Solutions – Comprehensive Bullet-Point Notes

Objectives of the Unit

• After completing the unit you should be able to:
– Describe the formation of different kinds of solutions (gas-gas, gas-liquid, …, solid-solid).
– Express concentration in several units (%, ppm, mole-fraction, molarity, molality).
– State, write and use Henry’s law and Raoult’s law.
– Distinguish ideal from non-ideal (real) solutions and explain deviations.
– Relate colligative properties (RLVP, ΔTb, ΔTf, Π) to molar mass.
– Rationalise abnormal colligative behaviour via association/dissociation (van’t Hoff factor).

1. Basics & Terminology

• Solution = homogeneous mixture of \ge 2 components with uniform composition & properties.
• Component present in maximum amount → solvent (defines physical state); all others → solute(s).
• Binary solution = 2-component system; each component can be gas/liquid/solid.

2. Types of Solutions (Component-wise)

• Gaseous solutions
– Gas + Gas : air (\text{O}2 in \text{N}2).
– Liquid + Gas : chloroform vapour in \text{N}2. – Solid + Gas : camphor in \text{N}2.
• Liquid solutions
– Gas + Liquid : \text{O}2 in water. – Liquid + Liquid : ethanol–water. – Solid + Liquid : glucose in water. • Solid solutions – Gas + Solid : \text{H}2 in Pd.
– Liquid + Solid : Na–Hg amalgam.
– Solid + Solid : Au–Cu alloy.

3. Quantitative Ways to Express Concentration

• Mass % (w/w) \displaystyle \text{Mass %}=\frac{w{\text{solute}}}{w{\text{solution}}}\times100
• Volume % (v/v) \displaystyle \text{Vol %}=\frac{V{\text{solute}}}{V{\text{solution}}}\times100
• Mass/Volume % (w/v) – widespread in medicine (g per 100 mL).
• Parts per million (ppm) \displaystyle \text{ppm}=\frac{\text{parts of component}}{\text{total parts}}\times10^{6}
– Suitable for trace levels (pollutants, dissolved gases, fluoride in water).
• Mole fraction xi \displaystyle xi=\frac{ni}{\sum n}; \sum xi=1.
• Molarity (M) \displaystyle M=\frac{n{\text{solute}}}{V{\text{solution(L)}}} (T-dependent).
• Molality (m) \displaystyle m=\frac{n{\text{solute}}}{\text{kg solvent}} (T-independent). • Comparison: M varies with temperature (volume changes) whereas m,\;xi,\;%, and ppm do not.

4. Solubility Phenomena

4.1 Solubility of Solids in Liquids

• Dynamic equilibrium: \text{solute}{(s)} + \text{solvent} \rightleftharpoons \text{solution}. • Saturated solution = at equilibrium; solubility equals concentration. • Effect of T: If dissolution is endothermic (\Delta H{\text{sol}}>0) solubility ↑ with T; exothermic ↓.
• Effect of P: negligible (solids/liquids are incompressible).

4.2 Solubility of Gases in Liquids – Henry’s Law

• Statement (I): p \propto x at constant T.
• Mathematical form: p = KH x – p = partial pressure of gas, x = mole fraction in solution, KH = Henry constant.
• High KH ⇒ lower solubility. • Temperature effect: KH ↑ with T ⇒ gases less soluble in warm water (aquatic life prefers cold).
• Applications:
– Carbonation of soft drinks (CO₂ packed at high p).
– Scuba diving (He–N₂–O₂ mixture avoids bends).
– High-altitude anoxia.

5. Vapour-Pressure Relations

5.1 Raoult’s Law (binary liquid–liquid)

• For ideal volatile components:
p1=x1 p1^{0},\; p2=x2 p2^{0}
p{\text{total}} = p1 + p2 = x1 p1^{0} + x2 p_2^{0}.
• Linear p–x plots; vapour richer in more volatile component.

5.2 Solutions of Solids in Liquids (non-volatile solute)

• Solvent’s vapour pressure lowers:
\Delta p = p1^{0} - p1 = x2 p1^{0} (Relative lowering =x_2).

5.3 Ideal vs Non-Ideal Solutions

• Ideal: obey Raoult over full range; \Delta{\text{mix}}H = 0, \Delta{\text{mix}}V = 0; e.g., benzene–toluene.
• Positive deviation (p{\text{obs}} > p{\text{ideal}}): weaker A–B interactions; \Delta H{\text{mix}}>0; minimum-bp azeotrope (ethanol–water). • Negative deviation (p{\text{obs}} < p{\text{ideal}}): stronger A–B; \Delta H{\text{mix}}<0; maximum-bp azeotrope (HNO₃–H₂O).

6. Colligative Properties (depend only on number of solute particles)

6.1 Relative Lowering of Vapour Pressure (RLVP)

\displaystyle \frac{p1^{0}-p1}{p1^{0}} = \frac{n2}{n1+n2} \xrightarrow{dilute} \frac{n2}{n1}

6.2 Elevation of Boiling Point (ΔT_b)

• \Delta Tb = Kb m; K_b = ebullioscopic constant (Table values: water 0.52 K kg mol⁻¹, …).
• Derivation uses p–T curves (solution needs higher T to reach 1 atm).

6.3 Depression of Freezing Point (ΔT_f)

• \Delta Tf = Kf m; K_f = cryoscopic constant.
• Based on equality of vapour pressures of solid solvent vs solution.

6.4 Osmosis & Osmotic Pressure (Π)

• Semipermeable membrane allows solvent only.
• \Pi = CRT = \dfrac{n2RT}{V} (analogous to ideal-gas law). • Isotonic (\Pi1 = \Pi_2), hypertonic, hypotonic definitions (medical relevance – normal saline 0.9%).
• Reverse osmosis: applying P > \Pi forces pure solvent out (desalination, RO water purifiers).

7. Determining Molar Mass via Colligative Properties

• Use formulae rearranged for M2 (molar mass of solute): – RLVP: M2 = \dfrac{w2 M1}{w1} \; \dfrac{p1^{0}}{p1^{0}-p1} (dilute ≈ eqn (1.28)).
– ΔTb: M2 = \dfrac{Kb w2 \times1000}{\Delta Tb \; w1}.
– ΔTf: M2 = \dfrac{Kf w2 \times1000}{\Delta Tf \; w1}.
– Osmosis: M2 = \dfrac{w2RT}{\Pi V}.
• Useful for polymers & biomolecules (large M, low volatility).

8. Abnormal Molar Mass & van’t Hoff Factor (i)

• Association ↓ no. of particles ⇒ i < 1 (e.g., \text{CH}3\text{COOH} dimers in benzene). • Dissociation ↑ particles ⇒ i > 1 (salts in water). i = \dfrac{\text{observed colligative property}}{\text{calculated (ideal)}} = \dfrac{M{\text{normal}}}{M{\text{observed}}} • Modified relations: \Delta Tb = iK_b m, \Pi = iCRT, etc.

9. Illustrative Numerical Data & Constants

• Kb\;(\text{H}2\text{O}) = 0.52, Kf\;(\text{H}2\text{O}) = 1.86 K kg mol⁻¹.
• Typical KH values (298 K): \text{CO}2:1.67\,\text{kbar}, \text{N}2:76.5\,\text{kbar}. • Van’t Hoff factors for strong electrolytes (0.001 m): \text{NaCl}≈1.97, \text{K}2\text{SO}_4≈2.84.

10. Real-World & Ethical Connections

• Water fluoridation: 1 ppm prevents caries, >1.5 ppm causes mottling; illustrates ppm relevance.
• Pharmaceutical injections: isotonic solutions prevent cell lysis/shrinkage (medical ethics: patient safety).
• Environmental impact: gas solubility ↓ with warming oceans → threatens aquatic life (climate concern).
• Reverse osmosis plants provide potable water in arid/coastal regions (socio-economic significance).

11. Typical Concept-Checking Examples (Condensed)

• Mole-fraction calc: 20 % w/w \text{C}2\text{H}6\text{O}2 ⇒ x{EG}=0.068, x{H2O}=0.932.
• Molarity: 5 g NaOH in 450 mL ⇒ 0.278\,\text{M}.
• Henry’s law: x{N2}=1.29\times10^{-5} at p=0.987\,\text{bar} (water, 293 K).
• ΔTb: 18 g glucose in 1 kg water ⇒ \Delta Tb = 0.052\,\text{K} (boils at 373.202 K).
• van’t Hoff i: Benzoic acid in benzene gives i=0.504 ⇒ 99.2 % dimerisation.

12. Key Take-Away Formulae (Quick Reference)

• p = KH x (Henry) • p{tot}=x1p1^0+x2p2^0 (Raoult, binary).
• \frac{\Delta p}{p^0}=x2 (RLVP). • \Delta Tb=iKb m ; \Delta Tf=iK_f m.
• \Pi=iCRT.
• i=\dfrac{\text{particles after}}{\text{particles before}}.

13. Common Pitfalls & Tips

• Use molality or mole fraction when T varies; avoid molarity for high-precision T-dependent work.
• Remember: for electrolytes colligative effect multiplies by i – neglecting gives wrong molar mass.
• In numerical problems convert all masses to kg (for m) and volumes to L (for M).
• For extremely dilute gas solubility calculations, assume ideal-gas behaviour.

14. Inter-Chapter Links

• Thermodynamics: derivation of \Delta Tb and \Delta Tf uses Clausius–Clapeyron equation.
• Chemical equilibrium: Le Châtelier explains T/P effects on solubility.
• Electrochemistry: conductivity data gives degree of dissociation, complements colligative i.

15. End-of-Unit Reflection

• Colligative properties bridge microscopic particle count and macroscopic observables (T, p, Π).
• Deviations from ideality reveal intermolecular forces – vital for formulating pharmaceuticals, alloys, fuels.
• Mastery of concentration units, laws (Henry/Raoult) and i equips you for quantitative solution chemistry in lab & industry.