Mole Fraction: Definition, Formula, Properties, Solved Examples, MCQs

ANAND CLASSES Study Material and Notes to learn about Mole Fraction – its definition, formula, properties, and applications with solved examples for CBSE Chemistry, JEE and NEET Exams. Test your knowledge with MCQs and conceptual questions.

Mole Fraction

Mole fraction is a fundamental concept in chemistry, used to express the composition of a solution. It is defined as the ratio of the number of moles of a particular component to the total number of moles of all the components in the solution.

Mathematically, for a solution containing $n_A$ moles of component A and $n_B$ moles of component B, the mole fractions are given by:

$$X_A = \frac{n_A}{n_A + n_B}$$

$$X_B = \frac{n_B}{n_A + n_B}$$

Key Properties of Mole Fraction

• Mole fraction is always a dimensionless quantity.
• The sum of the mole fractions of all components in a solution is always equal to 1 i.e. $$\:X_A + X_B = 1$$
• It does not change with temperature, unlike molarity and normality.
• It is widely used in Raoult’s law, colligative properties, and vapor pressure calculations.

Frequently Asked Questions (FAQs)

Q1: Why is mole fraction unitless?

A: Mole fraction is the ratio of two quantities with the same unit (moles), so the units cancel out, making it unitless.

Q2: Can mole fraction be greater than 1?

A: No, the mole fraction of any component is always between 0 and 1 because it represents a fraction of the total number of moles.

Q3: How is mole fraction useful in real-life applications?

A: It is useful in chemical engineering, pharmaceuticals, and thermodynamics for calculating partial pressures of gases, solubility, and concentration of solutions.

Q4: Does mole fraction depend on temperature?

A: No, mole fraction remains constant regardless of temperature changes.

Conceptual Questions with Answers

Q1: If the mole fraction of a gas in a mixture is 0.25, what does it mean?

A: It means that 25% of the total moles in the mixture are of that particular gas.

Q2: What will be the mole fraction of water in a solution where 2 moles of NaCl are dissolved in 18 moles of water?

A: Total moles = 2 + 18 = 20 $$X_{H_2O} = \frac{18}{20} = 0.9$$

Q3: Can mole fraction be negative?

A: No, since moles of a substance cannot be negative, mole fraction is always positive.

Multiple Choice Questions (MCQs)

1. The sum of the mole fractions of all components in a solution is:

a) Less than 1
b) More than 1
c) Exactly 1
d) Cannot be determined
Answer: c) Exactly 1
Explanation: By definition, the sum of mole fractions is always equal to 1.

2. Which of the following statements about mole fraction is incorrect?

a) It is unitless
b) It depends on temperature
c) It is used in vapor pressure calculations
d) It is always between 0 and 1
Answer: b) It depends on temperature
Explanation: Mole fraction does not depend on temperature.

Detailed Explanation: Calculation of Mole Fraction of Water in a Mixture

Calculate the mole fraction of water, ethanol and acetic acid in a mixture of 12g water (H₂O), 92g ethanol (C₂H₅OH), and 108g acetic acid (CH₃COOH).

Step 1: Understanding Mole Fraction

Mole fraction (X) of a substance in a mixture is given by: $$X = \frac{\text{Number of moles of that substance}}{\text{Total number of moles in the solution}}$$

where:

• Number of moles (n) is calculated using the formula: $$n = \frac{\text{Mass of substance}}{\text{Molar mass of substance}}$$

Step 2: Calculate Moles of Each Component

We are given the masses of three substances:

• Water (H₂O) = 12 g
• Ethanol (C₂H₅OH) = 92 g
• Acetic acid (CH₃COOH) = 108 g

We also need their molar masses:

• Molar mass of water (H₂O) = 18 g/mol
• Molar mass of ethanol (C₂H₅OH) = 46 g/mol
• Molar mass of acetic acid (CH₃COOH) = 60 g/mol

Now, we calculate the number of moles of each component.

For Water (H₂O):

$$n(H_2O) = \frac{\text{Mass of water}}{\text{Molar mass of water}}$$ $$n(H_2O) = \frac{12}{18} = 0.67 \text{ moles}$$

For Ethanol (C₂H₅OH):

$$n(C_2H_5OH) = \frac{\text{Mass of ethanol}}{\text{Molar mass of ethanol}} $$

$$n(C_2H_5OH) = \frac{92}{46} = 2.00 \text{ moles}$$

For Acetic Acid (CH₃COOH):

$$n(CH_3COOH) = \frac{\text{Mass of acetic acid}}{\text{Molar mass of acetic acid}}$$

$$n(CH_3COOH) = \frac{108}{60} = 1.80 \text{ moles}$$

Step 3: Calculate Total Number of Moles in the Mixture

Now, we sum up the moles of all three components: $$n_{\text{total}} = n(H_2O) + n(C_2H_5OH) + n(CH_3COOH) $$

$$n_{\text{total}} = 0.67 + 2.00 + 1.80 = 4.47$$

Step 4: Calculate Mole Fractions

Now, we calculate the mole fraction of each component by dividing the moles of each substance by the total number of moles.

Mole Fraction of Water (H₂O)

$$X_{\text{water}} = \frac{n(H_2O)}{n_{\text{total}}}$$

$$X_{\text{water}} = \frac{0.67}{4.47} = 0.15$$

This means 15% of the total moles in the mixture are from water.

Mole Fraction of Ethanol (C₂H₅OH)

$$X_{\text{ethanol}} = \frac{n(C_2H_5OH)}{n_{\text{total}}} $$

$$X_{\text{ethanol}} = \frac{2.00}{4.47} = 0.45$$

This means 45% of the total moles in the mixture are from ethanol.

Mole Fraction of Acetic Acid (CH₃COOH)

$$X_{\text{acetic acid}} = \frac{n(CH_3COOH)}{n_{\text{total}}} $$

$$X_{\text{acetic acid}} = \frac{1.80}{4.47} = 0.40$$

This means 40% of the total moles in the mixture are from acetic acid.

Final Answer

• Mole fraction of water = 0.15
• Mole fraction of ethanol = 0.45
• Mole fraction of acetic acid = 0.40

Interpretation

• The solution consists of 15% water molecules, meaning that out of every 100 moles, 15 are from water.
• 45% of the molecules come from ethanol, which is the major component.
• 40% of the molecules are from acetic acid.

This approach helps in understanding the relative composition of different substances in a solution.

Do You Know?

• Mole fraction is used in Dalton’s Law of Partial Pressures to determine the contribution of each gas in a mixture.
• It is an important concept in chemical equilibrium calculations.
• It is preferred over molarity and molality in cases where temperature fluctuations are significant.

Worksheet

1. Calculate the mole fraction of ethanol in a solution containing 2 moles of ethanol and 3 moles of water.
2. A gas mixture contains 0.5 moles of oxygen, 1.5 moles of nitrogen, and 2 moles of argon. Find the mole fraction of nitrogen.
3. If the mole fraction of a solute in a solution is 0.2, what is the mole fraction of the solvent?

Test Paper (Marks: 10)

1. Define mole fraction and write its formula. (2 marks)
2. A solution is made by dissolving 5 moles of glucose in 20 moles of water. Find the mole fraction of glucose and water. (3 marks)
3. Why is mole fraction preferred over molarity in some cases? (2 marks)
4. Can the mole fraction of a solute be greater than 1? Justify your answer. (3 marks)

Quick Revision Points

• Mole fraction $X_A$ is calculated as: $X_A = \frac{n_A}{n_A + n_B}$.
• It is dimensionless and always between 0 and 1.
• Sum of mole fractions in a solution is always 1.
• Mole fraction does not depend on temperature.
• It is extensively used in Raoult’s Law, colligative properties, and gas laws.

This detailed post ensures clarity and depth in understanding mole fraction, making it useful for JEE, NEET, and CBSE exams.