn problem-solving strategies effectively.

Practical Learning through Practice

It is highly recommended that students master Mole Fraction through practice, cross-referencing their solutions with answers provided on our website. This approach ensures a solid grasp of the concept and can lead to impressive exam results with minimal effort.

Mole Fraction Formula

In a solution containing two substances, A and B, the mole fraction of each substance is calculated as follows:

Mole fraction of solute (XA) = (Moles of Solute) / (Total moles of Solute and Solvent)

Mole fraction of solvent (XB ) = (Moles of Solvent) / (Total moles of Solute and Solvent)

Note that in a mixture, the sum of all mole fractions equals one: XA + XB = 1. When multiplied by 100, mole fractions provide the mole percentage. Mole fraction is a dimensionless expression.

Advantages of Mole Fraction

Mole Fraction offers several advantages:

Temperature Independence: Mole Fraction remains unaffected by temperature changes.

No Need for Density Data: Unlike some other methods, Mole Fraction calculations do not require density information.

Applicability to Ideal Gas Mixtures: In ideal gas mixtures, the mole fraction relates to the ratio of partial pressure to total pressure.

Disadvantages of Mole Fraction

The only drawback of Mole Fraction is its inconvenience when applied to liquid solutions.

Properties of Mole Fraction

Mole Fraction exhibits the following properties:

Temperature Independence: It remains constant despite temperature fluctuations and doesn't rely on phase densities.

Preparation of Known Mixture: By weighing the actual masses of constituents, a mixture with a specific mole fraction can be prepared.

Symmetry: In mole fractions such as x = 0.1 and x = 0.9, the roles of 'solvent' and 'solute' can be reversed.

Ternary Mixtures: Mole fractions of one component in a ternary mixture can be expressed in terms of other component mole fractions and binary mole ratios.

Mole Fraction Formula Solved Examples

Example 1: Calculating Mole Fraction of NaCl and H₂O

In this example, we are asked to find the mole fraction of NaCl and H₂O when 0.010 moles of NaCl are dissolved in 100 grams of pure water.

Solution:

First, calculate the number of moles of water in 100 grams of pure water. We'll use the molecular weight of water, which is approximately 18.0153 grams per mole.

Number of moles of water = 100 grams / 18.0153 grams/mole ≈ 5.56 moles

Next, find the mole fraction of NaCl. We have 0.010 moles of NaCl.

Mole fraction of NaCl = (0.010 moles) / (0.010 moles + 5.56 moles)

Mole fraction of NaCl ≈ 0.010 / 5.57 ≈ 0.0018 (rounded to three decimal places)

Finally, calculate the mole fraction of H₂O:

Mole fraction of H₂O = (5.56 moles) / (0.010 moles + 5.56 moles)

Mole fraction of H₂O ≈ 5.56 / 5.57 ≈ 0.9982 (rounded to three decimal places)

So, the mole fraction of NaCl is approximately 0.0018, and the mole fraction of H₂O is approximately 0.9982.

Example 2: Mole Fraction in a Binary Gas Mixture

A mixture of two gases contains 4 moles of oxygen (O₂) and 6 moles of nitrogen (N₂). Calculate the mole fraction of each gas in the mixture.

Solution:

Calculate the total number of moles in the mixture:

Total moles in the mixture = Moles of O₂ + Moles of N₂

Total moles = 4 moles + 6 moles = 10 moles

Find the mole fraction of O₂:

Mole fraction of O₂ = (Moles of O₂) / (Total moles in the mixture)

Mole fraction of O₂ = 4 moles / 10 moles = 0.4

Calculate the mole fraction of N₂:

Mole fraction of N₂ = (Moles of N₂) / (Total moles in the mixture)

Mole fraction of N₂ = 6 moles / 10 moles = 0.6

So, the mole fraction of O₂ is 0.4, and the mole fraction of N₂ is 0.6 in the mixture.

Example 3: Mole Fraction in a Liquid Mixture

A solution is prepared by mixing 40 grams of ethanol (C₂H₅OH) and 60 grams of methanol (CH₃OH). Calculate the mole fraction of each component in the solution.

Solution:

Calculate the number of moles of ethanol and methanol:

The molecular weight of ethanol is approximately 46.07 g/mol.

The molecular weight of methanol is approximately 32.04 g/mol.

Moles of ethanol = 40 grams / 46.07 g/mol ≈ 0.868 moles

Moles of methanol = 60 grams / 32.04 g/mol ≈ 1.872 moles

Calculate the total number of moles in the solution:

Total moles in the solution = Moles of ethanol + Moles of methanol

Total moles in the solution ≈ 0.868 moles + 1.872 moles ≈ 2.74 moles

Find the mole fraction of ethanol:

Mole fraction of ethanol = (Moles of ethanol) / (Total moles in the solution)

Mole fraction of ethanol ≈ 0.868 moles / 2.74 moles ≈ 0.317 (rounded to three decimal places)

Calculate the mole fraction of methanol:

Mole fraction of methanol = (Moles of methanol) / (Total moles in the solution)

Mole fraction of methanol ≈ 1.872 moles / 2.74 moles ≈ 0.683 (rounded to three decimal places)

So, the mole fraction of ethanol is approximately 0.317, and the mole fraction of methanol is approximately 0.683 in the solution.