Colloidal

Colloidal

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

A colloid is a heterogeneous, two-phase system in which the dispersed phase (particles 1–1000 nm) is distributed uniformly through a dispersion medium. Size sits between true solutions (<1 nm) and suspensions (>1000 nm). The three diagnostic properties every JEE Advanced question hinges on are: Tyndall effect (scattering of light when particle diameter exceeds ~10⁻⁷ m), Brownian motion (zig-zag jitter of particles that prevents sedimentation), and charge stabilization (a zeta potential of ±30 mV or more keeps lyophobic sols from coagulating). Lyophilic sols (e.g. gum, starch, protein in water) are solvent-loving and self-stabilized; lyophobic sols (e.g. metals, metal sulfides) need a charge or protective colloid. The Hardy–Schulze rule is the single highest-yield fact: coagulation power of an electrolyte rises with the sixth power of the valency of the counter-ion (the ion of charge opposite to that on the sol). CMC (Critical Micelle Concentration) and Kraft temperature define when surfactant monomers assemble into micelles — a hot JEE topic.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Classification

Based on the physical states of dispersed phase (DP) and dispersion medium (DM), eight colloidal types exist: sol (solid DP, liquid DM — e.g. gold sol), gel (liquid DP, solid DM — e.g. jelly), emulsion (liquid DP, liquid DM — e.g. milk, oil-in-water), foam (gas DP, liquid DM — e.g. whipped cream), aerosol (solid/liquid DP, gas DM — e.g. smoke, fog), and the three solid-medium counterparts. A second axis distinguishes lyophilic (reversible, viscosity-affecting) from lyophobic (irreversible, charge-stabilized) systems. A third axis — based on particle nature — splits colloids into multimolecular (e.g. S₈ aggregates in sulphur sol), macromolecular (e.g. proteins, polymers, where the molecule itself is colloidal), and associated colloids/micelles (surfactants that aggregate only above CMC).

Origin of Charge and Stability

Lyophobic particles acquire charge by preferential adsorption of common ions from added electrolyte (e.g. AgI sol adsorbs I⁻ → negative sol; Ag⁺ → positive sol), by ionization of surface groups (e.g. –COOH on protein), or by frictional electron transfer. The adsorbed layer plus a diffuse layer of counter-ions form the electrical double layer (Helmholtz/Stern/Gouy–Chapman model). The potential at the slipping plane is the zeta potential (ζ); |ζ| ≥ ~30 mV gives kinetic stability.

Tyndall Effect and Brownian Motion

A colloidal particle has diameter d > wavelength of visible light, so it scatters light (I ∝ 1/λ⁴ for d ≪ λ, Mie–Rayleigh regime). True solutions (ions, small molecules) show no Tyndall cone. Brownian motion, caused by uneven molecular bombardment from the DM, counteracts gravity; its kinetic energy equals (3/2)kT per particle. The sedimentation rate is given by Stokes’ law: v = (2 r² (ρ − ρ₀) g) / 9η, showing why colloids do not settle appreciably.

Coagulation and Protective Action

According to Hardy–Schulze, coagulation power ∝ (valency of counter-ion)⁶. Coagulation value is the minimum mmol L⁻¹ of electrolyte that coagulates a sol in 2 h. Gold number (Zsigmondy) measures protective action: lower gold number = better protection. A protective colloid converts a lyophobic sol into a lyophilic one (e.g. gelatin protects a gold sol).

Emulsions, Gels, and Micelles

Emulsions are lyophobic and need an emulsifier (surfactant) for stability — Bancroft’s rule: the phase in which the emulsifier is more soluble becomes the continuous phase. Micelles form above CMC and above the Kraft temperature; the aggregation number N = 4πr³/(3v₀), where v₀ is the volume of one hydrocarbon tail. Below CMC or below Kraft temperature, the surfactant is a true solution.

Exam Pattern

JEE Advanced asks 1–2 questions per year (≈3% weight). Frequent formats: match-the-column (colloid type ↔ example), single-correct MCQ (Tyndall / Brownian / Hardy–Schulze), and integer-type (CMC, gold number, valency power). Numericals often test the 6th-power rule, sedimentation velocity, or N from micelle geometry.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Double Layer in Detail

The Stern model places a fixed layer of specifically adsorbed counter-ions (Stern layer) at the particle surface, followed by a diffuse Gouy–Chapman layer. The total potential drop is ψ₀ (surface) → ψ_δ (Stern plane) → 0 (bulk). The zeta potential ζ ≈ ψ_δ. When an indifferent electrolyte is added, ζ falls, the double layer compresses (Debye length κ⁻¹ ∝ 1/√I), and coagulation occurs once ζ falls below the critical value (~25–30 mV). This explains Hardy–Schulze quantitatively: higher-valency counter-ions screen the surface charge far more effectively per unit concentration.

Ostwald Ripening and Kinetic Stability

In polydisperse sols, smaller particles have higher solubility (Kelvin equation), dissolve, and redeposit on larger ones, shifting particle size upward with time. This Ostwald ripening is a slow degradation mechanism distinct from coagulation. Brownian motion provides only kinetic (not thermodynamic) stability; given enough time, all lyophobic sols ultimately coagulate.

Purification Methods

Dialysis uses a semipermeable membrane to remove soluble impurities from a colloid. Ultrafiltration uses a graded filter (e.g. collodion) — colloids are retained while small ions pass. Electro-dialysis accelerates dialysis using an applied field. Coagulation can be reversed by peptization: washing a freshly precipitated Fe(OH)₃ with a trace of FeCl₃ re-disperses it as a positive sol because the adsorbed Fe³⁺ ions recreate the double layer.

Worked Numeric

A gold sol particle has radius 50 nm, density 19.3 g cm⁻³ dispersed in water (η = 1.0 × 10⁻³ Pa·s, ρ₀ = 1.0 g cm⁻³). Sedimentation velocity: v = (2 × (50 × 10⁻⁹)² × (19.3 − 1.0) × 10³ × 9.8) / (9 × 1.0 × 10⁻³) = (2 × 2.5 × 10⁻¹⁵ × 18.3 × 10³ × 9.8) / (9 × 10⁻³) ≈ 9.97 × 10⁻⁸ m s⁻¹ ≈ 0.1 µm s⁻¹ — confirming why colloids do not settle under gravity.

Connections and Common Mistakes

• Brownian motion vs. Tyndall: both arise from the size range, but Tyndall is optical, Brownian is mechanical. JEE traps students by offering options that swap the two.
• Hardy–Schulze: the power is 6 (not 3, not 2) and it is the counter-ion (not the co-ion). Mixing these up is the most common integer-type error.
• Lyophilic sols do coagulate at high electrolyte concentration (salting out, e.g. protein precipitation by (NH₄)₂SO₄), but the mechanism is dehydration, not double-layer compression.
• Micelle questions: only above both CMC and Kraft temperature will micelles form; below Kraft temperature, solubility is too low and surfactant crystallizes out.

Practice Prompts

1. A negatively charged arsenious sulphide sol is coagulated by 0.04 M NaCl, 0.013 M BaCl₂, and 0.0007 M AlCl₃. Verify Hardy–Schulze and compute the relative coagulation values.
2. A soap solution at CMC = 1.0 × 10⁻³ M forms spherical micelles of radius 2.0 nm with tail volume 3.0 × 10⁻²⁸ m³. Estimate the aggregation number N and the average molecular mass if the surfactant molar mass is 300 g mol⁻¹.

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