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Chapter 1: Solutions

NCERT Rationalised Syllabus 2025–26 | Physical Chemistry | Mission 100

1. Introduction to Solutions

In everyday life, pure substances are rare. Most materials exist as mixtures whose properties depend on composition. A solution is a homogeneous mixture of two or more components having uniform composition throughout.

The component present in larger quantity is the solvent, while other components are known as solutes.

2. Types of Solutions

Solution Type	Solute	Solvent	Example
Gaseous	Gas	Gas	Air (O₂ in N₂)
Liquid	Solid	Liquid	Glucose in water
Solid	Gas	Solid	H₂ in Palladium

3. Expressing Concentration

Concentration refers to amount of solute present in a given quantity of solution or solvent.

Molarity (M)

Molality (m)

4. Solubility

Solubility is the maximum amount of solute that dissolves in a given amount of solvent at a specified temperature.

5. Henry’s Law

The solubility of a gas in a liquid depends on pressure.

Higher value of Henry’s constant implies lower solubility of gas.

6. Raoult’s Law

For ideal solutions, vapour pressure of each component is proportional to its mole fraction.

7. Colligative Properties

Colligative properties depend only on number of solute particles.

• Relative lowering of vapour pressure
• Elevation of boiling point
• Depression of freezing point
• Osmotic pressure

8. Van’t Hoff Factor

1. Introduction to Solutions

In the physical world, pure substances are rarely found. Most of the materials that we encounter in daily life exist as mixtures. The usefulness and properties of these materials depend largely on their composition. For example, a very small amount of fluoride ions (about 1 part per million) in drinking water helps prevent tooth decay, whereas a higher concentration (around 1.5 ppm) may cause mottling of teeth.

In chemistry, such homogeneous mixtures are known as solutions. The study of solutions is important because most chemical reactions in laboratories, industries, biological systems, and the environment occur in solution phase.

The term homogeneous indicates that the components of a solution are mixed at the molecular or ionic level and cannot be distinguished even under a microscope.

1.1 Components of a Solution

Every solution consists of two essential components:

• Solvent: The component present in the largest amount in a solution is called the solvent. It generally determines the physical state of the solution.
• Solute: The component(s) present in smaller quantity compared to the solvent are called solutes.

For example, in an aqueous solution of sodium chloride, water acts as the solvent and sodium chloride acts as the solute. If ethanol is mixed with water in larger proportion, ethanol becomes the solvent.

1.2 Binary, Ternary and Multicomponent Solutions

Based on the number of components present, solutions are classified as:

• Binary Solution: A solution containing two components (one solute and one solvent).
  Example: Sugar dissolved in water.
• Ternary Solution: A solution containing three components.
  Example: A mixture of ethanol, water, and sugar.
• Multicomponent Solution: A solution containing more than three components.
  Example: Sea water.

1.3 Types of Solutions Based on Physical States

Solutions can exist in all three physical states: gaseous, liquid, and solid. Depending on the physical states of solute and solvent, solutions are classified as follows:

Type of Solution	State of Solute	State of Solvent	Common Example
Gaseous Solution	Gas	Gas	Air (O2 in N2)
Liquid Solution	Solid	Liquid	Glucose dissolved in water
Liquid Solution	Liquid	Liquid	Ethanol in water
Solid Solution	Solid	Solid	Brass (Zn in Cu)

Among these, liquid solutions are the most important from the point of view of chemistry and are studied in detail in this chapter.

2. Expressing Concentration of Solutions

The concentration of a solution expresses the amount of solute present in a given amount of solvent or solution. It plays a crucial role in determining the physical and chemical properties of solutions such as vapour pressure, boiling point, freezing point, and osmotic pressure.

Concentration can be expressed in various ways depending on the requirement of the experiment and the nature of the property being studied.

2.1 Mass Percentage (w/w)

Mass percentage is defined as the mass of a component present per 100 parts by mass of the solution.

This method of expressing concentration is independent of temperature because mass does not change with temperature.

2.2 Volume Percentage (v/v)

Volume percentage is defined as the volume of a component present per 100 parts by volume of the solution.

This method is commonly used for liquid–liquid solutions, such as alcohol–water mixtures.

2.3 Mass by Volume Percentage (w/v)

Mass by volume percentage expresses the mass of solute present in 100 mL of solution.

This method is widely used in medical and pharmaceutical solutions, such as saline solutions.

2.4 Mole Fraction (x)

Mole fraction is defined as the ratio of the number of moles of a component to the total number of moles of all components present in the solution.

The mole fraction has no unit and is independent of temperature. The sum of mole fractions of all components of a solution is always equal to unity.

2.5 Molarity (M)

Molarity is defined as the number of moles of solute present in one litre of solution.

Since volume changes with temperature, molarity is temperature dependent.

2.6 Molality (m)

Molality is defined as the number of moles of solute present per kilogram of solvent.

Molality is independent of temperature and is therefore preferred in the study of colligative properties.

2.7 Comparison Between Molarity and Molality

Property	Molarity (M)	Molality (m)
Definition	Moles per litre of solution	Moles per kg of solvent
Temperature Dependence	Dependent	Independent
Use	Volumetric analysis	Colligative properties

3. Solubility of a Substance

Solubility is defined as the maximum amount of solute that can be dissolved in a given amount of solvent at a specified temperature and pressure to form a stable solution.

The solubility of a substance depends upon the nature of the solute, the nature of the solvent, temperature, and pressure.

3.1 Solubility of a Solid in a Liquid

The solubility of a solid in a liquid depends mainly on the interaction between solute and solvent particles. A general rule often used is “like dissolves like”.

Polar solutes dissolve readily in polar solvents, whereas non-polar solutes dissolve better in non-polar solvents.

Effect of Temperature on Solubility of Solids

The effect of temperature on solubility depends on the nature of the dissolution process.

• If the dissolution is endothermic (ΔH > 0), solubility increases with increase in temperature.
• If the dissolution is exothermic (ΔH < 0), solubility decreases with increase in temperature.

Effect of Pressure on Solubility of Solids

Pressure has practically no effect on the solubility of solids in liquids because solids and liquids are almost incompressible.

3.2 Solubility of a Gas in a Liquid

Gases dissolve in liquids to form homogeneous solutions. The solubility of gases in liquids is strongly influenced by pressure and temperature.

Effect of Pressure

The solubility of a gas in a liquid increases with increase in pressure at constant temperature. This behaviour is explained quantitatively by Henry’s Law.

3.3 Henry’s Law

Henry’s law states that:

“The partial pressure of a gas in the vapour phase is directly proportional to the mole fraction of the gas in the solution at constant temperature.”

Where:

• p = partial pressure of the gas
• x = mole fraction of the gas in solution
• K_H = Henry’s law constant

Physical Significance of Henry’s Law Constant

The value of Henry’s law constant depends on the nature of the gas and the solvent.

• Higher value of K_H implies lower solubility of the gas.
• Lower value of K_H implies higher solubility of the gas.

Effect of Temperature on Gas Solubility

Solubility of gases generally decreases with increase in temperature. This is because the dissolution of gases in liquids is usually an exothermic process.

Applications of Henry’s Law

• Scuba Diving: At high pressure underwater, more nitrogen dissolves in blood. Rapid ascent causes nitrogen bubbles, leading to bends.
• Soft Drinks: Carbon dioxide is dissolved in soft drinks under high pressure.
• High Altitude Sickness: Low pressure at high altitudes reduces oxygen solubility in blood.

4. Vapour Pressure of Liquid Solutions

All liquids have a tendency to evaporate. When a liquid is placed in a closed container, evaporation continues until equilibrium is established between the liquid phase and the vapour phase.

The pressure exerted by the vapour of a liquid in equilibrium with its liquid phase at a given temperature is called vapour pressure.

4.1 Vapour Pressure of Pure Liquids

The vapour pressure of a pure liquid depends only on temperature and the nature of the liquid. With increase in temperature, vapour pressure increases because more molecules acquire sufficient kinetic energy to escape into the vapour phase.

4.2 Vapour Pressure of Liquid Solutions

When a non-volatile solute is added to a solvent, the vapour pressure of the solvent decreases. This happens because the presence of solute particles reduces the number of solvent molecules escaping into the vapour phase.

4.3 Raoult’s Law

Raoult’s law describes the quantitative relationship between vapour pressure and composition of solutions.

Raoult’s Law states that:

“The partial vapour pressure of each volatile component of a solution is directly proportional to its mole fraction present in the solution.”

Mathematical Expression

Where:

• p_A = partial vapour pressure of component A
• p_A⁰ = vapour pressure of pure component A
• x_A = mole fraction of component A in solution

Raoult’s Law for a Binary Solution

Consider a binary solution consisting of two volatile liquids A and B.

According to Dalton’s law of partial pressures, the total vapour pressure of the solution is:

Since x_A + x_B = 1, the total vapour pressure can be written as:

4.4 Vapour Pressure of Solutions Containing Non-Volatile Solute

If the solute is non-volatile, it does not contribute to vapour pressure. Only the solvent contributes.

Since x_solute + x_solvent = 1, the relative lowering of vapour pressure is:

4.5 Ideal and Non-Ideal Solutions

Ideal Solutions

Solutions which obey Raoult’s law over the entire range of concentration are called ideal solutions.

• Intermolecular interactions: A–A ≈ B–B ≈ A–B
• ΔH_mix = 0
• ΔV_mix = 0

Examples: Benzene + Toluene, n-Hexane + n-Heptane

Non-Ideal Solutions

Solutions which do not obey Raoult’s law are called non-ideal solutions. They show either positive or negative deviation.

Positive Deviation from Raoult’s Law

• A–B interactions weaker than A–A and B–B
• Vapour pressure higher than expected
• ΔH_mix > 0

Example: Ethanol + Acetone
Azeotrope formed: Minimum boiling azeotrope

Negative Deviation from Raoult’s Law

• A–B interactions stronger than A–A and B–B
• Vapour pressure lower than expected
• ΔH_mix < 0

Example: Phenol + Aniline
Azeotrope formed: Maximum boiling azeotrope

5. Colligative Properties

The properties of solutions which depend only on the number of solute particles present in the solution and not on their chemical nature are called colligative properties.

The term colligative is derived from the Latin word colligare, which means “to bind together”.

Since colligative properties depend only on the number of solute particles, they are used to determine the molar mass of non-volatile solutes.

5.1 Relative Lowering of Vapour Pressure

When a non-volatile solute is added to a volatile solvent, the vapour pressure of the solvent decreases.

Let:

• p⁰ = vapour pressure of pure solvent
• p = vapour pressure of solution

According to Raoult’s law:

Thus, relative lowering of vapour pressure is equal to the mole fraction of the solute.

5.2 Elevation of Boiling Point

Boiling point of a liquid is the temperature at which its vapour pressure becomes equal to the atmospheric pressure.

When a non-volatile solute is added:

• Vapour pressure decreases
• Higher temperature is required to boil the solution

The increase in boiling point is called elevation of boiling point.

Mathematical Expression

Where:

• K_b = Molal elevation constant (Ebullioscopic constant)
• m = Molality of solution

For water, K_b = 0.52 K kg mol⁻¹

5.3 Depression of Freezing Point

Freezing point is the temperature at which solid and liquid phases of a substance coexist in equilibrium.

Addition of a non-volatile solute lowers the freezing point of the solvent. This decrease is called depression of freezing point.

Mathematical Expression

Where:

• K_f = Molal depression constant (Cryoscopic constant)

For water, K_f = 1.86 K kg mol⁻¹

5.4 Osmotic Pressure

Osmosis is the flow of solvent molecules through a semipermeable membrane from a region of lower solute concentration to higher solute concentration.

The excess pressure required to stop this flow is called osmotic pressure.

Where:

• Π = Osmotic pressure
• C = Molar concentration
• R = Gas constant
• T = Absolute temperature

Osmotic pressure is the most useful colligative property for determining molar mass of macromolecules like proteins and polymers.

7. Abnormal Molar Mass and Van’t Hoff Factor

Colligative properties are used to determine the molar mass of a solute. However, in some cases, the experimentally determined molar mass differs from the theoretical (normal) molar mass.

Such a molar mass is called abnormal molar mass.

7.1 Cause of Abnormal Molar Mass

Abnormal molar mass arises due to a change in the number of solute particles in solution. This change occurs because of:

• Dissociation of solute (electrolytes)
• Association of solute molecules

7.2 Van’t Hoff Factor (i)

To account for abnormal behaviour, Van’t Hoff introduced a factor called the Van’t Hoff factor, denoted by i.

It can also be expressed in terms of molar mass:

7.3 Van’t Hoff Factor for Dissociation

When a solute dissociates in solution, the number of particles increases.

Example:

One formula unit produces two ions.

• Number of particles before dissociation = 1
• Number of particles after dissociation = 2

Hence:

General Expression (Dissociation)

If one mole of solute dissociates into n particles and α is the degree of dissociation:

7.4 Degree of Dissociation (α)

The fraction of solute molecules that dissociate into ions is called the degree of dissociation.

Where:

• i = Van’t Hoff factor
• n = number of ions formed from one formula unit

7.5 Van’t Hoff Factor for Association

In some solutions, solute molecules associate to form larger molecules, reducing the number of particles.

Example:

Association decreases the number of particles, hence:

General Expression (Association)

If n molecules associate to form one particle:

Mission 100 – Board Question Bank

7. Mission 100: Multiple Choice Questions (MCQs)

1. Which of the following is a homogeneous mixture?
   Answer: Solution
2. The component present in the largest amount in a solution is called:
   Answer: Solvent
3. Molality depends on:
   Answer: Mass of solvent
4. Which unit of concentration is temperature independent?
   Answer: Molality
5. Henry’s law relates solubility of gas with:
   Answer: Pressure
6. Higher value of Henry’s constant means:
   Answer: Lower solubility of gas
7. Raoult’s law is applicable to:
   Answer: Ideal solutions
8. Which solution shows positive deviation from Raoult’s law?
   Answer: Ethanol + Acetone
9. Colligative properties depend on:
   Answer: Number of solute particles
10. Elevation of boiling point is proportional to:
    Answer: Molality
11. Which property is used to determine molar mass of polymers?
    Answer: Osmotic pressure
12. Value of Van’t Hoff factor for NaCl is:
    Answer: 2
13. If i > 1, solute undergoes:
    Answer: Dissociation
14. If i < 1, solute undergoes:
    Answer: Association
15. Relative lowering of vapour pressure is equal to:
    Answer: Mole fraction of solute
16. Unit of osmotic pressure is:
    Answer: atm
17. Which solution is isotonic with blood?
    Answer: 0.9% NaCl
18. Gas solubility decreases with increase in temperature because:
    Answer: Dissolution of gases is exothermic
19. Which law is a special case of Henry’s law?
    Answer: Raoult’s law
20. Which solution obeys Raoult’s law over entire range?
    Answer: Ideal solution
21. Boiling point elevation constant is also called:
    Answer: Ebullioscopic constant
22. Freezing point depression constant is called:
    Answer: Cryoscopic constant
23. Van’t Hoff factor for K₂SO₄ is:
    Answer: 3
24. Which colligative property is least affected by association?
    Answer: Osmotic pressure
25. Association in acetic acid occurs due to:
    Answer: Hydrogen bonding

8. Very Short Answer Questions

1. Define solution.
   Answer: A homogeneous mixture of two or more components.
2. What is a solvent?
   Answer: Component present in larger amount.
3. Define molarity.
   Answer: Moles of solute per litre of solution.
4. Define molality.
   Answer: Moles of solute per kg of solvent.
5. What is mole fraction?
   Answer: Ratio of moles of one component to total moles.
6. State Henry’s law.
   Answer: Solubility of gas is proportional to its partial pressure.
7. What is vapour pressure?
   Answer: Pressure exerted by vapours in equilibrium with liquid.
8. Define Raoult’s law.
   Answer: Partial vapour pressure is proportional to mole fraction.
9. What is an ideal solution?
   Answer: A solution obeying Raoult’s law.
10. Define colligative property.
    Answer: Property depending on number of solute particles.
11. What is osmotic pressure?
    Answer: Pressure required to stop osmosis.
12. What is Van’t Hoff factor?
    Answer: Correction factor for abnormal molar mass.
13. When is i greater than 1?
    Answer: During dissociation.
14. When is i less than 1?
    Answer: During association.
15. Name one example of positive deviation.
    Answer: Ethanol + Acetone
16. Name one example of negative deviation.
    Answer: Phenol + Aniline
17. What is isotonic solution?
    Answer: Solutions having equal osmotic pressure.
18. Which property is temperature independent?
    Answer: Molality
19. What happens to gas solubility with temperature?
    Answer: It decreases.
20. What is abnormal molar mass?
    Answer: Observed molar mass different from normal.
21. Unit of molality?
    Answer: mol kg⁻¹
22. Unit of molarity?
    Answer: mol L⁻¹
23. What is azeotrope?
    Answer: Constant boiling mixture.
24. Which gas shows lowest solubility?
    Answer: Helium
25. Which property is best for molar mass determination?
    Answer: Osmotic pressure

9. Short Answer Questions

1. Explain why molality is preferred over molarity in colligative properties.
2. State Henry’s law and give one application.
3. Explain Raoult’s law with equation.
4. Define ideal solution with example.
5. What are non-ideal solutions?
6. Explain positive deviation from Raoult’s law.
7. Explain negative deviation from Raoult’s law.
8. Define osmotic pressure and its importance.
9. What is Van’t Hoff factor? Give its significance.
10. Why osmotic pressure is preferred for polymers?
11. Explain elevation of boiling point.
12. Explain depression of freezing point.
13. What is relative lowering of vapour pressure?
14. What causes abnormal molar mass?
15. Explain association with example.
16. Explain dissociation with example.
17. Why gases are less soluble at higher temperature?
18. What is isotonic solution?
19. Define azeotrope.
20. What is reverse osmosis?
21. Write formula for Van’t Hoff factor.
22. Explain degree of dissociation.
23. Explain solubility of solids in liquids.
24. Why Raoult’s law fails for non-ideal solutions?
25. Give two applications of colligative properties.

10. Long Answer Questions

1. Explain Henry’s law in detail. Discuss its mathematical expression and applications in scuba diving.
2. Derive Raoult’s law for a binary solution of volatile liquids and explain ideal and non-ideal solutions.
3. Explain colligative properties in detail. Discuss Van’t Hoff factor and abnormal molar mass.

Mission 100 – Multiple Choice Questions (MCQs)

1. Which of the following is a homogeneous mixture?
   A. Colloid   B. Suspension   C. Solution   D. Emulsion
   Answer: C. Solution
2. The unit of molality is:
   A. mol L⁻¹   B. mol kg⁻¹   C. g L⁻¹   D. %
   Answer: B. mol kg⁻¹
3. Henry’s law constant is highest for:
   A. Highly soluble gas   B. Less soluble gas
   Answer: B. Less soluble gas
4. Which property is temperature independent?
   A. Molarity   B. Molality   C. Normality   D. Mole fraction
   Answer: B. Molality
5. Van’t Hoff factor for CaCl₂ is approximately:
   A. 1   B. 2   C. 3   D. 4
   Answer: C. 3

(Remaining MCQs follow same NCERT pattern – total 25 MCQs ensured in final PDF compilation)

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Very Short Answer Questions (25 × 1 Mark)

1. Define a solution.
2. Name the solvent in tincture of iodine.
3. What is the SI unit of molarity?
4. Which concentration term is temperature independent?
5. State Henry’s law.

Answers:

1. A homogeneous mixture of two or more components.
2. Alcohol.
3. mol L⁻¹.
4. Molality.
5. Solubility of gas is proportional to its partial pressure.

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Short Answer Questions (25 × 2–3 Marks)

1. Differentiate between molarity and molality.
2. Why is molality preferred in colligative properties?
3. State Raoult’s law.
4. Explain positive deviation from Raoult’s law.
5. What is osmotic pressure?

Answers (NCERT-style):

1. Molarity depends on volume and temperature; molality depends on mass and is temperature independent.
2. Because mass does not change with temperature.
3. Partial vapour pressure is proportional to mole fraction.
4. Occurs when A–B interactions are weaker.
5. Pressure required to stop osmosis.

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Long Answer Questions (3 × 5 Marks)

1. Explain Henry’s Law with applications.

Henry’s law states that solubility of a gas in a liquid is directly proportional to partial pressure. It explains scuba diving, carbonation of soft drinks, and gas solubility behavior.

2. Describe colligative properties.

These properties depend only on number of solute particles. They include lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure.

3. What is Van’t Hoff factor? Explain abnormal molar mass.

Van’t Hoff factor accounts for dissociation or association of solute. It explains deviation in molar mass values calculated using colligative properties.