Overview — Module 3: Solutions

When sugar or salt is added to water, it dissolves to form a solution. Solutions are central to life and industry — countless chemical reactions are carried out in solution. From the saline drip in hospitals to the electrolyte in a car battery, from the sugar in your tea to the dissolved oxygen that sustains aquatic ecosystems, solutions surround us. Study of how substances dissolve and how dissolved particles affect physical properties is therefore essential for chemistry, biology, and engineering.

This lesson covers the components of solutions, ways to express concentration, types of solutions, vapour pressure, Henry's and Raoult's laws, ideal and non-ideal behaviour, colligative properties (relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure), abnormal colligative properties, and the van't Hoff factor with numerical applications. By the end you should be able to express concentrations in multiple units, predict how mixtures behave relative to ideal Raoult's law, calculate boiling and freezing point changes, determine molar masses from colligative data, and correct for electrolyte dissociation using i.

Section 1: Components and Concentration (7.1)

7.1 Components of a Solution

When solute mixes homogeneously with solvent: solute + solvent → solution. A solution is a homogeneous mixture of two or more substances. The solvent is the component with the same physical state as the solution; the solute is dissolved in it. In sugar water, water is solvent and sugar is solute.

7.1.1 Concentration Units

Properties like sweetness or colour depend on how much solute is present relative to solvent — the concentration. NIOS covers five main expressions:

• Molarity (M): moles of solute per litre of solution. M = n/V. Example: 2.0 M H₂SO₄ has 2.0 mol per litre. Changes with temperature because solution volume expands or contracts.
• Molality (m): moles of solute per kilogram of solvent. m = n_B×1000/W_A. Does not change with temperature — used in colligative property calculations.
• Normality (N): gram equivalent weights per litre. Eq. wt = mol. wt / acidity (acid), basicity (base), or valency. N = strength (g/L) / eq. wt.
• Mole fraction (x): x_A = n_A/(n_A+n_B); sum of all x = 1.
• Mass percentage: grams of solute per 100 g solution (5% KMnO₄ = 5 g per 100 g solution).

Example 7.2: 50% H₂SO₄, density 1.20 g/cm³ → 600 g acid + 600 g water in 1 L → molality ≈ 6.8 m. Example 7.3: 36 g water + 46 g ethanol → x_water = 0.67, x_ethanol = 0.33. Example 7.4: 0.4 g NaOH in 100 mL → 0.1 N.

Choosing the right unit matters in exams: molarity is convenient for volumetric lab work (titrations) because solutions are measured in litres, but molality is mandatory when temperature changes during an experiment would alter the volume and hence molarity. Normality is especially useful in redox and acid–base calculations where reactions depend on equivalents rather than moles — one equivalent of acid neutralises one equivalent of base regardless of whether the acid is monobasic or dibasic.

Equivalent weight of an acid = molecular weight / basicity; of a base = molecular weight / acidity; of a salt = molecular weight / total metal valency. Oxidising and reducing agents may have different equivalent weights under different reaction conditions, calculated from the specific redox reaction they undergo.

Section 2: Types of Solutions and Henry's Law (7.2)

Binary solutions can be gas–gas (air), gas–liquid (soda water), gas–solid (H₂ in Pd), liquid–gas (humidity), liquid–liquid (alcohol in water), liquid–solid (Hg in Au), solid–gas (camphor in air), solid–liquid (sugar in water), solid–solid (brass, bronze). Common cases:

• Liquids in liquids: completely miscible (alcohol–water), partially miscible (water–phenol), or immiscible (water–benzene). Solubility generally increases with temperature.
• Gases in liquids: O₂ dissolves enough for aquatic life; CO₂ and NH₃ are highly soluble. Depends on pressure, temperature, and nature of gas/solvent.
• Solids in liquids: e.g. NaCl in water — extent of dissolution varies by substance.

Henry's law valid when: pressure not too high, temperature not too low, gas does not associate, dissociate, or react with solvent. CO₂ solubility in water: 0.88 cm³/cm³ at 20°C but 0.53 at 40°C — heating expels dissolved gas, which is why warm soda goes flat faster than cold soda.

Table 7.1 lists all nine binary solution types. In liquid–liquid solutions the component in smaller amount is usually called solute and the larger amount solvent, though this is a convention rather than a strict rule. Partial miscibility (water–phenol) produces two layers each saturated with the other component at a given temperature.

Gas solubility trends: CO₂, HCl, NH₃ are highly soluble in water; H₂, O₂, N₂ are sparingly soluble. This explains why fish need dissolved O₂ but soft drinks can hold large amounts of CO₂ under pressure.

Section 3: Vapour Pressure and Raoult's Law (7.3–7.5)

7.3 Vapour Pressure

When a pure liquid evaporates in a closed vessel, an equilibrium is reached between evaporation and condensation. The pressure exerted by the vapour is the vapour pressure of the liquid (Fig. 7.1).

7.4 Raoult's Law for Volatile Liquids

For miscible volatile liquids, partial vapour pressure of each component is proportional to its mole fraction: P_A = P_A°·X_A and P_B = P_B°·X_B. Total pressure P = P_A°·X_A + P_B°·X_B. Solutions obeying Raoult's law at all concentrations and temperatures are ideal solutions. A plot of P_A and P_B versus mole fraction gives straight lines from P_A° (at X_A=1) to zero (at X_A=0); the total pressure line connects P_A° and P_B° (Fig. 7.2). Raoult's law applies only when liquids are miscible — immiscible pairs form separate phases each with its own vapour pressure contribution.

The more volatile component (higher P°) contributes more to the vapour phase at any composition. Distillation of liquid mixtures exploits differences in partial vapour pressures — the vapour is enriched in the more volatile component, which is the industrial basis for separating ethanol from water and petroleum fractions.

7.5 Raoult's Law for Non-Volatile Solute

For aqueous sugar/salt solutions, only solvent vapour is present. Since X_A < 1, vapour pressure drops below pure solvent. Derivation gives:

Section 4: Ideal and Non-Ideal Solutions (7.6)

Ideal solutions: obey Raoult's law; ΔH_mix = 0 and ΔV_mix = 0 — intermolecular forces between A–B are similar in strength to A–A and B–B. Benzene–toluene approximates ideal behaviour. Non-ideal solutions: most real solutions — deviate from Raoult's law with heat/volume change on mixing. Positive deviation releases heat on mixing (endothermic, ΔH_mix > 0 in some cases) when breaking stronger self-interactions costs energy; negative deviation is often exothermic when new stronger A–B interactions form.

• Positive deviation: A–B interactions weaker than A–A or B–B → total P higher than predicted (maximum at intermediate composition). Examples: ethanol–cyclohexane, water–propanol, acetone–CS₂.
• Negative deviation: A–B interactions stronger → total P lower (minimum at intermediate composition). Examples: chloroform–acetone, water–H₂SO₄, phenol–aniline.

Understanding deviations helps explain azeotrope formation — mixtures that boil at constant composition because the vapour has the same composition as the liquid at a particular mole fraction, often near the maximum or minimum of the vapour pressure curve for non-ideal pairs. Ethanol–water forms an azeotrope near 95.6% ethanol, which is why simple distillation cannot produce 100% ethanol without adding a third component.

Section 5: Colligative Properties (7.7)

Colligative properties depend only on the number of solute particles, not their chemical nature. Four colligative properties: (1) relative lowering of vapour pressure, (2) elevation of boiling point, (3) depression of freezing point, (4) osmotic pressure. The term colligative (Latin: bound together) reflects that these effects are collectively controlled by particle count in dilute solutions.

7.7.1 Relative Lowering of Vapour Pressure

From Section 7.5: (P°−P)/P° = X_B. For dilute solutions, X_B ≈ (W_B/M_B)/(W_A/M_A). Example 7.5: RLVP = 0.00715 with 7.2 g solute in 100 g water → M_B ≈ 181 g mol⁻¹. VP lowering is the root cause of all other colligative effects — reduced solvent escaping tendency shifts every phase equilibrium.

7.7.2 Elevation of Boiling Point

Boiling point = temperature where vapour pressure equals atmospheric pressure. Solution VP < pure solvent → higher boiling point (Fig. 7.5 — solution curve lies below solvent curve, so it meets 1 atm at higher T). Derivation: ΔT_b ∝ Δp ∝ X_B ∝ m, giving ΔT_b = K_b·m where K_b is the molal elevation constant (elevation when 1 mol non-volatile solute dissolves in 1 kg solvent). Adding salt to water raises boiling point — used in cooking (salted water boils above 100°C at 1 atm) and in antifreeze formulations.

7.7.3 Depression in Freezing Point

Freezing point = temperature where solid and liquid have equal vapour pressure (Fig. 7.6). Solution VP is lower → freezing point depressed. ΔT_f = K_f·m where K_f is the molal cryoscopic constant (depression when 1 mol solute in 1 kg solvent). Spreading salt on icy roads lowers the freezing point of surface water — a practical application of colligative properties. Example 7.6: 0.520 g glucose in 80.2 g water gives m = 0.036, ΔT_b = 0.018 K, ΔT_f = 0.66 K, so new FP = 272.34 K.

7.7.4 Osmosis and Osmotic Pressure

Osmosis: spontaneous flow of solvent from lower to higher concentration (or pure solvent to solution) through a semipermeable membrane. Raisins swell in water; solvent moves until concentrations equalise. Osmotic pressure (π) is the excess pressure applied to the concentrated side to stop solvent flow (Fig. 7.7). Equal π → isotonic solutions.

Osmotic pressure is preferred for macromolecules/proteins because other colligative effects are too small at low concentrations, but π remains measurable at room temperature where biomolecules are stable. Medical saline (0.9% NaCl) is approximately isotonic with blood — same osmotic pressure prevents haemolysis or cell shrinkage. Reverse osmosis applies pressure greater than π to force pure water through a membrane from seawater — used for desalination and water purification plants.

All four colligative properties are interrelated through the same thermodynamic origin: adding non-volatile solute lowers solvent chemical potential, reducing vapour pressure, which shifts boiling and freezing equilibria and creates osmotic pressure differences across membranes.

Section 6: Abnormal Colligative Properties (7.8)

Abnormal results occur when: (i) solution is too concentrated (solute–solute interactions), (ii) association reduces effective particles (i < 1, observed M > true M — benzoic acid dimer in benzene, i ≈ ½), (iii) dissociation increases particles (i > 1, observed M < true M — NaCl in water, i ≈ 2).

Degree of association (x): 2C₆H₅COOH ⇌ dimer → at equilibrium: (1−x) mol monomer + x/2 mol dimer → effective moles = 1 − x/2. Benzoic acid i ≈ 0.5. Degree of dissociation (x): KCl ⇌ K⁺ + Cl⁻ → (1−x) + x + x = 1 + x total moles; i = 1 + x. Example 7.8: acetic acid in benzene, ΔT_b gives i = 0.51, degree of association 98%. Example 7.9: 0.5% KCl freezes at 272.76 K; observed M = 38.75 vs normal 74.5 → i = 1.92, 92% dissociation.

Modified colligative equations with i: (P°−P)/P° = i·X_B; ΔT_b = iK_bm; ΔT_f = iK_fm; πV = inRT. For non-electrolytes like glucose and urea, i = 1 exactly. Very concentrated solutions also show abnormal results because solute particles interact with each other, invalidating the dilute-solution assumption underlying the derivations.

Worked logic for Example 7.9 (KCl): observed M from ΔT_f is half the true M because twice as many particles exist after dissociation — hence i = 74.5/38.75 = 1.92. Setting 1 + x = 1.92 gives x = 0.92 or 92% dissociated. The same logic applies to NaCl (i → 2), CaCl₂ (i → 3 if fully dissociated), and any electrolyte where each formula unit produces (1 + number of ions − 1) extra particles upon complete dissociation.

Exam Connections and Chapter Summary

Comparison of colligative methods for molar mass: RLVP requires precise manometry; ΔT_b and ΔT_f need accurate thermometry but work well for small organic molecules; π is ideal for polymers and proteins (Example 7.7: M ≈ 61000 g mol⁻¹) because even dilute solutions produce measurable pressure at 300 K. Freezing point depression is often used in organic chemistry labs (cryoscopy) because many organic solvents have convenient K_f values.

Key numerical skills: convert between M and m using density; calculate mole fractions from masses; use RLVP, ΔT_b, ΔT_f, or π to find molar mass; compute i from observed vs normal M; find degree of dissociation from i. Water constants to remember: K_f = 1.86 K kg mol⁻¹, K_b = 0.52 K kg mol⁻¹ (textbook values). Always identify whether solute is electrolyte (i > 1) or associates (i < 1) before applying colligative formulas.

Terminal exercise covers: defining colligative properties; predicting SF₆ is outside this chapter; computing M, m, N; explaining why osmotic pressure suits proteins; calculating i and degree of dissociation for electrolytes; comparing positive vs negative Raoult deviations. Intext 7.1 lists concentration methods. Intext 7.2: Raoult's and Henry's laws. Intext 7.3: colligative properties and why π is best for biomolecules.

A solution is a homogeneous mixture. Concentration is expressed as M, m, N, mole fraction, or mass %. Henry's law governs gas solubility; Raoult's law links vapour pressure to mole fraction. Ideal solutions obey Raoult's law; real solutions show positive or negative deviations. Colligative properties — RLVP, ΔT_b, ΔT_f, π — depend on particle count; electrolyte dissociation and solute association are corrected using i. Together these concepts explain everyday phenomena from boiling point elevation in cooking to medical saline isotonicity and reverse-osmosis water purification.

The logical flow of Module 3 builds from defining what a solution is (7.1), through classifying types and gas solubility (7.2), to vapour pressure as the underlying property (7.3), Raoult's law as the quantitative link between composition and VP (7.4–7.6), and finally colligative properties as practical consequences of VP lowering (7.7–7.8). Mastering the derivations is less important than knowing which formula applies in which situation and whether the van't Hoff correction is needed — that decision tree is what NIOS terminal and board questions typically test.