Chemistry Solutions JEE Syllabus

Pure substances often behave differently when they are mixed with other substances. A small amount of solute can change the boiling point, freezing point, vapor pressure, and many other physical properties of a liquid. Solutions explores these changes and explains the principles that control the behavior of homogeneous mixtures.

Knowing what Solutions covers before starting the chapter can make revision more effective. The chapter introduces concentration terms, solubility, Raoult's law, ideal and non-ideal solutions, colligative properties, and osmotic pressure while building the concepts needed for molecular mass calculations and JEE-level numerical problems.

Types of Solutions and Concentration Terms

A solution is a homogeneous mixture of two or more substances. The component present in a larger amount is called the solvent, while the substance present in a smaller amount is called the solute.

Composition of Solutions and Methods of Expressing Concentration

Solutions may exist in different physical states depending on the nature of the solute and solvent.

Common examples include:

• Gas in gas: Air

• Gas in liquid: Oxygen in water

• Liquid in liquid: Ethanol in water

• Solid in liquid: Salt in water

• Solid in solid: Brass

The composition of a solution can be expressed in several ways.

Mass Percentage

Mass % = (Mass of Solute / Mass of Solution) × 100

Volume Percentage

Volume % = (Volume of Solute / Volume of Solution) × 100

Mass by Volume Percentage

Mass/Volume % = (Mass of Solute in g / Volume of Solution in mL) × 100

Parts Per Million (ppm)

ppm = (Amount of Solute / Amount of Solution) × 10⁶

This unit is commonly used for very dilute solutions.

Mole Fraction

Mole Fraction (X) = Number of Moles of Component / Total Number of Moles

For a binary solution:

X₁ + X₂ = 1

Molarity (M)

M = Moles of Solute / Volume of Solution in Litres

Molarity depends on temperature because the volume of a solution changes with temperature.

Molality (m)

m = Moles of Solute / Mass of Solvent in kg

Molality is temperature independent and is widely used in colligative property calculations.

The relationship between different concentration terms is frequently used in JEE numerical problems.

Solubility and Vapor Pressure of Liquid Solutions

The amount of solute that can dissolve in a solvent is limited by solubility, while the tendency of solvent molecules to escape into the vapor phase is measured by vapor pressure.

Solubility Equilibrium and Raoult's Law

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

The solubility of gases in liquids is affected by pressure.

Henry's Law

The partial pressure of a gas above a solution is directly proportional to its mole fraction in the solution.

p = KHx

where:

• p = partial pressure

• KH = Henry's law constant

• x = mole fraction of the gas

Henry's Law explains many practical phenomena, such as:

• Carbonated beverages.

• Breathing at high altitudes.

• Deep-s diving.

The vapor pressure of a pure liquid depends on temperature. When a non-volatile solute is dissolved in a solvent, the vapor pressure of the solvent decreases.

According to Raoult's Law:

P₁ = X₁P₁°

where:

• P₁ = vapor pressure of solvent in solution

• X₁ = mole fraction of solvent

• P₁° = vapor pressure of pure solvent

The lowering of vapor pressure is:

ΔP = P₁° - P₁

Relative lowering of vapor pressure:

ΔP/P₁° = X₂

where X₂ is the mole fraction of the solute.

Raoult's Law forms the basis for the study of colligative properties and molecular mass determination.

Ideal and Non-Ideal Solutions

Not all liquid mixtures behave in the same way. Some solutions obey Raoult's law throughout the entire range of concentration, while others show deviations because of differences in intermolecular forces between their components.

 Intermolecular Interactions and Azeotropes

An ideal solution obeys Raoult's law over the complete range of concentration.

For an ideal binary solution:

PA = XA PA°

PB = XB PB°

Total vapor pressure:

Ptotal = PA + PB

Ideal solutions have the following characteristics:

• They obey Raoult's law at all concentrations.

• ΔHmix = 0

• ΔVmix = 0

• The intermolecular forces between unlike molecules are nearly equal to those between like molecules.

Examples:

• Benzene and toluene

• n-Hexane and n-heptane

Many real solutions, however, do not follow Raoult's law exactly and are called non-ideal solutions.

Positive Deviation from Raoult's Law

In these solutions, the attraction between unlike molecules is weaker than that between like molecules.

As a result:

• Vapor pressure increases.

• ΔHmix > 0

• ΔVmix > 0

Examples:

• Ethanol and acetone

• Ethanol and cyclohexane

Negative Deviation from Raoult's Law

In these solutions, unlike molecules, attract each other more strongly.

Therefore:

• Vapor pressure decreases.

• ΔHmix < 0

• ΔVmix < 0

Examples:

• Acetone and chloroform

• Nitric acid and water

Certain non-ideal solutions form azeotropes, which boil at a constant temperature and have the same composition in both liquid and vapor phases.

Types of azeotropes:

Minimum Boiling Azeotrope

• Formed by positive deviation.

• Example: Ethanol and water.

Maximum Boiling Azeotrope

• Formed by negative deviation.

• Example: Nitric acid and water.

Questions based on deviations and azeotropes are common in JEE because they combine theory with graphical interpretation.

Colligative Properties of Dilute Solutions

Some physical properties of a solution depend only on the number of dissolved particles and not on their chemical nature. These are called colligative properties.

Properties Depending on the Number of Solute Particles

Colligative properties are particularly important because they help determine the molar mass of unknown substances.

The four colligative properties are:

Relative Lowering of Vapor Pressure

When a non-volatile solute is added to a solvent, fewer solvent molecules escape into the vapor phase.

According to Raoult's law:

ΔP/P° = Xsolute

For dilute solutions:

ΔP/P° = nsolute / nsolvent

Elevation of Boiling Point

The boiling point of a solution is higher than that of the pure solvent.

ΔTb = Kb m

where:

• ΔTb = elevation in boiling point

• Kb = molal elevation constant

• m = molality

Depression of Freezing Point

The freezing point of a solution is lower than that of the pure solvent.

ΔTf = Kf m

where:

• ΔTf = depression in freezing point

• Kf = molal depression constant

This principle is used for:

• Salting icy roads.

• Antifreeze solutions in automobiles.

Osmotic Pressure

Osmosis is the movement of solvent molecules through a semipermeable membrane from a dilute solution to a concentrated solution.

The pressure required to stop this process is called osmotic pressure.

π = CRT

or

π = nRT/V

where:

• π = osmotic pressure

• C = molar concentration

• R = gas constant

• T = absolute temperature

Osmotic pressure is one of the most accurate methods for determining the molar masses of biomolecules because it can be measured even in very dilute solutions.

Abnormal Molar Mass and van't Hoff Factor

Sometimes the experimentally observed colligative properties do not match theoretical values because solute particles may combine together or split into smaller particles.

Association, Dissociation, and van't Hoff Factor

The van't Hoff factor (i) accounts for the change in the number of particles in a solution.

i = Observed Colligative Property / Calculated Colligative Property

or

i = Normal Molar Mass / Abnormal Molar Mass

If a solute dissociates:

i > 1

Examples:

• NaCl

• KCl

• CaCl₂

If solute particles associate:

i < 1

Examples:

• Acetic acid in benzene

• Benzoic acid in benzene

The modified colligative property equations become:

ΔTb = iKb m

ΔTf = iKf m

π = iCRT

Relative lowering of vapor pressure:

ΔP/P° = iXsolute

Degree of dissociation (α) and degree of association are often calculated using the van't Hoff factor.

For dissociation:

i = 1 + (n - 1)α

For association:

i = 1 - α + α/n

where n represents the number of particles formed or associated.

These relationships are frequently used in JEE numerical problems involving electrolytes and associated molecules.

Molecular Mass Determination and Applications of Solutions

The concepts developed in this chapter are widely used in chemistry, biology, and industry for determining unknown molecular masses and understanding the behavior of mixtures.

Practical Applications and Important Relationships

Colligative properties provide experimental methods for determining molar masses of dissolved substances.

Molecular masses can be determined using:

• Relative lowering of vapor pressure.

• Elevation of boiling point.

• Depression of freezing point.

• Osmotic pressure.

Among these, osmotic pressure is especially useful for proteins and polymers because they decompose before boiling or freezing point methods can be applied.

The study of solutions also explains many natural and industrial processes, such as:

• Preservation of food using concentrated salt or sugar solutions.

• Reverse osmosis for water purification.

• Preparation of pharmaceutical solutions.

• Manufacture of alloys.

• Biological transport of nutrients and gases.

Many concepts from this chapter are connected with Chemical Thermodynamics, Electrochemistry, and Ionic Equilibrium, making Solutions an important part of physical chemistry.