Chapter 1: Solutions

Solutions and Concentration

Definition and Constituents

A solution is a homogeneous mixture of two or more pure substances. It consists of two main constituents:

• Solute: The substance dissolved in lesser amount, e.g., sugar or salt in water.
• Solvent: The substance in which the solute is dissolved in larger amount, e.g., water or milk.

The solvent determines the physical state of the solution.

Types of Solutions

Solutions can be classified based on the physical states of solute and solvent. There are nine possible types:

• Solid in solid: e.g., brass
• Solid in liquid: e.g., sugar in water
• Solid in gas: e.g., camphor in air
• Liquid in solid: e.g., amalgam
• Liquid in liquid: e.g., alcohol in water
• Liquid in gas: e.g., mist
• Gas in solid: e.g., hydrogen in palladium
• Gas in liquid: e.g., oxygen in water
• Gas in gas: e.g., oxygen in nitrogen

Aqueous solutions have water as solvent, while non-aqueous solutions have solvents other than water.

Concentration of Solutions

Concentration expresses the amount of solute in a given quantity of solution or solvent. Common expressions include:

• Mass percentage (w/w): Mass of solute per 100 g of solution.
• Volume percentage (v/v): Volume of solute per 100 mL of solution.
• Mass by volume percentage (w/v): Mass of solute per 100 mL of solution.
• Parts per million (ppm): Parts of solute per million parts of solution, used for trace quantities.
• Mole fraction: Ratio of moles of a component to total moles in solution.
• Molarity (M): Moles of solute per litre of solution.
• Molality (m): Moles of solute per kilogram of solvent.
• Normality (N): Gram equivalents of solute per litre of solution.

Solubility of Gases and Henry’s Law

Solubility is the maximum amount of a solute that can dissolve in 100 g of solvent at a given temperature. Factors affecting solubility include the nature of the solute and solvent, temperature, and pressure.

Henry’s Law states that the mass of a gas dissolved in a liquid at constant temperature is proportional to the pressure of the gas above the liquid. Mathematically, p = K_H × x, where p is partial pressure, x is mole fraction, and K_H is Henry’s constant.

Applications include carbonation of soft drinks, scuba diving gas mixtures, and the effect of altitude on oxygen levels.

Solved Examples

Example 1: Calculating Nitrogen Gas Solubility Using Henry’s Law

Given: Partial pressure of nitrogen = 0.987 bar, Henry’s constant = 76480 bar, temperature = 293 K.

Using Henry’s law:

x = p/K_H = 0.987/76480 = 1.29 × 10^-5

Thus, the mole fraction of nitrogen dissolved in water is 1.29 × 10^-5.

Amount dissolved in 1 L water = x × 1000 = 0.0129 mmol/L.

Practice Set

• Level 1: Define solute and solvent with examples.
• Level 2: Explain the difference between molarity and molality.
• Level 3: Calculate the mole fraction of a gas dissolved in a liquid given its partial pressure and Henry’s constant.

Answer Key

• Level 1: Solute is the substance dissolved in lesser amount (e.g., sugar), and solvent is the substance in which the solute dissolves in larger amount (e.g., water).
• Level 2: Molarity is moles of solute per litre of solution; molality is moles of solute per kilogram of solvent. Molarity depends on temperature, while molality does not.
• Level 3: Use Henry’s law: mole fraction = partial pressure / Henry’s constant.

Raoult’s Law

Vapour Pressure and Factors

Vapour pressure is the pressure exerted by vapours over a liquid at equilibrium at constant temperature. It depends on:

• Nature of liquid: Liquids with weak intermolecular forces have higher vapour pressure.
• Temperature: Vapour pressure increases with temperature.

Raoult’s Law for Volatile Liquids

For a solution of volatile liquids, the partial vapour pressure of each component is proportional to its mole fraction:

p_A = p°_A x_A

p_B = p°_B x_B

For a binary solution, the total vapour pressure is the sum of the partial pressures:

P_total = p_A + p_B = p°_A x_A + p°_B x_B

where p°_A and p°_B are the vapour pressures of the pure components, and x_A and x_B are their mole fractions.

Raoult’s Law for Non-Volatile Solute

For a solution containing a non-volatile solute, only the solvent contributes to vapour pressure. The vapour pressure of the solution is lower than that of the pure solvent and is given by:

p_A = p°_A x_A

The relative lowering of vapour pressure is:

(p°_A - p_A) / p°_A = x_B

where x_B is the mole fraction of the solute.

For dilute solutions, if n_A is the number of moles of solvent and n_B is the number of moles of solute, then:

x_B = n_B / (n_A + n_B)

and for very dilute solutions, x_B ≈ n_B / n_A.

Ideal and Non-Ideal Solutions

Ideal solutions obey Raoult’s law over the entire range of concentrations. In such solutions, the intermolecular forces between like and unlike molecules are nearly the same, so there is no heat or volume change on mixing.

Non-ideal solutions do not obey Raoult’s law and show deviations:

• Positive deviation: A–B interactions are weaker than A–A and B–B interactions, so vapour pressure is higher than expected. Such solutions may show a decrease in temperature on mixing and are more likely to form minimum boiling azeotropes.
• Negative deviation: A–B interactions are stronger than A–A and B–B interactions, so vapour pressure is lower than expected. Such solutions may show an increase in temperature on mixing and are more likely to form maximum boiling azeotropes.

Azeotropes

Mixtures that boil without change in composition are called azeotropes:

• Minimum boiling azeotropes: positive deviation, boil below components’ boiling points.
• Maximum boiling azeotropes: negative deviation, boil above components’ boiling points.

Solved Examples

Example 2: Vapour Composition Calculation

Given mole fractions and vapour pressures of two volatile liquids A and B, calculate total vapour pressure and vapour phase composition using Raoult’s and Dalton’s laws.

• Let the mole fractions in the liquid phase be xA and xB, with xA + xB = 1.
• By Raoult’s law, the partial vapour pressures are pA = xA p°A and pB = xB p°B, where p°A and p°B are the vapour pressures of pure A and pure B.
• The total vapour pressure is Ptotal = pA + pB.
• By Dalton’s law, the mole fractions in the vapour phase are yA = pA/Ptotal and yB = pB/Ptotal.
• If required, check that yA + yB = 1.

Result: Use Raoult’s law to find the partial pressures, add them to get total pressure, and then apply Dalton’s law to obtain the vapour composition.

Example 2: Vapour Composition Calculation

Given mole fractions and vapour pressures of two volatile liquids A and B, calculate total vapour pressure and vapour phase composition using Raoult’s and Dalton’s laws.

• Let the mole fractions in the liquid phase be xA and xB, with xA + xB = 1.
• By Raoult’s law, the partial vapour pressures are pA = xA p°A and pB = xB p°B, where p°A and p°B are the vapour pressures of pure A and pure B.
• The total vapour pressure is Ptotal = pA + pB.
• By Dalton’s law, the mole fractions in the vapour phase are yA = pA/Ptotal and yB = pB/Ptotal.
• If required, check that yA + yB = 1.

Result: Use Raoult’s law to find the partial pressures, add them to get total pressure, and then apply Dalton’s law to obtain the vapour composition.

Practice Set

• Level 1: State Raoult’s law for volatile liquids.
• Level 2: Differentiate between ideal and non-ideal solutions with examples.
• Level 3: Explain positive and negative deviations from Raoult’s law with examples.

Answer Key:

• Level 1: Raoult’s law states that for a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction in the solution. Thus, pA = xA p°A and pB = xB p°B, where p°A and p°B are the vapour pressures of the pure components.
• Level 2: An ideal solution obeys Raoult’s law over the entire range of composition; it has similar intermolecular forces between like and unlike molecules and shows no heat or volume change on mixing. Examples: benzene + toluene, n-hexane + n-heptane. A non-ideal solution does not obey Raoult’s law, shows deviation from ideal behaviour, and usually has heat and/or volume change on mixing. Examples: acetone + chloroform, ethanol + water.
• Level 3: Positive deviation occurs when A–B interactions are weaker than A–A and B–B interactions, so vapour pressure is higher than predicted by Raoult’s law; examples include ethanol + acetone and carbon disulphide + acetone. Negative deviation occurs when A–B interactions are stronger than A–A and B–B interactions, so vapour pressure is lower than predicted by Raoult’s law; examples include chloroform + acetone and nitric acid + water.

Answer Key

• Level 1: Partial vapour pressure of a component equals its mole fraction times vapour pressure of pure component. For a component A, p_A = x_Ap°_A.
• Level 2: Ideal solutions obey Raoult’s law; non-ideal solutions do not. Examples: ideal - benzene and toluene; non-ideal - water and ethanol.
• Level 3: Positive deviation occurs when A–B interactions are weaker; negative deviation occurs when A–B interactions are stronger than A–A and B–B interactions.

Colligative Properties

Definition and Types

Colligative properties depend only on the number of solute particles, not their nature. They include:

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

Relative Lowering of Vapour Pressure

It is the ratio of lowering of vapour pressure to vapour pressure of pure solvent, and is equal to the mole fraction of solute. For a dilute solution,

(p° − p) / p° = x₂

where p° is the vapour pressure of the pure solvent, p is the vapour pressure of the solution, and x₂ is the mole fraction of the solute. This property depends only on the number of solute particles present.

For an ideal solution, the vapour pressure of the solvent is also given by Raoult’s law:

p = x₁p°

where x₁ is the mole fraction of the solvent. Hence,

(p° − p) / p° = x₂

This relation is valid for dilute solutions containing a non-volatile solute.

Elevation of Boiling Point

The boiling point of a solution is higher than that of pure solvent. The elevation is proportional to molality:

ΔT_b = K_b m

where ΔT_b is the elevation in boiling point, K_b is the ebullioscopic constant of the solvent, and m is the molality of the solution.

Since boiling occurs when the vapour pressure of the liquid equals atmospheric pressure, the addition of a non-volatile solute lowers the vapour pressure and therefore raises the boiling point.

The value of K_b depends on the nature of the solvent.

Depression of Freezing Point

The freezing point of a solution is lower than that of pure solvent. The depression is proportional to molality:

ΔT_f = K_f m

where ΔT_f is the depression in freezing point, K_f is the cryoscopic constant of the solvent, and m is the molality of the solution.

The addition of a solute interferes with the formation of the solid solvent lattice, so the solution freezes at a lower temperature.

The value of K_f depends on the nature of the solvent.

Osmosis and Osmotic Pressure

Osmosis is the flow of solvent through a semipermeable membrane from pure solvent or a dilute solution to a concentrated solution. Osmotic pressure is the pressure required to stop this flow completely. It is a colligative property and is proportional to molar concentration:

π = C R T

where π is osmotic pressure, C is molar concentration, R is the gas constant, and T is the absolute temperature.

Osmotic pressure is especially useful for determining the molar mass of solutes, particularly macromolecules such as proteins and polymers.

For dilute solutions, osmotic pressure can also be written as:

πV = nRT

where V is the volume of solution and n is the number of moles of solute.

Reverse Osmosis

Applying pressure greater than osmotic pressure reverses osmosis, used for water purification.

In reverse osmosis, solvent passes from the concentrated solution to the dilute side or pure solvent side when external pressure exceeds the osmotic pressure. It is widely used for desalination and purification of drinking water.

Abnormal Molecular Mass and Van’t Hoff Factor

Abnormal molecular mass occurs when the molecular mass calculated from colligative properties differs from the theoretical molecular mass due to association or dissociation of solute particles.

When solute particles associate, the number of particles decreases and the observed colligative property is smaller than expected. When solute particles dissociate, the number of particles increases and the observed colligative property is larger than expected.

The extent of association or dissociation is expressed by the Van’t Hoff factor.

For a solute undergoing association or dissociation, the colligative property becomes:

observed colligative property = i × calculated colligative property

Thus, the molar mass obtained from colligative property data is affected by the value of i.

Example 3: Molecular Mass from Freezing Point Depression

Given: volume of benzene = 75 mL, density of benzene = 0.879 g/mL, mass of solute = 0.721 g, freezing point of pure benzene = 5.51 °C, freezing point of solution = 5.03 °C, and K_f for benzene = 5.12 K kg mol⁻¹.

Mass of benzene = density × volume = 0.879 × 75 = 65.925 g = 0.06593 kg

Depression in freezing point, ΔT_f = 5.51 − 5.03 = 0.48 °C

Using ΔT_f = K_f m,

0.48 = 5.12 × m

So, m = 0.48 / 5.12 = 0.09375 mol kg⁻¹

Let molecular mass of the solute be A.

Moles of solute = 0.721 / A

Molality = moles of solute / mass of benzene in kg = (0.721 / A) / 0.06593

0.09375 = 0.721 / (A × 0.06593)

A = 0.721 / (0.09375 × 0.06593)

A ≈ 116.7 g mol⁻¹

Van’t Hoff Factor

The Van’t Hoff factor is the ratio of the observed colligative property to the calculated colligative property. It indicates the degree of dissociation or association of solute particles.

i = observed value / calculated value

For example, for elevation of boiling point,

i = (ΔT_b)_obs / (ΔT_b)_cal

For dissociation, i > 1. For association, i < 1.

If a solute neither dissociates nor associates, then i = 1.

It is also related to the extent of dissociation or association. For electrolytes, a higher value of i indicates greater dissociation into ions, while for associated substances, a lower value of i indicates association of molecules.

Osmotic Solutions

Hypertonic solution: A solution having higher solute concentration than the surrounding solution separated by a semipermeable membrane.

Hypotonic solution: A solution having lower solute concentration than the surrounding solution.

Isotonic solution: Solutions having equal osmotic pressure; no net osmosis occurs between them.

These terms are useful in understanding the movement of water across cell membranes and in biological systems.

When a cell is placed in a hypertonic solution, water moves out of the cell; in a hypotonic solution, water enters the cell; and in an isotonic solution, there is no net movement of water.

Mnemonics for Colligative Properties

Ravina Likes Vipul Pandey During Fasting Praying. This helps remember the four colligative properties in order:

• R — Relative lowering of vapour pressure
• L — Lowering of freezing point
• V — Vapour pressure relation / elevation of boiling point context
• P — Pressure of osmotic pressure

Ella Bought Pink Orange Pasta. This can be used as a quick reminder for the same list in a simple sequence:

• E — Elevation of boiling point
• B — Boiling point
• P — Pressure osmotic pressure
• O — Osmotic pressure
• P — Property-based memory cue

Note: Mnemonics may vary by teacher or textbook; the main purpose is to recall that colligative properties depend only on the number of solute particles.

Solved Examples

Example 2: Vapour Composition Calculation

Suppose a solution is prepared by mixing two volatile liquids, A and B. Let x_A and x_B be their mole fractions, and p_A and p_B their partial vapour pressures.

According to Raoult’s law:

p_A = p°_A x_A

p_B = p°_B x_B

Using Dalton’s law:

p_total = p_A + p_B = x_A p°_A + x_B p°_B

= (1 − x_B) p°_A + x_B p°_B

= p°_A + (p°_B − p°_A) x_B

The vapour phase composition can be found from:

x_A^(vapour) = p_A/p_total

x_B^(vapour) = p_B/p_total

Thus, the component with the higher vapour pressure will be present in greater proportion in the vapour phase.

Exam point: In a volatile binary solution, the component with the larger partial vapour pressure contributes more to the vapour phase, even if its mole fraction in the liquid is smaller.

Mnemonics for Raoult’s Law

R.L. is Very Poor Student = Most Failure Student

Interpretation: Relative lowering of vapour pressure equals mole fraction of solute.

This helps recall that in a dilute solution of a non-volatile solute, the lowering of vapour pressure depends on the mole fraction of the solute.

Key relation: Relative lowering of vapour pressure = (p° − p)/p° = x_solute

Mnemonics for Ideal Solutions

ISRaeL: Ideal Solution Obeys Raoult's Law

Interpretation: An ideal solution follows Raoult’s law over the entire range of composition and shows no enthalpy or volume change on mixing.

Quick recall: For an ideal solution, A–A, B–B and A–B interactions are nearly equal.

Mnemonics for Non-Ideal Solutions

Nano Scale Device: Not in Other Research Laboratory

Interpretation: Non-ideal solutions do not obey Raoult’s law.

They show either positive or negative deviation because the intermolecular interactions between unlike molecules are not the same as those between like molecules.

Quick recall: If A–B interactions differ significantly from A–A and B–B interactions, the solution is non-ideal.

Positive and Negative Deviations

Positive deviation occurs when A–B interactions are weaker than A–A or B–B, increasing vapour pressure.

Negative deviation occurs when A–B interactions are stronger, decreasing vapour pressure.

In positive deviation, the solution shows higher vapour pressure than expected from Raoult’s law, while in negative deviation it shows lower vapour pressure than expected.

Exam point: Positive deviation favours escape of molecules into vapour phase, whereas negative deviation suppresses vapour pressure because the unlike interactions hold the molecules more strongly.

Graphs of Vapour Pressure vs Mole Fraction

Graph (a) shows positive deviation with vapour pressure higher than ideal; graph (b) shows negative deviation with vapour pressure lower than ideal.

In a graph of vapour pressure versus mole fraction, the ideal solution gives a straight line, while positive and negative deviations show curves above and below this line respectively.

Exam point: In an ideal binary solution, each partial vapour pressure varies linearly with mole fraction, and the total vapour pressure is also a straight-line function of composition.

Example 2: Vapour Composition Calculation

Suppose a solution is prepared by mixing two volatile liquids, A and B. Let x_A and x_B be their mole fractions, and p_A and p_B their partial vapour pressures.

According to Raoult’s law:

p_A = p°_A x_A

p_B = p°_B x_B

Using Dalton’s law:

p_total = p_A + p_B = x_A p°_A + x_B p°_B

= (1 − x_B) p°_A + x_B p°_B

= p°_A + (p°_B − p°_A) x_B

The vapour phase composition can be found from:

x_A^(vapour) = p_A/p_total

x_B^(vapour) = p_B/p_total

Thus, the component with the higher vapour pressure will be present in greater proportion in the vapour phase.

Exam point: In a volatile binary solution, the component with the larger partial vapour pressure contributes more to the vapour phase, even if its mole fraction in the liquid is smaller.

Mnemonics for Raoult’s Law

R.L. is Very Poor Student = Most Failure Student

Interpretation: Relative lowering of vapour pressure equals mole fraction of solute.

This helps recall that in a dilute solution of a non-volatile solute, the lowering of vapour pressure depends on the mole fraction of the solute.

Key relation: Relative lowering of vapour pressure = (p° − p)/p° = x_solute

Mnemonics for Ideal Solutions

ISRaeL: Ideal Solution Obeys Raoult's Law

Interpretation: An ideal solution follows Raoult’s law over the entire range of composition and shows no enthalpy or volume change on mixing.

Quick recall: For an ideal solution, A–A, B–B and A–B interactions are nearly equal.

Mnemonics for Non-Ideal Solutions

Nano Scale Device: Not in Other Research Laboratory

Interpretation: Non-ideal solutions do not obey Raoult’s law.

They show either positive or negative deviation because the intermolecular interactions between unlike molecules are not the same as those between like molecules.

Quick recall: If A–B interactions differ significantly from A–A and B–B interactions, the solution is non-ideal.

Positive and Negative Deviations

Positive deviation occurs when A–B interactions are weaker than A–A or B–B, increasing vapour pressure.

Negative deviation occurs when A–B interactions are stronger, decreasing vapour pressure.

In positive deviation, the solution shows higher vapour pressure than expected from Raoult’s law, while in negative deviation it shows lower vapour pressure than expected.

Exam point: Positive deviation favours escape of molecules into vapour phase, whereas negative deviation suppresses vapour pressure because the unlike interactions hold the molecules more strongly.

Graphs of Vapour Pressure vs Mole Fraction

Graph (a) shows positive deviation with vapour pressure higher than ideal; graph (b) shows negative deviation with vapour pressure lower than ideal.

In a graph of vapour pressure versus mole fraction, the ideal solution gives a straight line, while positive and negative deviations show curves above and below this line respectively.

Exam point: In an ideal binary solution, each partial vapour pressure varies linearly with mole fraction, and the total vapour pressure is also a straight-line function of composition.

Example 2: Vapour Composition Calculation

Suppose a solution is prepared by mixing two volatile liquids, A and B. Let x_A and x_B be their mole fractions, and p_A and p_B their partial vapour pressures.

According to Raoult’s law:

p_A = p°_A x_A

p_B = p°_B x_B

Using Dalton’s law:

p_total = p_A + p_B = x_A p°_A + x_B p°_B

= (1 − x_B) p°_A + x_B p°_B

= p°_A + (p°_B − p°_A) x_B

The vapour phase composition can be found from:

x_A^(vapour) = p_A/p_total

x_B^(vapour) = p_B/p_total

Thus, the component with the higher vapour pressure will be present in greater proportion in the vapour phase.

Exam point: In a volatile binary solution, the component with the larger partial vapour pressure contributes more to the vapour phase, even if its mole fraction in the liquid is smaller.

Mnemonics for Raoult’s Law

R.L. is Very Poor Student = Most Failure Student

Interpretation: Relative lowering of vapour pressure equals mole fraction of solute.

This helps recall that in a dilute solution of a non-volatile solute, the lowering of vapour pressure depends on the mole fraction of the solute.

Key relation: Relative lowering of vapour pressure = (p° − p)/p° = x_solute

Mnemonics for Ideal Solutions

ISRaeL: Ideal Solution Obeys Raoult's Law

Interpretation: An ideal solution follows Raoult’s law over the entire range of composition and shows no enthalpy or volume change on mixing.

Quick recall: For an ideal solution, A–A, B–B and A–B interactions are nearly equal.

Mnemonics for Non-Ideal Solutions

Nano Scale Device: Not in Other Research Laboratory

Interpretation: Non-ideal solutions do not obey Raoult’s law.

They show either positive or negative deviation because the intermolecular interactions between unlike molecules are not the same as those between like molecules.

Quick recall: If A–B interactions differ significantly from A–A and B–B interactions, the solution is non-ideal.

Positive and Negative Deviations

Positive deviation occurs when A–B interactions are weaker than A–A or B–B, increasing vapour pressure.

Negative deviation occurs when A–B interactions are stronger, decreasing vapour pressure.

In positive deviation, the solution shows higher vapour pressure than expected from Raoult’s law, while in negative deviation it shows lower vapour pressure than expected.

Exam point: Positive deviation favours escape of molecules into vapour phase, whereas negative deviation suppresses vapour pressure because the unlike interactions hold the molecules more strongly.

Graphs of Vapour Pressure vs Mole Fraction

Graph (a) shows positive deviation with vapour pressure higher than ideal; graph (b) shows negative deviation with vapour pressure lower than ideal.

In a graph of vapour pressure versus mole fraction, the ideal solution gives a straight line, while positive and negative deviations show curves above and below this line respectively.

Exam point: In an ideal binary solution, each partial vapour pressure varies linearly with mole fraction, and the total vapour pressure is also a straight-line function of composition.

Quick Reference Table

• Solution: A homogeneous mixture of two or more pure substances.
• Solute: The substance dissolved in lesser amount.
• Solvent: The substance in which the solute is dissolved in larger amount; it generally decides the physical state of the solution.
• Types of solutions: Classified by the physical states of solute and solvent, such as solid in liquid, liquid in liquid, gas in liquid, solid in solid and gas in gas.
• Aqueous solution: A solution in which water is the solvent.
• Non-aqueous solution: A solution in which a solvent other than water is used.
• Mass percentage (w/w): Mass of solute per 100 g of solution.
• Volume percentage (v/v): Volume of solute per 100 mL of solution.
• Mass by volume percentage (w/v): Mass of solute per 100 mL of solution.
• Parts per million (ppm): Parts of solute per million parts of solution; used for trace quantities.
• Mole fraction: Moles of a component divided by total moles of all components in the solution.
• Molarity (M): Moles of solute per litre of solution.
• Molality (m): Moles of solute per kilogram of solvent.
• Normality (N): Gram equivalents of solute per litre of solution.
• Solubility: The maximum amount of solute dissolved in 100 g of solvent at a given temperature.
• Henry’s law: At constant temperature, the mass of a gas dissolved in a liquid is proportional to the pressure of the gas above the liquid.
• Henry’s law equation: p = K_H × x, where p is partial pressure, x is mole fraction and K_H is Henry’s constant.
• Relative lowering of vapour pressure: (p° − p)/p° = x₂ for a dilute solution of a non-volatile solute.
• Raoult’s law for volatile liquids: pA = p°A xA and pB = p°B xB.
• Relative lowering for non-volatile solute: The lowering of vapour pressure divided by the vapour pressure of pure solvent equals the mole fraction of solute.
• Ideal solution: Obeys Raoult’s law over the entire range of composition and shows similar intermolecular forces between like and unlike molecules.
• Non-ideal solution: Deviates from Raoult’s law and may show positive or negative deviation.
• Positive deviation: Occurs when A–B interactions are weaker than A–A and B–B interactions; vapour pressure increases.
• Negative deviation: Occurs when A–B interactions are stronger than A–A and B–B interactions; vapour pressure decreases.
• Azeotrope: A mixture that boils without change in composition.
• Minimum boiling azeotrope: An azeotrope showing positive deviation and boiling below the component boiling points.
• Maximum boiling azeotrope: An azeotrope showing negative deviation and boiling above the component boiling points.
• Colligative properties: Properties that depend only on the number of solute particles, not on their nature.
• Four colligative properties: Relative lowering of vapour pressure, elevation of boiling point, depression of freezing point and osmotic pressure.
• Elevation of boiling point: ΔT_b = K_bm.
• Depression of freezing point: ΔT_f = K_fm.
• Osmotic pressure: π = C R T, where C is molar concentration, R is the gas constant and T is the absolute temperature.
• Osmosis: Flow of solvent through a semipermeable membrane from pure solvent or a dilute solution to a concentrated solution.
• Reverse osmosis: Application of pressure greater than osmotic pressure to reverse the direction of osmosis.
• Abnormal molecular mass: The molecular mass calculated from colligative properties differs from the theoretical molecular mass because of association or dissociation.
• Van’t Hoff factor: i = observed colligative property / calculated colligative property.
• Dissociation: Increases the number of particles and gives i > 1.
• Association: Decreases the number of particles and gives i < 1.
• Hypertonic solution: A solution having higher solute concentration than the surrounding solution.
• Hypotonic solution: A solution having lower solute concentration than the surrounding solution.
• Isotonic solution: Solutions having equal osmotic pressure; no net osmosis occurs between them.
• Key exam idea: Many numerical problems in solutions depend on correct use of mole fraction, molarity, molality, Henry’s law, Raoult’s law and colligative-property relations.

Common Mistakes and Misconceptions

• Confusing solute and solvent: The solute is present in the lesser amount and is dissolved, while the solvent is present in the larger amount and dissolves the solute.
• Mixing up concentration terms: Molarity means moles of solute per litre of solution, molality means moles of solute per kilogram of solvent, and normality means gram equivalents of solute per litre of solution.
• Using molarity where molality is needed: Molarity changes with temperature because volume changes, but molality does not because it is based on mass of solvent.
• Confusing mole fraction with percentage concentration: Mole fraction is the ratio of moles of a component to total moles in the solution, not mass per 100 parts or volume per 100 parts.
• Misapplying Henry’s law: At constant temperature, the solubility of a gas in a liquid is proportional to its partial pressure above the liquid; the relation is p = K H × x.
• Applying Raoult’s law to the wrong case: For volatile liquids, each component’s partial vapour pressure is proportional to its mole fraction; for a non-volatile solute, the relative lowering of vapour pressure equals the mole fraction of the solute.
• Confusing ideal and non-ideal solutions: Ideal solutions obey Raoult’s law over the entire range of composition, while non-ideal solutions show positive or negative deviation.
• Reversing positive and negative deviation: Positive deviation occurs when A–B interactions are weaker than A–A and B–B interactions, while negative deviation occurs when A–B interactions are stronger.
• Mixing up colligative property formulas: Relative lowering of vapour pressure = x₂, ΔT b = K b m, ΔT f = K f m, and π = C R T.
• Forgetting the temperature unit in osmotic pressure: In π = C R T, temperature must be in kelvin.

Glossary

• Solution: A homogeneous mixture of two or more pure substances.
• Solute: The substance dissolved in a solution, usually present in lesser amount.
• Solvent: The substance in which the solute is dissolved, usually present in larger amount and deciding the physical state of the solution.
• Aqueous solution: A solution in which water acts as the solvent.
• Non-aqueous solution: A solution in which the solvent is other than water.
• Concentration of solution: The amount of solute present in a given quantity of solution or solvent.
• Mass percentage (w/w): Mass of solute present per 100 g of solution.
• Volume percentage (v/v): Volume of solute present per 100 mL of solution.
• Mass by volume percentage (w/v): Mass of solute present per 100 mL of solution.
• Parts per million (ppm): The number of parts of solute per million parts of solution, used for very dilute solutions.
• Mole fraction: The ratio of moles of a component to the total number of moles of all components in the solution.
• Molarity (M): Number of moles of solute present in 1 litre of solution.
• Molality (m): Number of moles of solute present in 1 kilogram of solvent.
• Normality (N): Number of gram equivalents of solute present in 1 litre of solution.
• Solubility: The maximum amount of solute that can dissolve in a given amount of solvent at a specified temperature.
• Henry’s law: At constant temperature, the mass of a gas dissolved in a liquid is directly proportional to the pressure of the gas above the liquid.
• Henry’s constant (K_H): The proportionality constant in Henry’s law.
• Partial pressure: The pressure exerted by one component of a gaseous mixture.
• Vapour pressure: The pressure exerted by vapours over a liquid when the liquid and vapour are in equilibrium at a given temperature.
• Raoult’s law: In an ideal solution, the partial vapour pressure of each component is directly proportional to its mole fraction.
• Ideal solution: A solution that obeys Raoult’s law over the entire range of composition.
• Non-ideal solution: A solution that does not obey Raoult’s law and shows deviation from ideal behaviour.
• Positive deviation: A deviation in which the vapour pressure of the solution is higher than expected from Raoult’s law.
• Negative deviation: A deviation in which the vapour pressure of the solution is lower than expected from Raoult’s law.
• Azeotrope: A mixture that boils without any change in composition.
• Colligative properties: Properties of dilute solutions that depend only on the number of solute particles, not on their nature.
• Relative lowering of vapour pressure: The ratio of lowering of vapour pressure to the vapour pressure of the pure solvent.
• Elevation of boiling point: The increase in boiling point of a solution compared with the pure solvent.
• Depression of freezing point: The decrease in freezing point of a solution compared with the pure solvent.
• Osmosis: The flow of solvent through a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration.
• Osmotic pressure: The pressure required to stop osmosis completely.
• Reverse osmosis: The process in which pressure greater than osmotic pressure is applied to reverse the flow of solvent.
• Hypertonic solution: A solution having higher solute concentration than the surrounding solution separated by a semipermeable membrane.
• Hypotonic solution: A solution having lower solute concentration than the surrounding solution.
• Isotonic solution: Solutions having equal osmotic pressure, so there is no net osmosis between them.
• Abnormal molecular mass: The molecular mass calculated from colligative properties that differs from the theoretical molecular mass because of association or dissociation.
• Association: The coming together of solute particles to form larger aggregates, reducing the number of particles in solution.
• Dissociation: The splitting of solute molecules or ions into smaller particles, increasing the number of particles in solution.
• Van’t Hoff factor (i): The ratio of the observed colligative property to the calculated colligative property.