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Class 12 Chemistry Chapter 10 of 15

Chapter 5 — Surface Chemistry

Overview

This chapter introduces Surface Chemistry — the study of phenomena that occur at interfaces (surface or boundary between two phases). It covers adsorption (how molecules concentrate at surfaces), catalysis (how reaction rates are altered at surfaces or in solution), and colloids and emulsions (systems with dispersed microscopic particles). The chapter explains why surfaces behave differently from the bulk, how adsorption isotherms describe surface coverage, how heterogeneous and homogeneous catalysts work (with industrial and biological examples), and how colloidal systems are classified, prepared, characterized and stabilized or destabilized. Importance: surface chemistry underpins catalysts in industry (Haber, catalytic converters), detergency and emulsification (soaps, food), medicines (drug delivery via colloids), water purification, and many environmental and technological processes. Students will learn key concepts, experimental observations, rules (e.g., Hardy–Schulze), qualitative forms of adsorption isotherms (Langmuir/Freundlich), methods of preparing and purifying colloids, properties such as Tyndall effect, Brownian motion and electrophoresis, and practical…

Learning Objectives

  • Define adsorption and desorption and distinguish between physisorption and chemisorption with suitable examples.
  • Explain factors affecting adsorption (nature of adsorbent/adsorbate, surface area, temperature, pressure) and their qualitative effects.
  • Derive the Langmuir adsorption isotherm and obtain its linear form for determination of monolayer capacity.
  • Apply Langmuir and Freundlich isotherms to analyse experimental adsorption data and calculate relevant parameters.
  • Describe key applications of adsorption in industry and environmental control (e.g., gas masks, chromatography, removal of impurities).
  • Define catalysis and differentiate between homogeneous and heterogeneous catalysis with representative examples.
  • Explain the role of adsorption in heterogeneous catalytic mechanisms and describe concepts of catalytic activity and selectivity.
  • Analyze the role of catalysts in major industrial processes (e.g., Haber and Contact processes) and evaluate their economic importance.

Topics in this chapter

18 topics · tap a topic title to jump straight to it.

⚡1

Surface phenomena and surface energy

Introduction
Surface phenomena are effects that occur at the interface between two phases (solid–gas, liquid–gas, solid–liquid, etc.). Molecules at a surface experience unbalanced forces and therefore have higher potential energy than molecules in the bulk. This extra energy per unit area is called surface energy. Surface phenomena include surface tension, capillarity, adsorption and wetting.

Surface energy and surface tension
Surface energy (E_s) = surface tension (γ) × area (A). Surface tension γ is the work required to increase the surface area of a liquid by unit amount (or force per unit length along a line in the surface):

  • γ = dW / dA (work per unit area), units: N m−1 (or J m−2).
  • Surface energy E_s = γA.

Molecular origin: molecules at the surface have fewer neighbors so net cohesive (attractive) forces pull them into the bulk. To create new surface, work must be done against these cohesive forces; that is surface energy.

Surface tension — qualitative effects and measurement
Surface tension makes the surface behave like a stretched elastic membrane. Consequences: formation of droplets, spherical shape of small drops (minimizes surface area), capillary rise, meniscus curvature, ability of some insects to walk on water, and stability of bubbles and foams. Common measurement methods include capillary rise method, drop-weight (or stalagmometer) and du Noüy ring method.

Capillarity
When a narrow tube (capillary) is placed in a liquid, the liquid rises or falls inside the tube depending on the adhesive force between liquid and tube relative to liquid cohesion. Capillary rise (or fall) height is given by:

h = (2γ cos θ) / (ρ g r)

Here θ is the contact angle, ρ liquid density, g acceleration due to gravity and r capillary radius. Liquids that wet the surface (θ < 90°) rise; non-wetting liquids (θ > 90°) fall.

Contact angle and Young's equation
The contact angle θ (angle between liquid surface and solid surface inside the liquid) quantifies wetting. Young's equation relates interfacial tensions:

γ_SG = γ_SL + γ_LG cos θ

where γ_SG, γ_SL and γ_LG are solid–gas, solid–liquid and liquid–gas interfacial tensions respectively. Smaller θ → better wetting.

Pressure difference across a curved surface (Laplace pressure)
A curved liquid surface produces a pressure difference between the two sides. The general form is:

ΔP = γ (1/R_1 + 1/R_2)

For a spherical liquid drop of radius r: ΔP = 2γ/r (inside pressure higher). For a soap bubble (two surfaces) ΔP = 4γ/r.

Adsorption (a surface phenomenon)
Adsorption is the accumulation of molecules (adsorbate) at an interface (adsorbent surface). It differs from absorption (bulk uptake). Adsorption can be physical (physisorption, weak van der Waals forces, reversible, low heat of adsorption) or chemical (chemisorption, stronger chemical bonds, often irreversible, higher heat of adsorption). Adsorption isotherms (variation of amount adsorbed with concentration or pressure at constant temperature) describe behaviour — common models: Langmuir (monolayer) and Freundlich (empirical, multilayer possible).

Gibbs adsorption and surface-active agents
Surfactants (surface-active agents) concentrate at interfaces and lower surface tension. The Gibbs adsorption equation (for dilute solutions) links surface excess concentration Γ to the change of surface tension with concentration:

Γ = -(1/RT) (dγ / d ln c)

At low concentrations, adding surfactant decreases γ significantly until the critical micelle concentration (CMC) is reached; beyond CMC, γ is almost constant.

Factors affecting surface tension

  • Nature of liquid (strong intermolecular forces → higher γ).
  • Temperature: γ decreases with increasing temperature and approaches zero at the critical temperature.
  • Presence of impurities or solutes: surfactants reduce γ; salts usually increase γ of water slightly.

Applications and importance
Surface phenomena are central to many technologies and natural processes: detergency and cleaning, emulsification, wetting and painting, capillary action in plants and porous materials, lung surfactants, stability of foams and aerosols, heterogeneous catalysis (surface adsorption of reactants), inkjet printing and microfluidics.

Summary (key ideas)

  • Molecules at surfaces have higher energy → surface energy.
  • Surface tension γ = work/area = force/length; drives shape and behavior of droplets and interfaces.
  • Capillary effects depend on γ, contact angle, tube radius and density.
  • Adsorption concentrates species at surfaces; surfactants lower γ and enable detergency, emulsions and micelle formation.
📌 Examples
  • Water rises in plant xylem and in thin glass tubes (capillary action) enabling sap transport in small plants.
  • Detergents and soaps reduce water's surface tension so it wets fabrics and removes dirt; at or above CMC they form micelles that solubilize oils.
  • A needle or water strider walking on water: surface tension supports small objects when they do not break the surface.
  • Mercury forms a convex meniscus in glass (non-wetting; large contact angle) while water forms a concave meniscus (wetting).
  • Soap bubbles (thin liquid films) and foams: stability depends on surface tension and surfactant layers.
  • Drop formation and inkjet printing: Laplace pressure and surface tension determine drop size and breakup.
🧮 Formulas
  1. Surface tension: γ = dW / dA (work per unit area), units N m⁻¹ or J m⁻²
  2. Surface energy: E_s = γ × A
  3. Force per unit length: γ = F / L
  4. Capillary rise: h = (2 γ cos θ) / (ρ g r)
  5. Young's equation (contact angle): γ_SG = γ_SL + γ_LG cos θ → cos θ = (γ_SG - γ_SL) / γ_LG
  6. Laplace pressure (general): ΔP = γ (1/R_1 + 1/R_2)
📊 Visual ideas
Surface tension (γ) vs Temperature (T): a smoothly decreasing curve; γ falls to zero at the critical temperature. (x-axis: T, y-axis: γ)
Surface tension (γ) vs log(concentration) for a surfactant: γ decreases steeply with concentration until the CMC, then levels off. Mark the CMC point. (x-axis: log c, y-axis: γ)
Adsorption isotherms: Langmuir isotherm plot of fractional coverage (θ) or amount adsorbed vs pressure (or concentration) showing a hyperbolic rise to a plateau (monolayer saturation). (x-axis: c or p, y-axis: θ or amount adsorbed)
Capillary rise height (h) vs 1/r (inverse radius): linear relationship (h ∝ 1/r) for fixed γ, θ and ρ. (x-axis: 1/r, y-axis: h)
🔬2

Surface tension

Surface tension is the property of a liquid surface that makes it behave like a stretched elastic membrane. It arises because molecules at the surface experience a net inward force (unbalanced cohesive forces) whereas molecules in the bulk are symmetrically attracted. Surface tension is important for shape of drops, capillarity, wetting, and formation of bubbles.

Definition and SI unit
Surface tension (γ) is defined as the force acting along the surface per unit length, or as work required to increase the surface area by unit amount. Its SI unit is newton per metre (N m−1) or equivalently joule per square metre (J m−2).

Microscopic origin
Molecules in the bulk are attracted equally in all directions; surface molecules lack neighbours on the gas side, so resultant inward cohesive force gives higher potential energy per molecule at the surface. Minimising surface area lowers the system energy, so liquids tend to adopt shapes with minimum surface area (e.g., spherical drops).

Key relations (conceptual)

  • Force picture: surface tension acts tangentially along any line on the surface, trying to minimize area.
  • Energy picture: surface free energy = γ × (surface area). Increasing surface area requires work.

Important formulas (derived at class 12 level)

  • Surface tension (force form): γ = F/L, where F is force along a line of length L on the surface (N m−1).
  • Work to create area: dW = γ dA, so total surface energy = γA (J).
  • Pressure difference across a curved liquid surface (spherical drop): ΔP = 2γ/r (inside pressure minus outside).
  • For a soap bubble (two surfaces): ΔP = 4γ/r.
  • Capillary rise (height h in a tube of radius r): h = (2γ cosθ)/(ρ g r), where θ is contact angle, ρ is liquid density, g is acceleration due to gravity.
  • Young’s equation (contact angle): γ_SV − γ_SL = γ_LV cosθ, relating interfacial tensions and contact angle θ.

Temperature and solute effects
Surface tension generally decreases with increasing temperature (dγ/dT < 0) and decreases strongly on addition of surfactants (surface-active agents). For surfactant solutions γ vs concentration shows a sharp drop until the critical micelle concentration (CMC), after which γ is nearly constant.

Short derivations (class 12 level)

  1. Capillary rise: Balance of weight of liquid column (π r^2 h ρ g) and upward surface force (2π r γ cosθ) gives h = 2γ cosθ/(ρ g r).
  2. Pressure difference for a drop: For a spherical surface, mechanical equilibrium gives ΔP = 2γ/r (derived from force balance or energy change on virtual increase in radius).

Practical consequences
Because of surface tension, small drops are spherical, needles can float on water if placed gently, insects can walk on water, capillary action moves liquid in thin tubes and porous media, and detergents reduce γ to improve wetting and cleaning.

Experimental measurement
Common methods: Du Noüy ring method, Wilhelmy plate method, capillary rise method, drop-weight or pendant-drop methods.

Summary
Surface tension is a measure of the energy cost to increase surface area and governs many surface phenomena: droplet shape, capillarity, wetting, and stability of foams and emulsions. It depends on temperature and chemical composition of the liquid surface.

📌 Examples
  • Water droplets on a waxed car roof form nearly spherical beads due to high surface tension and low adhesion to wax.
  • Insects (water striders) walk on pond surfaces because surface tension supports their weight by producing upward force along legs.
  • A sewing needle can be made to float on water if placed gently, as surface tension prevents it from breaking the surface.
  • Capillary rise in a thin tube: ink rises in the nib of a pen and water rises in narrow plant xylem vessels (cohesion-tension theory).
  • Soap reduces surface tension and helps wet and spread water on oily surfaces, enabling cleaning.
  • Soap bubbles demonstrate two-surface effect; internal pressure is higher than outside by ΔP = 4γ/r for a thin spherical bubble.
🧮 Formulas
  1. γ = F / L (surface tension as force per unit length; units N m^-1 or J m^-2)
  2. dW = γ dA (work to create surface area dA)
  3. Surface energy = γ A
  4. ΔP (spherical drop) = 2γ / r
  5. ΔP (soap bubble) = 4γ / r
  6. h (capillary rise) = 2γ cosθ / (ρ g r)
📊 Visual ideas
Surface tension (y-axis) vs Temperature (x-axis): smooth decreasing straight/curved line (negative slope). Label units N m^-1 and show approximate values for water vs temperature.
Surface tension (y-axis) vs Concentration of surfactant (x-axis): steep decline up to the CMC, then a plateau (mark CMC). This illustrates strong lowering of γ by surfactants.
Contact angle sketch: show a liquid droplet on a solid with vectors γ_SV, γ_SL, γ_LV at the contact point and label θ; include cases for θ &lt; 90° (wetting) and θ &gt; 90° (non-wetting).
Surface energy vs Surface area: linear plot with slope γ showing work required increases linearly with area.
📐3

Contact angle, wetting and spreading

What is contact angle? The contact angle (θ) is the angle formed at the three-phase boundary where a liquid, solid and vapour (or another immiscible liquid) meet. It is measured through the liquid between the solid surface and the tangent to the liquid drop surface. The contact angle quantifies how well a liquid wets a solid.

Wetting and classification by contact angle

  • Complete wetting: θ = 0°. The liquid spreads as a thin film over the solid (e.g., water on very clean glass).
  • Partial wetting: 0° < θ < 180°. The liquid forms a finite contact angle (typical drops on many solids).
  • Non-wetting (poor wetting): θ > 90°. The liquid forms a bead (e.g., water on wax).
  • Hydrophobic vs hydrophilic: For water specifically, θ > 90° is hydrophobic, θ < 90° is hydrophilic. Superhydrophobic surfaces have θ > 150° (e.g., lotus leaf).

Force balance and Young's equation
At equilibrium, the horizontal components of interfacial tensions balance at the contact line. Young's equation expresses this balance:

γ_SV = γ_SL + γ_LV cos θ

or equivalently

cos θ = (γ_SV − γ_SL) / γ_LV

where γ_SV, γ_SL and γ_LV are the solid–vapour, solid–liquid and liquid–vapour interfacial tensions respectively. This equation gives the equilibrium contact angle (Young contact angle) on an ideal, smooth, chemically homogeneous surface.

Spreading coefficient
The spreading coefficient S predicts whether a liquid will spread spontaneously on a solid (or on another liquid):

S = γ_SV − (γ_SL + γ_LV)

If S > 0 the liquid spreads and forms a continuous film (complete wetting). If S < 0 the liquid does not spread completely and forms a drop (partial wetting). Note that S > 0 is equivalent to θ = 0 in Young's relation.

Factors affecting wetting

  • Nature of liquid and solid (surface energies): higher solid surface energy (γ_SV) favours wetting by liquids with moderate γ_LV.
  • Surface roughness and heterogeneity: roughness amplifies intrinsic wettability (Wenzel model) and surface heterogeneity may lead to composite states (Cassie–Baxter model) and to contact angle hysteresis.
  • Presence of contaminants or surfactants: surfactants lower γ_LV and often increase spreading (wetting), used in detergents and paints.
  • Temperature: generally reduces γ_LV and can change wetting behaviour.

Brief notes on roughness models

  • Wenzel equation (rough homogeneous surface): cos θ_W = r cos θ_Y, where r is roughness factor (r > 1). Roughness enhances hydrophilicity if θ_Y < 90° and enhances hydrophobicity if θ_Y > 90°.
  • Cassie–Baxter equation (composite surface with air pockets): cos θ_C = f_s cos θ_Y + f_v cos θ_v (commonly cos θ_C = f_s cos θ_Y + f_v × cos 180° = f_s cos θ_Y − f_v), where f_s is solid fraction and f_v = 1 − f_s is air fraction beneath the drop.

Contact angle hysteresis and dynamics
Real surfaces show a range of contact angles: the advancing angle (when the drop expands) and the receding angle (when the drop shrinks). The difference (hysteresis) is due to pinning on defects and heterogeneities and affects droplet motion, adhesion and roll-off behaviour.

Importance and applications
Wetting and spreading are central to coatings, printing, painting, lubrication, detergency, ink-jet printing, microfluidics, biological adhesion, oil spill behaviour and development of water-repellent (self-cleaning) surfaces.

📌 Examples
  • Water on clean glass: wets well (θ ≈ 0° → spreads), useful for making thin films.
  • Water on a waxed car surface: poor wetting (θ &gt; 90°), forms beads that roll off, helping water runoff.
  • Mercury on glass: non-wetting; mercury forms nearly spherical beads (θ ≈ 140°) because of high surface tension.
  • Oil on water (e.g., oil spill): many oils spread on water (S &gt; 0) forming thin films; surfactants alter spreading.
  • Lotus leaf: superhydrophobic surface (θ &gt; 150°) due to micro/nano roughness and low surface energy → self-cleaning effect.
  • Detergent action: surfactants lower liquid-vapour surface tension γ_LV, reduce contact angle and improve wetting of fabrics and surfaces.
🧮 Formulas
  1. Young's equation: γ_SV = γ_SL + γ_LV cos θ
  2. Equivalently: cos θ = (γ_SV − γ_SL) / γ_LV
  3. Spreading coefficient: S = γ_SV − (γ_SL + γ_LV) ; spontaneous spreading if S > 0 (θ = 0)
  4. Wenzel equation (rough surface): cos θ_W = r cos θ_Y (r = roughness factor &gt; 1)
  5. Cassie–Baxter (composite surface): cos θ_C = f_s cos θ_Y + f_v cos θ_v (often written cos θ_C = f_s cos θ_Y − f_v for air pockets where cos θ_v = cos 180° = −1)
📊 Visual ideas
Schematic cross-sectional diagram of a droplet on a solid showing γ_SV, γ_SL, γ_LV and the contact angle θ with force-balance arrows (essential visual for Young's equation).
Plot sketch of cos θ (vertical) vs (γ_SV − γ_SL)/γ_LV (horizontal) showing they are proportional by Young's equation (straight line of slope 1).
Series of droplet profiles illustrating complete wetting (film), partial wetting (finite contact angle), and non-wetting (high contact angle).
Sketch of contact angle hysteresis: advancing and receding contact angles on a tilted surface, with a pinned contact line and difference indicated.
🔬4

Adsorption — basic concepts

Definition: Adsorption is the enrichment of a substance (adsorbate) at the surface of a solid or liquid (adsorbent) compared to the bulk. It is a surface phenomenon. Adsorption should not be confused with absorption (bulk uptake).

Adsorbent and adsorbate: The material on whose surface adsorption occurs is the adsorbent (e.g., activated carbon, silica gel). The substance that accumulates at the surface is the adsorbate (gas molecules, ions, dyes).

Nature and energetics: Adsorption is generally exothermic (heat is released). Two main types are recognised:

  • Physisorption (physical adsorption): due to weak van der Waals forces. It is usually reversible, has low heat of adsorption (≈ up to ~20–40 kJ mol-1, often quoted < 20 kJ mol-1 in textbooks), can form multilayers, and is favoured at low temperatures and high pressures.
  • Chemisorption (chemical adsorption): involves formation of chemical bonds (surface compound). It is usually specific, may be irreversible, has higher heat of adsorption (≈ 40–400 kJ mol-1), typically forms a monolayer, and often needs activation energy; it may increase with temperature up to an optimum and then decrease.

Mechanism (qualitative): Adsorption occurs because surface atoms or molecules have unsaturated bonds or excess surface energy; adsorbate molecules are held at the surface by physical or chemical forces until equilibrium between adsorption and desorption is reached.

Important quantities:

  • x = mass of adsorbate adsorbed
  • m = mass of adsorbent
  • x/m = amount adsorbed per unit mass of adsorbent
  • q (or q_e) = amount adsorbed per unit surface area/mass at equilibrium
  • θ = surface coverage = fraction of adsorption sites occupied

Adsorption isotherms (concept): An isotherm shows how the amount adsorbed (x/m or q) varies with pressure (for gases) or concentration (for solutions) at constant temperature. Two important models taught in Class 12:

  • Freundlich isotherm (empirical): x/m = k · P^(1/n) (for gases) or x/m = k · C^(1/n) (for solutions). In logarithmic form: log(x/m) = log k + (1/n) log P. Here k and n are constants dependent on temperature and the system.
  • Langmuir isotherm (monolayer adsorption) assumes a fixed number of identical sites and no interaction between adsorbed molecules. General form: q = (q_m · b · P) / (1 + b · P). Linear form: P/q = (1/(b q_m)) + (P/q_m). Here q_m is the maximum adsorption corresponding to monolayer coverage and b is related to adsorption affinity.

Gibbs adsorption equation (surface excess): For dilute solutions the surface excess concentration Γ (mol m-2) is related to change in surface tension γ with concentration c at constant T by

  • Γ = - (1 / (R T)) · (dγ / d ln c)
This relates adsorption from solution to measurable changes in surface tension.

Factors affecting adsorption:

  • Surface area and porosity of adsorbent (higher area → more adsorption).
  • Nature of adsorbate and adsorbent (polarity, chemical affinity).
  • Temperature: physisorption decreases with T; chemisorption may increase initially then decrease.
  • Pressure or concentration: adsorption of gases increases with pressure (up to saturation).
  • Presence of other substances (competitive adsorption).

Applications (brief): removal of impurities from gases and liquids (activated carbon), drying (silica gel), catalysts and catalytic converters, gas masks, chromatography, refrigeration (adsorption refrigerators), sensors and surface coatings.

Summary of differences (short):

  • Physisorption: weak forces, reversible, multilayer, favoured at low T.
  • Chemisorption: chemical bonds, often irreversible, usually monolayer, may require activation and higher T.

📌 Examples
  • Activated charcoal removing dyes and odours from water and air (water purification, decolourisation).
  • Silica gel packets used as desiccants to keep products dry (adsorption of water vapour).
  • Catalytic converters in automobiles: gases adsorb on metal surfaces where chemical reactions remove pollutants (chemisorption + catalysis).
  • Gas masks: activated carbon adsorbs toxic gases and vapours.
  • Chromatography: separation is based on differing adsorption affinities of components on the stationary phase.
  • Refrigeration by adsorption: using materials that adsorb and desorb refrigerant vapour to provide cooling.
🧮 Formulas
  1. Amount adsorbed per unit mass: x/m (mass adsorbed x; mass of adsorbent m).
  2. Freundlich isotherm: x/m = k · P^(1/n) (or x/m = k · C^(1/n) for solutions). Linear form: log(x/m) = log k + (1/n) log P.
  3. Langmuir isotherm: q = (q_m · b · P) / (1 + b · P). Linear form: P/q = (1/(b q_m)) + (P/q_m). Surface coverage θ = (b P)/(1 + b P).
  4. Gibbs adsorption equation (dilute solutions): Γ = - (1 / (R T)) · (dγ / d ln c) where Γ is surface excess, γ surface tension, c concentration, R gas constant, T temperature.
  5. Relationship: adsorption is generally exothermic (ΔH_ad &lt; 0). Typical enthalpy ranges: physisorption ≈ &lt; ~20–40 kJ·mol^-1, chemisorption ≈ 40–400 kJ·mol^-1 (order-of-magnitude).
📊 Visual ideas
Adsorption isotherm (Langmuir shape): plot q (amount adsorbed) on Y-axis vs P (pressure) on X-axis at constant temperature — curve rises steeply at low P and approaches a horizontal asymptote q = q_m (monolayer). Caption: 'Langmuir-type saturation curve (monolayer)'.
Freundlich plot (linearised): plot log(x/m) on Y-axis vs log P on X-axis — straight line with slope = 1/n and intercept = log k. Caption: 'Freundlich isotherm (log–log plot)'.
P/q vs P linear plot for Langmuir: plot P/q on Y-axis vs P on X-axis — straight line whose slope = 1/q_m and intercept = 1/(b q_m). Caption: 'Linear form of Langmuir isotherm'.
Temperature dependence: plot amount adsorbed (Y) vs temperature (X). For physisorption show a monotonically decreasing curve; for chemisorption show a curve that increases up to an optimum then decreases. Caption: 'Effect of temperature on physisorption and chemisorption'.
🔬5

Types of adsorption

Adsorption is the accumulation of molecules (adsorbate) at the surface of a solid or liquid (adsorbent). There are two principal types: physisorption (physical adsorption) and chemisorption (chemical adsorption).

  • Physisorption
    • Origin: weak intermolecular (van der Waals) forces.
    • Heat of adsorption: small (≈ 5–40 kJ mol⁻¹).
    • Reversibility: usually reversible; no new chemical bonds formed.
    • Layering: multilayer adsorption is possible.
    • Temperature dependence: decreases with increase of temperature (exothermic).
    • Kinetics: no large activation energy; fast.
    • Specificity: non-specific (depends on polarizability and surface area).
  • Chemisorption
    • Origin: formation of chemical bonds (covalent or ionic) between adsorbate and surface atoms.
    • Heat of adsorption: large (≈ 40–800 kJ mol⁻¹; often > 40 kJ mol⁻¹).
    • Reversibility: often irreversible (or only reversible with heating); new chemical species at surface.
    • Layering: essentially monolayer (surface sites are specific).
    • Temperature dependence: requires activation energy; may increase with temperature up to an optimum then fall due to desorption.
    • Kinetics: may be slow if an activation barrier exists.
    • Specificity: highly specific to surface and adsorbate (site-specific).

Important consequences and applications: Physisorption explains processes where large surface area materials (activated carbon, silica) trap gases or impurities. Chemisorption is fundamental to heterogeneous catalysis (reactants chemisorb on catalyst surface, react and desorb as products), catalyst poisoning, and sensor functioning.

Surface coverage concept: Fractional coverage θ = (number of occupied sites)/(total adsorption sites). For a simple Langmuir model (chemisorption on equivalent sites) θ = (KP)/(1 + KP), where P is pressure and K is an equilibrium constant.

📌 Examples
  • Physisorption: Adsorption of N2 and O2 on activated charcoal at low temperature; removal of organic impurities from water by activated carbon (multilayer adsorption).
  • Physisorption: Adsorption of gases on silica gel (used as desiccant) by hydrogen bonding/van der Waals forces.
  • Chemisorption: Adsorption of H2, N2 and CO on metal catalyst surfaces (e.g., H2 and CO on Pt, Ni) — crucial in hydrogenation and Haber process.
  • Chemisorption: Catalyst poisoning, e.g., CO strongly chemisorbs on Pt and blocks catalytically active sites.
  • Surface treatment: Formation of metal oxide layers by chemisorption of oxygen on metal surfaces (initial step in corrosion).
🧮 Formulas
  1. Langmuir adsorption isotherm (monolayer, chemisorption-like): θ = KP / (1 + KP) (θ = fractional coverage, P = pressure, K = adsorption equilibrium constant).
  2. Langmuir in amount form: x/m = (a b P) / (1 + b P) (x/m = amount adsorbed per unit mass of adsorbent, a = monolayer capacity, b = constant related to affinity).
  3. Freundlich adsorption isotherm (empirical, often for physisorption/multilayer): x/m = k P^(1/n) (k and n are constants; 1/n < 1 typically).
  4. Heat of adsorption (qualitative): physisorption ΔH ≈ 5–40 kJ mol⁻¹; chemisorption ΔH typically > 40 kJ mol⁻¹ (often much larger).
📊 Visual ideas
Amount adsorbed (x/m or θ) vs pressure (P) at constant temperature: show Langmuir curve saturating to a maximum (monolayer) and a Freundlich curve (non-saturating power-law) for comparison.
Amount adsorbed vs temperature (at fixed pressure): physisorption curve decreasing monotonically with T; chemisorption curve that rises (overcoming activation barrier) to a maximum and then falls at high T (desorption).
Potential energy vs distance from surface: shallow well without activation barrier for physisorption (weak binding) and deep well with an activation barrier then deep minimum for chemisorption (strong binding).
Schematic diagrams of monolayer (chemisorption) vs multilayer adsorption (physisorption) on a porous adsorbent surface (show surface sites and multiple adsorbate layers).
🔬6

Factors affecting adsorption

Definition: Adsorption is the accumulation of molecules (adsorbate) at the surface of a solid or liquid (adsorbent). It is a surface phenomenon and may be physical (physisorption) or chemical (chemisorption).

General principle: Adsorption is usually exothermic and depends on the nature of adsorbent/adsorbate and experimental conditions. Adsorption increases with availability of surface area and the strength of interaction between adsorbent and adsorbate.

  • 1. Nature of adsorbent: Adsorbents with large surface area and porosity (activated charcoal, silica gel, alumina) provide more sites for adsorption. Surface heterogeneity (different active sites) affects strength and capacity.
  • 2. Nature of adsorbate: Polar molecules and those that can form specific interactions (H-bonding, ionic, covalent) are adsorbed more strongly. Larger molecules with greater polarizability are often better physisorbates.
  • 3. Surface area and particle size: Smaller particle size → larger surface area per unit mass → higher adsorption capacity. Porous materials give especially high effective area.
  • 4. Concentration (for solutions) / Pressure (for gases): Adsorption increases with increasing concentration or partial pressure of the adsorbate, approaching a saturation value (monolayer for many systems).
  • 5. Temperature: Because adsorption is exothermic, physisorption generally decreases with increasing temperature (Le Chatelier). Chemisorption often has an activation barrier: adsorption may increase with temperature up to an optimum (to overcome activation energy) and then decrease at high temperature.
  • 6. Contact time and agitation: Rate of adsorption increases with agitation (reduces boundary layer) and with time the system approaches equilibrium (saturation of sites).
  • 7. Presence of other substances (competitive adsorption): Co-adsorbates compete for sites and can reduce adsorption of a given species. Impurities can block active sites.
  • 8. pH and ionic strength (for adsorption from solutions): pH changes ionization state of adsorbate and surface charge of adsorbent, strongly affecting ionic adsorption. Higher ionic strength can screen electrostatic interactions and reduce adsorption of ions.
  • 9. Chemical activation / surface treatments: Surface functional groups (e.g., –OH, –COOH) or metal dispersion on catalysts create specific active sites and change adsorption characteristics.

Thermodynamic note: Spontaneity is given by ΔG = –RT ln K (K = equilibrium constant for adsorption). For exothermic adsorption, equilibrium constant K normally decreases with temperature.

Kinetic aspect: Physisorption is usually fast (no chemical bond formation) while chemisorption may be slower and may require activation energy and occur with specificity.

📌 Examples
  • Activated charcoal removing impurities and colour from solutions (large surface area, physisorption and some chemisorption).
  • Silica gel and molecular sieves as desiccants (adsorption of water vapour; pore size selects molecules).
  • Catalytic converters: adsorption of CO, NOx and hydrocarbons on catalyst surfaces (chemisorption leads to reaction).
  • Gas masks and respirators using activated carbon to adsorb toxic gases and vapours.
  • Chromatography: separation based on different adsorption affinities of solutes to the stationary phase.
  • Ion-exchange resins for water softening and removal of heavy metal ions (specific adsorption/chemisorption).
🧮 Formulas
  1. Freundlich isotherm: x/m = k · p^(1/n) (x/m = amount adsorbed per unit mass, p = pressure or concentration; k, n = constants)
  2. Log form (Freundlich): log(x/m) = log k + (1/n) · log p
  3. Langmuir isotherm (monolayer): V = (V_m · b · P) / (1 + b · P) (V = volume adsorbed, V_m = monolayer capacity, b = Langmuir constant, P = pressure)
  4. Surface coverage (Langmuir): θ = (b · P) / (1 + b · P)
  5. Thermodynamics: ΔG° = –RT ln K (K = equilibrium constant for adsorption); for exothermic adsorption K decreases with increasing T
📊 Visual ideas
Adsorption (amount adsorbed) vs Pressure (or concentration): a curve rising steeply at low P and approaching a horizontal asymptote (Langmuir-type monolayer saturation). Label axes: x-axis = Pressure (P) or Concentration (C), y-axis = Amount adsorbed (x/m).
Log(x/m) vs log P (Freundlich): a straight line with slope = 1/n showing Freundlich behaviour. Label axes and show best-fit line.
Adsorption vs Temperature: for physisorption show a decreasing trend (amount adsorbed falls as T increases). For chemisorption show a curve that may rise initially (activation required) and decrease at high T — annotate difference between physisorption and chemisorption.
Amount adsorbed vs Time: a rapid initial rise that slows and asymptotically approaches equilibrium (saturation curve). Useful to illustrate kinetics and effect of agitation/particle size.
🔬7

Adsorption isotherms

Definition: An adsorption isotherm is a relation that describes how the amount of a substance adsorbed on the surface of a solid (adsorbent) varies with the pressure (for gases) or concentration (for solutes) of the adsorbate at constant temperature.

Context (Class 12 level): Adsorption is an interfacial phenomenon. Isotherms quantify equilibrium adsorption at a fixed temperature and help distinguish between monolayer and multilayer adsorption and between different adsorption mechanisms (physical vs chemical).

Types of adsorption relevant to isotherms:

  • Physisorption: due to van der Waals forces, low enthalpy (≈ 20–40 kJ mol⁻¹), usually multilayer, reversible and decreases with increasing temperature.
  • Chemisorption: due to chemical bond formation, higher enthalpy (≈ 40–400 kJ mol⁻¹), usually monolayer, often specific and may be irreversible; may increase with temperature up to an activation point.

Common isotherm models:

1) Freundlich isotherm (empirical): Suitable for heterogeneous surfaces and multilayer adsorption at low-to-moderate pressures/concentrations.

Mathematical form: x/m = k · p^(1/n) (for gases) or x/m = k · C^(1/n) (for solutions), where x/m = amount adsorbed per unit mass of adsorbent, p = equilibrium pressure, C = equilibrium concentration, k and n are constants dependent on temperature and system.

Linear form (for plotting): log(x/m) = log k + (1/n) · log p. A plot of log(x/m) vs log p is a straight line with slope = 1/n and intercept = log k.

2) Langmuir isotherm (monolayer adsorption on uniform sites): Based on assumptions: (a) adsorption occurs at specific homogeneous sites, (b) one molecule per site (monolayer), (c) no interaction between adsorbed molecules, (d) all sites equivalent.

Surface coverage θ = fraction of occupied sites = KP / (1 + KP), where K is adsorption equilibrium constant and P is pressure.

Amount adsorbed x/m = (a·b·P) / (1 + b·P), where a = maximum adsorption capacity (monolayer amount) and b (often = K) is related to adsorption affinity.

Linear form: P/(x/m) = (1/(a·b)) + (P/a). A plot of P/(x/m) vs P is linear; slope = 1/a and intercept = 1/(a·b).

3) BET isotherm (Brunauer–Emmett–Teller): Extension of Langmuir allowing multilayer adsorption; used to determine surface area. Valid typically for relative pressures (P/P0) ≈ 0.05–0.35.

BET equation (linear form): P / [v(P0 − P)] = 1/(v_m c) + [(c − 1)/(v_m c)] · (P/P0), where v = volume adsorbed at pressure P, v_m = monolayer adsorbed gas volume, P0 = saturation vapor pressure, and c is a constant related to adsorption heat.

Qualitative behavior with variables:

  • Pressure (gases): Physisorption increases with pressure and approaches a limit (for monolayer, Langmuir predicts saturation; Freundlich does not predict a strict saturation).
  • Concentration (solutions): Greater concentration → more adsorption until sites saturate (if monolayer behavior).
  • Temperature: Adsorption is generally exothermic, so increasing temperature reduces physisorption. Chemisorption's dependence is more complex (may require activation energy).
  • Surface area and porosity: Larger surface area (e.g., activated carbon) increases adsorption capacity.

Why isotherms matter: They help characterize adsorbents (surface area, porosity), design separation processes (adsorption columns), and understand catalysis and environmental removal (pollutants, gas masks, desiccants).

📌 Examples
  • Activated charcoal adsorbing gases and impurities in water purification: adsorption capacity follows isotherm behaviour depending on concentration/pressure.
  • Silica gel desiccant: water vapour adsorption follows a characteristic isotherm; useful for humidity control.
  • Catalyst surfaces (e.g., H2 adsorption on metal catalysts): often described by Langmuir-type isotherms for monolayer chemisorption.
  • Gas masks and respirators: porous adsorbents capture toxic gases; design uses isotherm data to estimate capacity and breakthrough time.
  • Chromatography stationary phases: adsorption isotherms influence retention and separation efficiency.
🧮 Formulas
  1. Freundlich: x/m = k · p^(1/n) (or x/m = k · C^(1/n)); linear: log(x/m) = log k + (1/n) log p
  2. Langmuir (surface coverage): θ = (K·P) / (1 + K·P); amount: x/m = (a·b·P) / (1 + b·P); linear: P/(x/m) = (1/(a·b)) + (P/a)
  3. BET (linear form): P / [v(P0 − P)] = 1/(v_m c) + [(c − 1)/(v_m c)] · (P/P0)
  4. Surface coverage relation: θ = (x/m) / (x/m)_max (fraction of occupied adsorption sites)
  5. Relationship to thermodynamics (van't Hoff-type): ln K = −(ΔH°/R)(1/T) + constant (K decreases with temperature for exothermic adsorption)
📊 Visual ideas
Freundlich: log(x/m) (y-axis) vs log p or log C (x-axis) — straight line; slope = 1/n, intercept = log k. Use low-to-moderate pressure range.
Langmuir (nonlinear): x/m (y-axis) vs P (x-axis) — rectangular hyperbola approaching saturation (a). Langmuir (linear): P/(x/m) (y-axis) vs P (x-axis) — straight line with slope = 1/a and intercept = 1/(a·b).
BET: P / [v(P0 − P)] (y-axis) vs P/P0 (x-axis) — straight line in the relative pressure range ≈ 0.05–0.35. From slope and intercept find v_m and c.
Qualitative comparison plot: amount adsorbed vs temperature at fixed pressure — shows decrease for physisorption (exothermic) and possible different trend for chemisorption.
🧴8

Adsorption from solutions and gases

Definition
Adsorption is the surface phenomenon in which the concentration of a substance (adsorbate) at the surface of a solid or liquid (adsorbent) becomes greater than in the bulk phase. Adsorption from gases and from solutions differ only in the phase of the adsorbate: gas molecules or solute molecules/ions are concentrated at the surface of a solid.

Types of adsorption

  • Physisorption (physical adsorption): Weak van der Waals forces, usually reversible, low heat of adsorption (≈ 5–40 kJ mol−1), may form multilayers, important at low temperatures.
  • Chemisorption (chemical adsorption): Formation of chemical bonds at surface, usually specific and often irreversible, higher heat of adsorption (≈ 40–400 kJ mol−1), usually monolayer, often requires activation energy.

Adsorption from gases
When a gas contacts a solid, gas molecules collide with and stick to the surface. At equilibrium, a dynamic balance exists between adsorption and desorption. The amount adsorbed depends on pressure, temperature and nature of gas and surface. For many gases on solids at constant temperature, adsorption increases with pressure and then tends to saturate (monolayer).

Adsorption from solutions
When a solute is in contact with a solid surface in a solvent, solute particles concentrate at the solid surface. The extent depends on solute concentration in bulk, temperature, pH, ionic strength (for ions), nature of solvent, and surface properties of the adsorbent. Examples: removal of dyes or ions by activated carbon.

Factors affecting adsorption

  • Surface area and porosity of the adsorbent (larger surface area → larger adsorption).
  • Nature of adsorbent and adsorbate (chemical affinity, polarity).
  • Concentration (or pressure for gases): more adsorbate available → more adsorption up to saturation.
  • Temperature: physisorption decreases with rising temperature; chemisorption may increase up to an optimum then decrease.
  • Presence of other species: competitive adsorption and common-ion effect (in solutions) can reduce adsorption.

Adsorption isotherms (relation at constant temperature)

Two commonly used empirical/theoretical isotherms in Class 12 level:

  • Freundlich isotherm (empirical, for heterogeneous surfaces and multilayer adsorption):
    x/m = k C^(1/n), where x = mass of adsorbate adsorbed, m = mass of adsorbent, C = equilibrium concentration in solution (or pressure for gases), k and n are constants. Linear form: log(x/m) = log k + (1/n) log C. A plot of log(x/m) vs log C is a straight line.
  • Langmuir isotherm (assumes monolayer adsorption on a homogeneous surface):
    x/m = (ab C)/(1 + b C), where a and b are constants (a = monolayer capacity, b related to adsorption energy). Another useful form for linear plotting: C/(x/m) = 1/(ab) + C/a. A plot of C/(x/m) vs C is a straight line.

Energetics and equilibrium
Adsorption is usually exothermic. For physisorption the heat released is small; hence increase in temperature shifts equilibrium to desorption (Le Chatelier). Chemisorption involves larger energies and may require activation energy.

Applications and importance

  • Purification and separation: activated charcoal removes coloured impurities, odours, and toxic substances from water and air.
  • Drying agents: silica gel adsorbs water vapour (desiccant).
  • Catalysis: reactant molecules adsorbed on catalyst surfaces to increase reaction rate (heterogeneous catalysis).
  • Gas masks and filters: adsorption of toxic gases on porous solids.
  • Chromatography: separation based on differential adsorption of solutes on stationary phase.
  • Determination of surface area: BET adsorption of N2 at low temperature is used to find specific surface area.

Desorption
Removal of adsorbed species (by heating, reducing pressure, changing solvent or pH) restores the surface and is important for regeneration of adsorbent.

Summary
Adsorption from gases and solutions is a surface phenomenon controlled by intermolecular forces, surface properties and external conditions (pressure/concentration and temperature). Freundlich and Langmuir isotherms are basic quantitative descriptions used at the Class 12 level.

📌 Examples
  • Activated charcoal adsorption of impurities and coloured matter from water (water purification and decolourisation of sugar).
  • Silica gel adsorbing water vapour in desiccant packets.
  • Adsorption of poisonous gases on charcoal in gas masks and respirators.
  • Heterogeneous catalysis: adsorption of reactant gases on catalyst surface (e.g., H2 and O2 adsorption on platinum in hydrogenation/combustion reactions).
  • Removal of dyes and heavy metal ions from wastewater using adsorbents (activated carbon, zeolites).
🧮 Formulas
  1. Freundlich isotherm: x/m = k C^(1/n); linear form: log(x/m) = log k + (1/n) log C
  2. Langmuir isotherm: x/m = (a b C)/(1 + b C); linear form: C/(x/m) = 1/(a b) + C/a
  3. Fractional coverage (Langmuir): θ = b C / (1 + b C)
  4. Heats: Physisorption heat ≈ 5–40 kJ mol−1 (low); Chemisorption heat ≈ 40–400 kJ mol−1 (high)
📊 Visual ideas
Amount adsorbed (x/m) vs pressure P (for gases) at constant T: show a curve that rises with P and tends to saturate (Langmuir-type monolayer behaviour).
Amount adsorbed (x/m) vs concentration C (for solutions) at constant T: similar saturation curve; Freundlich does not predict saturation and fits as a curve that increases less steeply at high C.
Log(x/m) vs log C: straight line for Freundlich isotherm; slope = 1/n and intercept = log k.
C/(x/m) vs C: straight line for Langmuir isotherm; slope = 1/a and intercept = 1/(a b).
🔬9

Applications of adsorption

What is adsorption? Adsorption is the accumulation of molecules (adsorbate) on the surface of a solid or liquid (adsorbent). It is surface phenomenon and can be physical (physisorption) or chemical (chemisorption). Adsorption is widely exploited because surfaces selectively attract, hold and release molecules under controllable conditions.

Why is adsorption useful? Adsorption concentrates trace species on surfaces making separation, purification, storage and catalysis possible. It is usually fast, reversible (for physisorption) and can be tuned by changing pressure, temperature and surface chemistry.

Major applications (summary):

  • Gas masks and respirators: Activated carbon adsorbs toxic gases and vapours, protecting the wearer.
  • Water purification and decolourization: Activated charcoal removes organic impurities, dyes and odours from water and industrial effluents.
  • Heterogeneous catalysis: Reactants adsorb on catalyst surfaces (e.g., Pt, Pd) where reaction rates are increased; supports (Al2O3, SiO2) increase active surface area.
  • Catalytic converters in automobiles: Adsorb and catalytically convert CO, NOx and hydrocarbons to less harmful gases.
  • Desiccants and drying: Silica gel and molecular sieves adsorb water vapour to keep environments dry.
  • Chromatography and separation: Adsorption chromatography separates components based on differing affinities for a stationary adsorbent (silica, alumina).
  • Pressure Swing Adsorption (PSA): Industrial gas separation (e.g., O2/N2, H2 purification) using differential adsorption at high pressure and desorption at low pressure.
  • Gas storage: Adsorbents such as activated carbon and metal–organic frameworks (MOFs) store H2, CH4 at moderate pressures by physisorption.
  • Sugar refining and food processing: Decolourization of sugar using activated carbon; removal of off‑flavours and colourants.
  • Air purification and VOC removal: Adsorbent beds remove volatile organic compounds (VOCs), odors and pollutants in HVAC and industrial air cleaning.
  • Pharmaceuticals and medicine: Activated charcoal is used to treat some poisonings by adsorbing toxins in the gut.
  • Recovery of solvents: Adsorption is used to recover and recycle solvents from gas streams (e.g., industrial solvent recovery).

How adsorption is controlled in applications — key variables include surface area and pore structure of adsorbent, nature and concentration of adsorbate, temperature (adsorption is generally exothermic so it decreases with increasing temperature), and pressure (for gases).

📌 Examples
  • Activated charcoal in gas masks adsorbs organic vapours and toxic gases to protect the wearer.
  • Water treatment plants use activated carbon to remove colour, odours and organic pollutants from drinking water.
  • Silica gel packets (desiccants) in packaging adsorb moisture to protect electronics and food.
  • Catalytic converters: gases adsorb on Pt, Pd and Rh surfaces where they are converted to CO2, N2 and H2O.
  • Pressure Swing Adsorption (PSA) units produce high‑purity oxygen or hydrogen by cyclic adsorption/desorption on zeolites or activated carbon.
  • Chromatography (adsorption mode) separates components of a mixture because they adsorb to silica/alumina to different extents.
🧮 Formulas
  1. Amount adsorbed per unit mass: x/m (mass of adsorbate adsorbed x per mass of adsorbent m)
  2. Freundlich isotherm (empirical): x/m = k · P^(1/n) (for gases) or x/m = k · C^(1/n) (for solutions); linear form: log(x/m) = log k + (1/n) log P
  3. Langmuir isotherm (monolayer adsorption): x/m = (x_m · b · P) / (1 + b · P), where x_m = maximum adsorption (monolayer), b = Langmuir constant
  4. Linear form of Langmuir: P / (x/m) = (1 / (x_m · b)) + P / x_m (useful to obtain x_m and b from plot of P/(x/m) vs P)
  5. Surface coverage (Langmuir): θ = bP / (1 + bP) where θ = fraction of surface sites occupied
  6. Temperature dependence (approximate): ln b = -ΔH_ads / (R T) + constant, indicating adsorption equilibrium constant b decreases with increasing T for exothermic adsorption
📊 Visual ideas
Adsorption isotherm (amount adsorbed x/m vs pressure P) showing Langmuir type: initial increase and saturation (monolayer plateau) — annotate x_m (monolayer capacity).
Freundlich plot: log(x/m) vs log P giving straight line; annotate slope (1/n) and intercept (log k).
Langmuir linear plot: P/(x/m) vs P showing straight line; label intercept = 1/(x_m · b) and slope = 1/x_m.
Temperature effect: plot amount adsorbed (y) vs temperature (x) at fixed pressure showing decrease of adsorption with increasing temperature (exothermic behaviour).
🔬10

Catalysis

Definition: Catalysis is the increase in the rate of a chemical reaction by a substance called a catalyst which remains chemically unchanged at the end of the reaction. A catalyst provides an alternative reaction pathway with a lower activation energy (Ea).

Types of Catalysis:

  • Homogeneous catalysis: Catalyst and reactants are in the same phase (usually liquid). Example: H3O+ catalysed esterification; acid/base catalysis.
  • Heterogeneous catalysis: Catalyst in a different phase (usually solid catalyst and gaseous/liquid reactants). Example: hydrogenation on Ni, catalytic converters (Pt/Rh).
  • Enzyme (biological) catalysis: Highly specific protein catalysts that operate under mild conditions (e.g., catalase, amylase).

Mechanism (general features):

  • Adsorption: Reactant molecules are adsorbed onto the catalyst surface (for heterogeneous catalysis). Adsorption may be physisorption (weak, van der Waals) or chemisorption (strong, involving bond formation).
  • Activation: Adsorption weakens bonds in reactants and brings them into favourable orientation for reaction, lowering Ea.
  • Reaction on the surface: Adsorbed species react via surface-bound intermediates (Langmuir–Hinshelwood mechanism: both reactants adsorbed; Eley–Rideal: one reactant adsorbed, the other from gas phase).
  • Desorption: Product molecules desorb from the catalyst surface freeing active sites.

Characteristics of catalysts: Catalysts increase reaction rate without being consumed, change the mechanism and activation energy, are selective (favour certain products), can be poisoned (deactivated by certain substances), and may need promoters (increase activity) or supports (increase surface area).

Enzyme catalysis: Enzymes have active sites where substrates bind (lock-and-key or induced-fit models). Enzyme activity depends on temperature, pH, substrate concentration and inhibitors (competitive and non-competitive).

Importance: Catalysis is central to industrial processes (Haber process, Ostwald process, hydrogenation), environmental control (automobile catalytic converters), laboratory syntheses, and biological systems (metabolism).

📌 Examples
  • Haber process: N2 + 3H2 ⇌ 2NH3 with Fe catalyst (promoted with K2O and Al2O3 support).
  • Ostwald process: NH3 oxidised to NO using Pt–Rh catalyst to produce HNO3.
  • Hydrogenation of vegetable oils: H2 addition over Ni catalyst to convert unsaturated fats to saturates.
  • Catalytic converter (automobile): oxidation of CO to CO2 and reduction of NOx using Pt, Pd, Rh.
  • Decomposition of H2O2 by MnO2 (heterogeneous) or catalase enzyme (biological) — rapid decomposition to H2O and O2.
  • Acid-catalysed esterification: RCOOH + R'OH ⇌ RCOOR' + H2O (H+ catalyst).
🧮 Formulas
  1. Arrhenius equation: k = A · e^(−Ea/RT) (catalyst lowers Ea → increases k).
  2. Langmuir adsorption isotherm: θ = (K·p) / (1 + K·p) where θ = fraction of surface sites occupied, p = pressure (or concentration), K = adsorption equilibrium constant.
  3. Simple surface rate (unimolecular step): r = k·θ = k·(K·p)/(1 + K·p).
  4. Turnover number (TON) = moles of product formed / moles of catalyst active sites (or catalyst).
  5. Turnover frequency (TOF) = TON / time (s⁻¹ or h⁻¹).
  6. Michaelis–Menten (enzyme kinetics): v = (Vmax·[S]) / (Km + [S]) where v = initial rate, [S] = substrate conc., Km = Michaelis constant.
📊 Visual ideas
Reaction coordinate diagram: Potential energy (y-axis) vs Reaction coordinate (x-axis) showing two curves—uncatalysed pathway with higher activation energy peak and catalysed pathway with lower peak; label Ea (uncat) and Ea (cat), reactants, products, and intermediate(s) if applicable.
Arrhenius plot: ln k (y-axis) vs 1/T (x-axis) showing two straight lines with slopes −Ea/R; catalysed line has smaller slope (lower Ea) and thus higher k at given T.
Langmuir adsorption isotherm: θ (y-axis) vs pressure or concentration p (x-axis) showing a hyperbolic curve approaching θ = 1 at high p.
Rate vs substrate (or reactant) concentration for enzyme-catalysed reaction: v (y-axis) vs [S] (x-axis) showing Michaelis–Menten rectangular hyperbola; also suggest Lineweaver–Burk double reciprocal plot (1/v vs 1/[S]) for linearization.
🔬11

Colloids — introduction and classification

What is a colloid?
A colloid (or colloidal dispersion) is a heterogeneous system in which one substance (dispersed phase) made up of particles of size roughly 1–1000 nm is distributed uniformly throughout another substance (dispersion medium). Colloids show properties intermediate between true solutions and suspensions.

Key characteristics

  • Particle size: ~1–1000 nm (10⁻⁹–10⁻⁶ m).
  • Tyndall effect: colloidal particles scatter light, making a beam visible in the medium.
  • Brownian motion: continuous, random motion of colloidal particles due to bombardment by molecules of the dispersion medium; this helps prevent sedimentation.
  • Stability: many colloids are kinetically stable because Brownian motion and interparticle repulsion (electrostatic or steric) balance gravitational settling.
  • Electrophoresis and coagulation: charged colloidal particles move in an electric field (electrophoresis); addition of opposite charged ions or high electrolyte concentration causes coagulation (precipitation).

Classification of colloids

1. On the basis of the physical state of dispersed phase and dispersion medium (common CBSE classification):

  • Solid in liquid: sols (e.g., gold sol, starch sol)
  • Liquid in liquid: emulsions (e.g., milk — oil-in-water emulsion)
  • Gas in liquid: foams (e.g., whipped cream, shaving foam)
  • Liquid in solid: gels (e.g., gelatin, agar)
  • Solid in gas: smoke (e.g., soot in air)
  • Liquid in gas: fog or mist (water droplets in air)

2. On the basis of interaction between dispersed phase and dispersion medium:

  • Lyophilic colloids (solvent-loving): strong affinity between phase and medium; easy to prepare and stable (e.g., starch, proteins in water).
  • Lyophobic colloids (solvent-hating): little affinity; less stable and prepared by special methods (e.g., metal sols like gold, silver).

3. On the basis of particle nature / origin:

  • Multimolecular colloids: aggregates of atoms or small molecules (e.g., gold sol, sulphur sol).
  • Macromolecular colloids: single large molecules dispersed (e.g., proteins, polymers such as gelatin, starch solutions behave as colloids).
  • Associated colloids (micellar): formed by association of amphiphilic molecules above the critical micelle concentration (CMC), e.g., sodium dodecyl sulfate micelles.

Why are colloids stable?
Stability arises from (a) Brownian motion that counters sedimentation of small particles, (b) electrostatic repulsion due to like surface charges (measured as zeta potential), and (c) steric stabilization when bulky molecules or polymers coat the particles.

Important observable phenomena

  • Tyndall effect — scattering of light by colloidal particles.
  • Brownian motion — visible under ultramicroscope or inferred by diffusion behavior.
  • Electrophoresis — movement under electric field used to determine sign of colloid charge.
  • Coagulation — destabilization by adding electrolytes or changing pH leading to aggregation and precipitation.

Typical preparations
Condensation methods (building up from smaller species, e.g., hydrolysis–condensation) and dispersion methods (breaking larger particles into colloidal size by milling or sonication).

Summary
Colloids are dispersions of particles 1–1000 nm showing special optical (Tyndall), kinetic (Brownian), electrical (electrophoresis) and stability (coagulation/protection) properties. They are classified by phase combination, solvent affinity (lyophilic/lyophobic), and particle origin (multimolecular, macromolecular, associated).

📌 Examples
  • Milk — an oil-in-water emulsion (liquid dispersed in liquid); fat droplets dispersed in water
  • Butter — water-in-oil emulsion (W/O), droplets of water dispersed in fat
  • Fog / Mist — liquid in gas colloid (water droplets in air)
  • Smoke — solid in gas colloid (soot or dust in air)
  • Gold sol (ruby-coloured gold colloid) — multimolecular solid in liquid sol
  • Starch solution — macromolecular colloid (polymeric chains dispersed in water)
🧮 Formulas
  1. Stokes' law for terminal (sedimentation) velocity: v = (2 r^2 (ρ_p − ρ_m) g) / (9 η) — where r = particle radius, ρ_p = particle density, ρ_m = medium density, g = acceleration due to gravity, η = viscosity of medium. (Shows why very small particles sediment very slowly.)
  2. Stokes–Einstein relation (diffusion coefficient of a spherical particle): D = k_B T / (6 π η r) — where D = diffusion coefficient, k_B = Boltzmann constant, T = absolute temperature, η = viscosity, r = particle radius. (D ∝ 1/r.)
  3. Smoluchowski equation for electrophoretic mobility: μ = (ε ζ) / η — where μ = electrophoretic mobility, ε = dielectric permittivity of medium, ζ = zeta potential, η = viscosity. (Relates mobility to surface charge potential.)
  4. Rayleigh scattering (qualitative): scattering intensity ∝ 1 / λ^4 for particles much smaller than wavelength λ. (Explains why shorter wavelengths scatter more — Tyndall effect.)
📊 Visual ideas
Particle radius (x-axis, log scale) vs diffusion coefficient D (y-axis): show inverse relationship (D ∝ 1/r). Useful to illustrate Brownian motion diminishing with larger particles.
Particle radius (x-axis) vs sedimentation velocity v (y-axis): parabolic increase (v ∝ r^2) from Stokes' law — shows why larger particles settle faster.
Wavelength λ (x-axis) vs scattering intensity I (y-axis): I ∝ 1/λ^4 — steeply higher intensity at shorter wavelengths to illustrate Tyndall effect (blue light scattered more).
pH (x-axis) vs zeta potential ζ (y-axis): curve crossing zero at isoelectric point (where coagulation is most likely). Useful to show stability regions (high |ζ| → stable).
⚖️12

Preparation of colloids

Overview
A colloid is a dispersion of particles (1–1000 nm) of one phase in another. Preparation of colloids is done by two broad approaches: Dispersion methods (breaking larger particles into colloidal size) and Condensation (or chemical) methods (building up particles from ions or molecules).

1. Dispersion methods
These involve physical breakup of bulk material into colloidal particles. Common techniques:

  • Mechanical dispersion (trituration): Grinding or attrition in presence of a suitable liquid (e.g., preparing graphite sols). Produces relatively large colloidal particles.
  • Bredig's arc method (electrical disintegration): An electric arc struck between metal electrodes (Au, Ag, Pt) submerged in water containing a stabilizer (e.g., sodium citrate) produces metal sols (gold, silver sols). Stabilizer prevents coagulation by adsorption and imparting charge.
  • Ultrasonic dispersion: High-frequency sound waves (sonication) break up particles; used for emulsions and nanoparticle suspensions.
  • Peptization: Conversion of a freshly prepared precipitate into a colloidal sol by shaking with a small amount of electrolyte (peptizing agent) whose ions adsorb on particle surfaces and disperse them. Example: washing a precipitated Fe(OH)3 then treating with a little FeCl3 (Fe3+ acts as peptizing ion) yields hydrated ferric oxide sol.
  • Emulsification: Vigorous shaking/ homogenization of two immiscible liquids with an emulsifier (soap, detergent) to form oil-in-water or water-in-oil colloids (e.g., milk, mayonnaise).

2. Condensation (chemical) methods
Small units (atoms, ions, molecules) combine to form colloidal particles. These methods commonly yield smaller and more uniform particles.

  • Chemical reduction: Reduction of metal salts by a reducing agent to give metal sols. Example: gold sol (ruby-coloured) prepared by reducing chloroauric acid with citrate (Turkevich method). General form: metal salt + reducing agent → metal (colloid) + oxidized products.
  • Hydrolysis and controlled precipitation: Slow hydrolysis or precipitation under controlled conditions produces sols. Example: gradual hydrolysis of AlCl3 or FeCl3 to form hydrated oxide sols.
  • Oxidation: Converts a soluble species to an insoluble colloidal oxide/sulfide. Example: formation of sulphur sols by oxidation of H2S or reduction/oxidation reactions.
  • Double decomposition: Mixing solutions so that very small amounts of insoluble product form and remain dispersed (e.g., certain sulfide sols).
  • Change of solvent: A polymer or substance is dissolved in a solvent and then a nonsolvent is added to precipitate very small particles (used in making some polymeric colloids).

Stabilization
Prepared colloids must be stabilized to avoid coagulation. Stabilization mechanisms include: electrostatic stabilization (adsorbed ions give surface charge and repulsion), steric stabilization (adsorbed polymers or surfactants physically block aggregation), or combined electrosteric stabilization. For example, citrate ions adsorb on gold nanoparticles giving negative charge and stability.

Practical notes & tips
- Dispersion methods typically give larger particles and require stabilizers. Condensation methods give smaller particles and allow better control of size (e.g., by controlling rate of nucleation vs growth — LaMer-type behaviour).
- Peptization requires the correct peptizing ion: it is usually the same ion as in the original salt (common-ion adsorption) which imparts charge to disperse the precipitate.

📌 Examples
  • Gold sol by chemical reduction (Turkevich method): chloroauric acid (HAuCl4) reduced by citrate → colloidal Au (ruby-coloured sol); citrate acts as both reducing and stabilizing agent.
  • Silver sol by Bredig's arc method: electric arc between Ag electrodes in water with a stabilizer (e.g., citrate) produces colloidal silver (yellow/brown sol).
  • Hydrated ferric oxide sol by peptization: FeCl3 + 3NH4OH → Fe(OH)3 (precipitate); wash and treat the precipitate with a small amount of FeCl3 and water + agitation → hydrated ferric oxide sol (Fe2O3·xH2O sol).
  • Sulphur sol by oxidation: H2S (or S2− species) oxidized under controlled conditions to form finely divided elemental sulfur colloid.
  • Emulsions (dispersion method + emulsifier): Milk and mayonnaise formed by emulsifying oil/water with proteins or surfactants as stabilizers.
🧮 Formulas
  1. General chemical-reduction: M^n+ + reducing agent → M(0) (colloidal metal) + oxidized products (e.g., AuCl3 + reducing agent → Au_colloid + products).
  2. Peptization example (conceptual): FeCl3 + 3NH4OH → Fe(OH)3 (ppt); Fe(OH)3 + small amount of FeCl3 (peptizing ion Fe3+) + agitation → Fe2O3·xH2O (colloidal sol).
  3. Hydrolysis/precipitation (example): AlCl3 + 3H2O → Al(OH)3 (colloid/precipitate) + 3HCl (controlled conditions yield sol).
  4. Emulsification stabilization (schematic): oil + water + surfactant + mechanical energy → oil-in-water emulsion (droplet size in colloidal range).
📊 Visual ideas
LaMer-type plot (recommended): supersaturation (vertical axis) vs time (horizontal). Show a rapid rise to nucleation threshold, a burst of nucleation, then a decrease (growth stage). Use to illustrate how controlled nucleation produces monodisperse colloids.
Particle size distribution: histogram showing narrower distribution for condensation (chemical) methods and broader distribution for dispersion (mechanical) methods.
Absorbance (or extinction) vs wavelength for gold nanoparticles: peak ~520 nm for ~20 nm Au particles; peak position and width shift with particle size (surface plasmon resonance). Useful to illustrate optical properties and size-dependence.
Zeta potential vs pH: plot showing zeta potential crossing zero at isoelectric point; regions of high |zeta potential| indicate stable sols, low |zeta potential| indicate propensity to coagulate.
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Purification of colloids

What is meant by purification of colloids?
Purification of a colloid means removal of dissolved impurities (mainly small ions and molecules) and unwanted suspended matter from a colloidal dispersion without destroying the dispersed phase. The aim is to obtain the colloidal particles free from soluble electrolytes, excess reagents or low‑molecular impurities.

Main methods

  • Dialysis: A colloidal sol is placed inside a bag made of a suitable semipermeable membrane (e.g. cellophane). Small solute particles (ions, molecules) pass through the pores of the membrane into the surrounding pure solvent by diffusion, while the colloidal particles are retained because of their large size. Repeated change of the outside solvent speeds the process. This is the most widely used method for desalting sols and protein solutions. (Historical: Graham's dialysis.)
  • Electrodialysis: An electric field is applied across the dialysis system. Mobile ions migrate through ion‑selective membranes toward electrodes and are thus removed from the colloid faster than by ordinary dialysis. Useful when ionic removal is slow by diffusion alone.
  • Ultrafiltration (pressure filtration): A porous membrane with a molecular‑weight cut‑off is used under applied pressure (or centrifugation) to force solvent and small solutes through the membrane while retaining colloidal particles. Common in concentrating and desalting protein and polymer colloids (e.g. Amicon filters, tangential flow filtration).
  • Centrifugation and washing (repeated decantation): If colloidal particles can be made to coagulate or are sufficiently large, centrifugation sediments impurities or the dispersed phase; the supernatant (containing soluble impurities) is removed and replaced with pure solvent, repeating the process. Care is needed to avoid irreversible coagulation.
  • Gel filtration / Size‑exclusion chromatography: Separation based on size; useful for macromolecular colloids (proteins, polymers) where small solutes enter pores in the stationary matrix and large colloidal species elute earlier.

Key points to remember

  • Dialysis relies on diffusion (small species move down concentration gradients); colloidal particles are retained due to their large hydrodynamic size.
  • Electrodialysis accelerates ion removal by electrical migration.
  • Ultrafiltration uses pressure and pore size to separate components by size; it is faster and scalable for industrial use.
  • Centrifugation can concentrate or wash colloids but may induce aggregation if conditions are not controlled.

Practical considerations

  • Choice of membrane: pore size (molecular weight cut‑off), chemical compatibility, and mechanical strength matter.
  • Buffer/bath volume and number of solvent changes determine dialysis efficiency; larger bath-to-sample volume and more changes speed purification.
  • Temperature and pH should be controlled to avoid destabilizing the colloid.

Analogy: Dialysis of colloids is analogous to kidney dialysis (hemodialysis) where waste small solutes are removed from blood while blood cells and proteins are retained.

📌 Examples
  • Desalting of protein solutions after ammonium sulfate precipitation using dialysis to remove excess salt.
  • Purification of colloidal gold (gold sol): removing excess ionic gold species and chloride ions by dialysis.
  • Ultrafiltration in the dairy industry: concentrating milk proteins (whey protein) and removing lactose/minerals.
  • Electrodialysis for demineralization of food solutions (e.g. demineralizing whey or sugar solutions).
  • Use of dialysis bags in biochemistry labs to remove small reaction byproducts from macromolecule solutions.
🧮 Formulas
  1. Fick's first law (diffusion driving dialysis): J = -D (dC/dx) — flux J is proportional to concentration gradient; D is diffusion coefficient.
  2. Stokes' law for sedimentation (useful for centrifugation concept): v = (2/9) * (r^2 (ρ_p - ρ_m) g) / η, where v is terminal velocity, r particle radius, ρ_p and ρ_m densities of particle and medium, g acceleration due to gravity, η viscosity.
  3. Electrophoretic migration (ion velocity in electrodialysis): v = μ_e * E, where μ_e is electrophoretic mobility and E is electric field strength.
  4. Simplified membrane flux for ultrafiltration (qualitative): J ≈ (ΔP - Δπ)/R, where J is volumetric flux, ΔP applied pressure, Δπ osmotic pressure, and R hydraulic resistance of membrane (practical performance also depends on fouling).
📊 Visual ideas
Dialysis: plot of concentration of small solute (e.g. salt) inside the dialysis bag versus time — an exponential decay approaching zero (semilog plot shows linear behaviour during well‑mixed conditions).
Ultrafiltration: flux (J) versus applied pressure (ΔP) — roughly linear at low pressures, deviating at higher pressure due to concentration polarization and membrane compaction.
Electrodialysis: ionic conductivity (or ion concentration) in the treated solution versus time under applied electric field — faster decline than simple dialysis; compare curves with and without field.
Centrifugation/washing: turbidity (optical density) of supernatant versus number of wash cycles — stepwise decrease as impurities are removed.
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Stability of colloids and coagulation

Overview
A colloid is said to be stable if its dispersed particles remain separated and do not aggregate (coagulate) for a long time. Stability arises from a balance of repulsive and attractive forces between particles. Coagulation (flocculation/precipitation) occurs when attractive forces overcome repulsion and particles aggregate.

Main factors controlling stability

  • Electrical charge and the electrical double layer: Most lyophobic colloidal particles carry a charge. An oppositely charged diffuse layer of ions surrounds each particle, producing an electrical double layer (Helmholtz/Stern + diffuse layer). The potential at the slipping plane is the zeta (ζ) potential. Larger magnitude of ζ (typically > ~30 mV or < -30 mV) gives stronger electrostatic repulsion and greater stability.
  • Solvation and steric effects: Lyophilic (solvent-loving) layers or adsorbed polymers (protective colloids) produce steric hindrance and solvation, preventing close approach and stabilizing the dispersion.
  • Van der Waals attraction: Universal attractive forces act between particles and favour coagulation when particles come sufficiently close.

DLVO concept (qualitative)
The DLVO theory describes total interaction energy V_total(r) between two particles as the sum of van der Waals attraction (V_A) and electrical double-layer repulsion (V_R): V_total = V_A + V_R. The energy curve versus separation typically shows an energy barrier (prevents aggregation) and possible primary/secondary minima. If the barrier >> thermal energy (kT) the colloid is stable; reducing the barrier (e.g., by adding electrolytes) leads to coagulation.

Coagulation by electrolytes
Adding electrolytes compresses the double layer (screening), lowers ζ-potential and decreases the repulsive barrier. Multivalent counterions are much more effective than monovalent ones in causing coagulation (Hardy–Schulze rule).

Hardy–Schulze rule
The coagulating power of an ion increases rapidly with its valency: for a negatively charged sol, higher-valency cations (e.g., Al3+) are much more effective than Na+.

Protective colloids and gold number
A protective colloid (lyophilic) stabilizes a lyophobic sol by adsorbing on particles and imparting steric/solvation protection. The gold number is an experimental measure of protective power: the smaller the gold number, the more effective the protective colloid.

Critical coagulation concentration (CCC)
The minimum concentration of an electrolyte that causes rapid coagulation is called the CCC (or coagulation value). CCC decreases sharply with increasing counterion valency.

Other coagulation methods
Coagulation may also be induced by heating (destroying solvation layers), mechanical stirring/centrifugation (bringing particles close), by changing pH (altering surface charge), or by applying electric fields (electrophoresis).

Kinetic note
Coagulation (perikinetic or orthokinetic) often follows second-order kinetics for particle number: -dn/dt = k n^2, where n is particle concentration and k is the coagulation rate constant (diffusion- or shear-controlled).

Practical importance
Understanding stability and coagulation is essential for water purification (use of alum/flocculants), pharmaceuticals (preventing aggregation of suspensions), food technology (milk stability, cheese-making), paints, and photographic emulsions.

📌 Examples
  • Water purification: Addition of alum (Al2(SO4)3) causes coagulation of colloidal impurities (negative colloids) and formation of flocs that settle.
  • Milk coagulation (curdling): Acid or enzymes reduce electrostatic repulsion/solvation of casein micelles and cause aggregation to form curd.
  • Photography: Gelatin acts as a protective colloid stabilizing silver halide particles; controlling coagulation affects image development.
  • Sewage treatment: Flocculants (polymers or multivalent ions) induce coagulation of suspended colloidal matter to remove turbidity.
  • Paints and inks: Stabilizers (protective colloids or surfactants) prevent pigment particles from aggregating, preserving uniform color and flow.
  • Industrial tanning: Multivalent metal salts (e.g., chrome) cause coagulation/precipitation of leather proteins, aiding tanning.
🧮 Formulas
  1. V_total(r) = V_A(r) + V_R(r) (DLVO total interaction energy as function of separation r)
  2. -dn/dt = k n^2 (second-order kinetic law for coagulation; n = particle concentration, k = rate constant)
  3. Gold number: minimum mg of protective colloid that prevents coagulation of 10 mL of gold sol on adding 1 mL of 10% NaCl (smaller = more protective)
  4. Critical coagulation concentration (CCC): minimum electrolyte concentration causing rapid coagulation (experimentally determined)
  5. Empirical Schulze–Hardy trend: coagulating power increases very rapidly with counter-ion valency (qualitative often cited as ∝ z^6 as an approximate dependence)
  6. Zeta potential criterion (practical): |ζ| ≳ 30 mV typically indicates a reasonably stable colloid (values depend on system)
📊 Visual ideas
Interaction energy vs separation distance: plot V_total(r) showing van der Waals attraction, double-layer repulsion, an energy barrier (activation barrier), and possible primary/secondary minima. Annotate barrier height relative to kT to indicate stability/instability.
Zeta potential magnitude vs electrolyte concentration: a curve showing ζ decreasing (in magnitude) as electrolyte concentration increases, with a marked point at CCC where rapid coagulation begins.
Coagulation rate (or turbidity) vs time for different electrolyte valencies: multiple curves showing faster drop in turbidity (or faster particle loss) with higher-valency counterions (e.g., Na+ vs Ca2+ vs Al3+).
Schematic bar chart of coagulating power (or inverse: coagulation value) vs counter-ion valency to illustrate the Hardy–Schulze rule (multivalent ions much more effective).
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Properties of colloids

Definition: A colloid (or colloidal dispersion) is a heterogeneous system in which one substance (dispersed phase) of particle size roughly 1–1000 nm is dispersed in another (dispersion medium). Colloids show properties intermediate between those of true solutions and suspensions.

Classification (brief)

  • On the basis of physical state: sols (liquid in solid or liquid), aerosols (liquid/solid in gas), emulsions (liquid in liquid), gel (semisolid), etc.
  • On the basis of interaction between phases: lyophilic (solvent-loving) and lyophobic (solvent-hating).

Key properties and explanations

  • Tyndall effect (scattering of light): Colloidal particles scatter visible light so the beam becomes visible when passed through a colloid. Scattering is stronger for shorter wavelengths (blue) — explains why colloids show bluish scattered light. This distinguishes colloids from true solutions (no scattering).
  • Brownian motion: Colloidal particles undergo continuous random motion due to collisions with molecules of the dispersion medium. This motion prevents settling and contributes to stability. Mean square displacement is proportional to time.
  • Electrophoresis: Colloidal particles usually carry electric charges and move under an applied electric field. The direction depends on the sign of the charge; this property is used in separation and purification.
  • Charge and double layer: Most colloidal particles acquire charge (adsorption of ions, ionization of surface groups). A layer of counterions (stern + diffuse layer) forms around the particle. The potential at the slipping plane (zeta potential) is an important measure of stability: higher magnitude zeta potential (positive or negative) usually means greater electrostatic repulsion and thus more stability.
  • Coagulation (flocculation) and stability: Addition of electrolytes, acids or removal of solvent can reduce repulsive forces and cause particles to aggregate (coagulate) and precipitate. The minimum electrolyte concentration needed to cause rapid coagulation is the critical coagulation concentration (CCC). Lyophilic colloids are more stable than lyophobic ones. Protective colloids (e.g., starch, gelatin) can stabilize lyophobic sols by adsorption and steric/electrostatic effects.
  • Dialysis: Separation of small ions/molecules from colloidal particles through a semipermeable membrane — used to purify colloids.
  • Optical and kinetic behavior: Colloids show optical properties (scattering, turbidity) and kinetic properties (diffusion, electrophoresis). Their chemical reactivity may be enhanced because of large surface area.

Mechanistic notes

  • Stability is governed by balance between attractive van der Waals forces and repulsive electrostatic forces (DLVO concept — qualitative at this level).
  • Protective colloids stabilize sols by forming a protective layer, preventing approach and aggregation of dispersed particles.

Importance and applications

  • Many biological systems are colloidal (blood, milk). Industrial products (paints, inks, cosmetics), environmental phenomena (fog, aerosols), and nanomaterials all involve colloids.

Note for students: Understand each property qualitatively and relate it to experiments such as observing Tyndall effect, Brownian motion under a microscope, electrophoresis in an apparatus, and coagulation by adding salt.

📌 Examples
  • Milk (an emulsion) — fat globules dispersed in water
  • Fog and clouds (liquid droplets in air) — aerosol
  • Smoke (solid particles in air) — aerosol
  • Blood (sols of proteins and cells in plasma)
  • Colloidal gold sol — shows red/violet colour due to scattering/absorption
  • Paints and inks — pigments dispersed in a medium
🧮 Formulas
  1. Stokes–Einstein relation (diffusion coefficient): D = k_B T / (6 π η r), where k_B = Boltzmann constant, T = temperature, η = viscosity, r = particle radius.
  2. Stokes' law (terminal settling velocity for small spherical particles): v = (2/9) (r^2 (ρ_p − ρ_f) g) / η, where ρ_p and ρ_f are particle and fluid densities, g = gravity.
  3. Smoluchowski electrophoretic mobility (approx.): u = ε ζ / η, where ε = permittivity of medium, ζ = zeta potential, η = viscosity.
  4. Rayleigh scattering (small particles): scattered intensity I ∝ r^6 / λ^4 (for particles much smaller than wavelength λ).
  5. Qualitative: Higher |ζ| ⇒ greater electrostatic repulsion ⇒ increased colloidal stability.
📊 Visual ideas
Scattering intensity vs wavelength: plot intensity on y-axis and wavelength (nm) on x-axis; curve rises steeply toward shorter wavelengths (illustrates Tyndall/Rayleigh trend — more blue scattering).
Mean squared displacement (⟨x^2⟩) vs time for Brownian motion: straight line through origin (linear relation ⟨x^2⟩ ∝ t) — label slope related to diffusion coefficient.
Electrophoretic mobility (or velocity) vs applied electric field: linear relation; slope gives mobility u.
Stability (zeta potential magnitude) vs coagulation tendency: plot zeta potential magnitude on x-axis and rate of coagulation on y-axis (downward trend — higher |ζ| means lower coagulation rate).
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Emulsions and micelles

Overview
Emulsions and micelles are colloidal systems important in surface chemistry. Both involve amphiphilic molecules (surfactants) that contain a hydrophilic (water‑loving) head and a hydrophobic (water‑loving) tail. Surfactants reduce interfacial tension and stabilize dispersed phases.

Emulsions
An emulsion is a heterogeneous system of two immiscible liquids where one liquid is dispersed as droplets (dispersed phase) in the other (continuous phase). Common types: oil‑in‑water (O/W) and water‑in‑oil (W/O). Multiple emulsions (e.g., W/O/W) also exist.

  • Formation: Mechanical agitation (shaking, homogenizer) in presence of an emulsifying agent (surfactant, protein, polymer) produces small droplets.
  • Stabilization: Surfactants adsorb at droplet interfaces forming a protective layer; steric and/or electrostatic repulsion prevents coalescence.
  • Instability processes: Creaming/sedimentation (density differences), coalescence (droplets fuse), flocculation (clustering), Ostwald ripening (smaller droplets dissolve and redeposit on larger ones), phase inversion (type change O/W ↔ W/O).
  • Emulsifying agents: Soaps & detergents, proteins (egg yolk in mayonnaise), gums, synthetic polymers (PEG derivatives).
  • Bancroft's rule: The phase in which the emulsifier is more soluble becomes the continuous phase (hydrophilic emulsifiers favor O/W; lipophilic emulsifiers favor W/O).
  • HLB (Hydrophile–Lipophile Balance): A numerical scale (0–20) used to choose emulsifiers: low HLB ~ lipophilic (W/O), high HLB ~ hydrophilic (O/W).

Micelles
Micelles are aggregates of surfactant molecules formed in a liquid when the surfactant concentration exceeds the critical micelle concentration (CMC). In aqueous media, hydrophobic tails pack inside and hydrophilic heads face water (normal micelles). In nonpolar solvents reverse micelles form (tails out, heads inside).

  • CMC: Minimum concentration of surfactant at which micelles form. Below CMC surfactant exists mainly as monomers at interfaces; above CMC, additional surfactant forms micelles.
  • Shapes: Spherical, cylindrical, disc-like, lamellar—shape depends on surfactant packing parameter.
  • Functions: Solubilization of oils and hydrophobic drugs, detergency (micelles encapsulate grease), enhanced transport in formulations.
  • Factors affecting CMC: Carbon chain length (longer chain → lower CMC), ionic strength (for ionic surfactants, added salt lowers CMC), temperature (nonionic surfactants show U‑shaped temp dependence), head group type.
  • Thermodynamics: Micellization is driven by the hydrophobic effect; standard free energy of micellization per mole of monomer can be estimated from CMC.

Key distinctions
Emulsions are two‑phase dispersions (droplets of one liquid in another) requiring an emulsifier to stabilize macroscopic droplets. Micelles are molecular assemblies (nanometre scale) formed above the CMC; they are single‑phase solutions from the macroscopic point of view.

Practical notes
Many everyday products use these phenomena: milk, creams, mayonnaise, paints, cosmetics (emulsions), and detergents, drug formulations, and enhanced oil recovery (micelles & surfactants).

📌 Examples
  • Milk and cream: oil‑in‑water emulsions stabilized by proteins and phospholipids.
  • Mayonnaise: O/W emulsion stabilized by lecithin (egg yolk).
  • Butter: W/O emulsion (water droplets dispersed in fat).
  • Soaps and detergents: form micelles that solubilize grease and oils.
  • Drug delivery: micellar carriers solubilize hydrophobic drugs (e.g., polymeric micelles).
  • Cosmetic lotions and creams: stabilized emulsions for skin application.
🧮 Formulas
  1. Gibbs adsorption equation (surface excess): Γ = - (1 / RT) (∂γ / ∂ ln c) [Γ: surface excess (mol m^-2), γ: surface tension, c: concentration (mol m^-3), R: gas constant, T: temperature]
  2. Standard free energy of micellization: ΔGº_mic ≈ RT ln X_CMC [X_CMC: CMC expressed as mole fraction]
  3. Griffin's HLB (for nonionic surfactants): HLB = 20 × (M_hydrophilic / M_total) [M: molecular mass of group(s)]
  4. Aggregation number (approx.): N ≈ (M_micelle) / (M_monomer) or experimentally from light scattering/other methods
  5. Surface pressure: π = γ_0 - γ [γ_0: surface tension of pure solvent; γ: surface tension at given surfactant concentration]
📊 Visual ideas
Surface tension (γ) versus log[surfactant concentration]: sharp decrease of γ with concentration up to CMC, then a plateau; the break indicates the CMC.
Conductivity versus surfactant concentration (for ionic surfactants): linear increase with one slope below CMC and a different (lower) slope above CMC; breakpoint gives CMC.
Intensity of scattered light or turbidity versus concentration: low below CMC, sharp rise at/above CMC as micelles form and scatter light (useful for some surfactants).
Fraction of monomer versus concentration: near 100% monomer below CMC, then monomer fraction levels off while micelle fraction increases above CMC.
🔬17

Soaps and synthetic detergents

Overview
Soaps and synthetic detergents are surface-active agents (surfactants) used for cleaning. They contain a polar (hydrophilic) head and a long non‑polar (hydrophobic) tail. This dual nature allows them to reduce surface tension of water, wet surfaces, emulsify oils and suspend dirt so it can be rinsed away.

Soaps — composition and preparation
Soaps are sodium or potassium salts of long‑chain fatty acids, produced by the saponification (alkaline hydrolysis) of fats and oils (triglycerides):

Triglyceride + NaOH (or KOH) → glycerol + soap (RCOO−Na+)

Example (structural idea): triglyceride + 3 NaOH → 3 RCOO− Na+ + glycerol.

Typical soap molecules: sodium stearate, CH3(CH2)16COO− Na+; sodium palmitate, CH3(CH2)14COO− Na+.

Cleaning (cleansing) action of soap
1. Wetting and adsorption: soap molecules adsorb at the water–oil and water–solid interfaces, lowering surface tension and allowing water to wet the dirt.

2. Emulsification: hydrophobic tails enter oil/grease, hydrophilic heads remain in water, breaking the oil into small droplets.

3. Micelle formation: above a characteristic concentration (critical micelle concentration, CMC) soap molecules aggregate to form micelles with hydrophobic cores that solubilize grease. The micelles remain dispersed in water and are washed away.

Limitations of soap
In hard water (containing Ca2+ and Mg2+) soaps form insoluble precipitates (soap scum):

2 RCOO− Na+ + Ca2+ → (RCOO)2Ca(s) + 2 Na+

Also, acid (HCl) converts soap back to fatty acid (insoluble):

RCOO− Na+ + HCl → RCOOH(s) + NaCl

Synthetic detergents
Detergents are synthetic surfactants designed to work in hard water and have specific functional groups. They are classified by the charge on the hydrophilic head:

  • Anionic (negatively charged head): e.g., alkyl sulfate (sodium dodecyl sulfate, SDS: CH3(CH2)11OSO3− Na+) and linear alkyl benzene sulfonates (LAS, e.g., C12H25–C6H4–SO3− Na+). Widely used in laundry and dishwashing.
  • Nonionic (no charge): e.g., alkyl polyethoxylates R–O–(CH2CH2O)n–H (used in detergents and cleaners); less sensitive to hard water, low foaming.
  • Cationic (positively charged head): quaternary ammonium salts R4N+X− (e.g., cetyltrimethylammonium bromide, CTAB). Used as fabric softeners, antiseptics and hair conditioners (antistatic agents).
  • Amphoteric (zwitterionic): contain both + and − charges (e.g., cocamidopropyl betaine) and are mild, used in shampoos and baby products.

Advantages of detergents over soaps

  • Work well in hard water (do not form scum with Ca2+/Mg2+).
  • Can be tailored for specific uses (high foaming, low foaming, antimicrobial).
  • Active at lower temperatures and over a wider pH range.

Environmental and practical issues
Earlier branched detergents were non‑biodegradable and caused foaming and pollution. Modern detergents use linear alkyl benzene sulfonates (LAS) which are more biodegradable. Builders such as sodium tripolyphosphate (STPP) improve cleaning but phosphates can cause eutrophication of water bodies — algal blooms and oxygen depletion. Biodegradability, wastewater treatment and reduced phosphate formulations are important considerations.

Important concepts and terms

  • Critical micelle concentration (CMC): the concentration above which micelles form; surface tension stops decreasing significantly above CMC.
  • Krafft temperature: the minimum temperature at which ionic surfactants form micelles and become soluble; below this temperature solubility is very low.
  • Hydrophilic–lipophilic balance (HLB): a scale indicating whether a surfactant is more water‑soluble (higher HLB) or oil‑soluble (lower HLB), used to select surfactants for emulsions.

Summary (stepwise cleansing)

  1. Soap/detergent molecules adsorb at interfaces and lower surface tension.
  2. Hydrophobic tails penetrate grease/oil; hydrophilic heads interact with water.
  3. Micelles form around oil droplets, emulsifying and solubilizing them.
  4. Micelles with trapped dirt are rinsed away in water.
📌 Examples
  • Sodium stearate (soap): CH3(CH2)16COO− Na+. Used in bath soaps.
  • Sodium palmitate (soap): CH3(CH2)14COO− Na+. Another common soap component.
  • Sodium dodecyl sulfate (SDS, aka sodium lauryl sulfate): CH3(CH2)11OSO3− Na+. An anionic detergent used in shampoos and lab applications.
  • Linear alkyl benzene sulfonate (LAS): C12H25–C6H4–SO3− Na+. Major laundry detergent surfactant.
  • Cetyltrimethylammonium bromide (CTAB): a cationic surfactant used as antiseptic/fabric softener (general formula R4N+X−).
  • Cocamidopropyl betaine: an amphoteric surfactant used in mild shampoos and baby products.
🧮 Formulas
  1. Saponification (general): triglyceride + 3 NaOH → 3 RCOO− Na+ + glycerol
  2. Soap (example): sodium stearate: CH3(CH2)16COO− Na+
  3. Anionic detergent (example): sodium dodecyl sulfate (SDS): CH3(CH2)11OSO3− Na+
  4. Reaction with hard water (precipitation): 2 RCOO− Na+ + Ca2+ → (RCOO)2Ca(s) + 2 Na+
  5. Acid reaction (soap neutralized): RCOO− Na+ + HCl → RCOOH(s) + NaCl
  6. General cationic surfactant: R4N+ X− (quaternary ammonium salt)
📊 Visual ideas
Surface tension (y‑axis) vs log[surfactant concentration] (x‑axis): sharp fall in surface tension up to the CMC, then plateau. Mark the CMC point.
Conductivity (y‑axis) vs concentration (x‑axis) for ionic surfactant: two linear regions with a break at CMC (change in slope) — useful to determine CMC.
Solubility (y‑axis) vs temperature (x‑axis) showing Krafft temperature: below TK solubility is very low; above TK solubility increases sharply allowing micelle formation.
Schematic micelle diagram: spherical micelle with hydrophobic tails inward, hydrophilic heads outward; show oil droplet solubilized inside micelle.
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Applications and importance of surface chemistry

What is surface chemistry? Surface chemistry deals with phenomena that occur at the interface between two phases (solid–gas, solid–liquid, liquid–gas). These phenomena include adsorption, surface tension, wetting, contact angle, catalysis at surfaces and stability of colloids. Surface effects often dominate when the ratio of surface area to volume is large (e.g., nanoparticles, powders, thin films).

Why is it important? Surface chemistry explains and controls many industrial, environmental and biological processes by manipulating interactions that occur at interfaces. It enables purification, catalysis, formulation of stable products (paints, medicines, foods), control of wetting and adhesion, and the design of sensors and nanomaterials.

Major application areas (brief explanation):

  • Heterogeneous catalysis: Reactions take place on catalyst surfaces (e.g., Haber process for NH3, catalytic converters in automobiles). Adsorption of reactants on the surface, bond weakening, and desorption of products are key steps that speed up reactions dramatically.
  • Adsorption-based separation & purification: Adsorbents (activated carbon, silica gel) remove impurities, dyes, gases or ions from water and air. This principle is used in water treatment, gas masks, and chromatography.
  • Chromatography: Separation relies on differential adsorption of components on stationary phase surfaces vs mobile phase. Surface chemistry controls retention and selectivity.
  • Surfactants, soaps and detergents: Surface-active agents lower surface tension, form micelles above critical micelle concentration (CMC) and enable cleaning, emulsification and wetting.
  • Colloids and emulsions: Stability or coagulation of colloids depends on interfacial forces and adsorption of stabilizers (electrostatic or steric stabilization). Important in foods, paints, pharmaceuticals.
  • Froth flotation: Separation of ores uses differential wetting/adsorption to separate valuable minerals from gangue by making them hydrophobic.
  • Surface tension & capillarity: Phenomena like droplet formation, capillary rise, wicking in porous materials, and inkjet printing are controlled by surface tension and contact angle.
  • Coatings, paints and adhesives: Adhesion, spreading and wetting depend on interfacial energies; surface treatments modify adhesion and corrosion resistance.
  • Biological systems & medicine: Lung surfactant lowers alveolar surface tension preventing collapse; adsorption phenomena underlie drug delivery, biosensors, protein-surface interactions.

How surface chemistry principles are exploited:

  • Designing catalysts with high surface area and appropriate active sites to maximize adsorption of reactants and product turnover.
  • Choosing adsorbents (activated carbon, zeolites) with suitable pore structure and surface chemistry for targeted removal of pollutants.
  • Formulating surfactants and stabilizers (ionic, non-ionic) to control CMC, foaming, emulsification and colloid stability.
  • Tuning surface treatments (plasma, silanization) to modify wettability, adhesion or biocompatibility.

Practical importance (summary): Surface chemistry enables energy-efficient chemical processes (via catalysts), cleaner water and air (via adsorption), stable consumer products (cosmetics, paints, foods), advanced materials (nanoparticles, sensors), and critical biomedical functions (lung surfactant, implants). Understanding and controlling interfacial phenomena is central to modern chemistry, materials science and environmental technology.

📌 Examples
  • Haber process: iron catalyst surface adsorbs N2 and H2 — increases rate of ammonia formation.
  • Automobile catalytic converter: Pt/Pd/Rh surfaces catalyze oxidation of CO and hydrocarbons and reduction of NOx.
  • Activated carbon filters: adsorption of organic pollutants and chlorine from water and air purification.
  • Chromatography (TLC, GC, HPLC): separation based on different adsorption affinities to stationary phase surfaces.
  • Detergents and soaps: surfactants lower surface tension and form micelles to solubilize oils and grease.
  • Froth flotation in ore dressing: collectors adsorb on mineral surfaces to make them hydrophobic for separation.
🧮 Formulas
  1. Surface tension (definition): γ = F / L (force per unit length, N m^-1).
  2. Young–Laplace (pressure difference across a curved surface): ΔP = 2γ / r (for a spherical drop of radius r).
  3. Capillary rise (Jurin's law): h = 2γ cosθ / (ρ g r) where θ is contact angle, ρ density, g gravity, r capillary radius.
  4. Young's equation (contact angle): γ_SV = γ_SL + γ_LV cosθ (relates solid–vapor, solid–liquid, liquid–vapor interfacial tensions).
  5. Gibbs adsorption equation (dilute solutions): Γ = -(1/RT) (dγ / d ln c) where Γ is surface excess, c is concentration, R gas constant, T temperature.
  6. Langmuir adsorption isotherm (monolayer adsorption): θ = (K C) / (1 + K C) or amount adsorbed x/m = (a b C) / (1 + b C) (K or b = adsorption constant).
📊 Visual ideas
Adsorption isotherms (amount adsorbed vs concentration): show Langmuir curve that levels off to a plateau (monolayer saturation) and Freundlich curve (log–log near-linear). Axes: x-axis = concentration C (mol L^-1), y-axis = amount adsorbed x/m (mol g^-1).
Surface tension vs log(concentration) for surfactants: γ decreases with increasing concentration and shows a sharp change at CMC (critical micelle concentration). Axes: x-axis = log(concentration), y-axis = surface tension γ (mN m^-1).
Capillary rise (h) vs 1/r: linear relation (h ∝ 1/r) predicted by Jurin's law. Axes: x-axis = 1/r (m^-1), y-axis = capillary rise h (m).
Contact angle illustration (schematic): solid surface with droplets showing different contact angles (θ < 90° wetting/spreading, θ > 90° non-wetting). Axes not required — use annotated sketches to compare θ values and relate to γ values.

Key Concepts

Adsorption
Accumulation of molecules (gas/liquid) on the surface of a solid or liquid (surface phenomenon).
Absorption
Uptake of a substance throughout the bulk of another phase (volume phenomenon).
Adsorbate
The substance (molecules or ions) that gets accumulated on the surface during adsorption.
Adsorbent
The solid or liquid surface on which adsorption takes place.
Physisorption (Physical adsorption)
Adsorption due to weak van der Waals forces; usually reversible, low activation energy, multilayer possible and favours low temperature.
Chemisorption (Chemical adsorption)
Adsorption involving formation of chemical bonds between adsorbate and surface; usually irreversible, monolayer and requires activation energy.
Freundlich adsorption isotherm
An empirical relationship (x/m = k·p^(1/n)) describing non-ideal adsorption on heterogeneous surfaces where x/m is amount adsorbed per unit mass.
Surface tension
Energy required to increase the surface area of a liquid per unit area; arises from unequal intermolecular forces at the surface.
Capillarity (Capillary action)
Rise or fall of a liquid in a narrow tube due to adhesive and cohesive forces and surface tension.
Colloid
A heterogeneous system in which one substance (dispersed phase) is finely distributed in another (dispersion medium) with particle sizes ~1–1000 nm.
Sol
A colloidal system where solid particles are dispersed in a liquid medium.
Gel
A semi-solid colloidal system in which a liquid is dispersed in a solid network, giving elastic properties.
Lyophilic colloid
Colloids in which dispersed particles have strong affinity for the dispersion medium and are readily formed and stable.
Lyophobic colloid
Colloids in which dispersed particles have little affinity for the medium; difficult to form and less stable.
Emulsion
A colloidal system of two immiscible liquids where one liquid is dispersed as droplets in the other.
Micelle
An aggregate of surfactant molecules in solution with hydrophobic tails inward and hydrophilic heads outward, forming above a certain concentration.
Critical Micelle Concentration (CMC)
The minimum concentration of surfactant above which micelles start to form and surface tension levels off.
Tyndall effect
Scattering of light by colloidal particles, making a light beam visible in the medium.
Brownian movement
Random zigzag motion of colloidal particles resulting from collisions with molecules of the dispersion medium.
Coagulation (Flocculation)
Process by which colloidal particles aggregate and precipitate on addition of electrolytes, by changing charge or reducing repulsion.

End-of-Chapter Trial Paper & Test Questions

Topic-wise questions to test your understanding of every concept in this chapter.

  1. Distinguish between physisorption and chemisorption. / भौतिक अधिशोषण तथा रासायनिक अधिशोषण में अंतर बताइए।
    Show answer

    Physisorption involves weak van der Waals forces, low heat (~20-40 kJ/mol), is reversible and multilayer and decreases with temperature; chemisorption involves chemical bonds, high heat (~40-400 kJ/mol), is often irreversible, monolayer and may need activation energy. / भौतिक अधिशोषण में दुर्बल वान्डरवाल्स बल, कम ऊष्मा (~20-40 kJ/mol), उत्क्रमणीय व बहुपरतीय होता है तथा ताप बढ़ने पर घटता है; रासायनिक अधिशोषण में रासायनिक बंध, उच्च ऊष्मा (~40-400 kJ/mol), प्रायः अनुत्क्रमणीय, एकपरतीय होता है तथा सक्रियण ऊर्जा चाहिए।

  2. Write the Freundlich adsorption isotherm and its linear form. / फ्रॉयन्डलिक अधिशोषण समतापी तथा उसका रैखिक रूप लिखिए।
    Show answer

    x/m = k·p^(1/n); taking log gives log(x/m) = log k + (1/n) log p, so a plot of log(x/m) versus log p is a straight line with slope 1/n and intercept log k. / x/m = k·p^(1/n); लॉग लेने पर log(x/m) = log k + (1/n) log p, अतः log(x/m) बनाम log p का आलेख सरल रेखा है जिसका ढाल 1/n तथा अंतःखंड log k होता है।

  3. State the assumptions of the Langmuir adsorption isotherm. / लैंगम्यूर अधिशोषण समतापी की मान्यताएँ बताइए।
    Show answer

    Adsorption occurs on a fixed number of identical, homogeneous sites; only a monolayer forms (one molecule per site); there is no interaction between adsorbed molecules; and a dynamic equilibrium exists between adsorption and desorption. / अधिशोषण निश्चित संख्या के समरूप, समांगी स्थलों पर होता है; केवल एकपरत बनती है (प्रति स्थल एक अणु); अधिशोषित अणुओं में कोई अन्योन्यक्रिया नहीं होती; तथा अधिशोषण व विशोषण के बीच गतिक साम्य रहता है।

  4. Why does physisorption decrease with rise in temperature? / ताप वृद्धि के साथ भौतिक अधिशोषण क्यों घटता है?
    Show answer

    Physisorption is exothermic, so by Le Chatelier's principle a rise in temperature shifts the adsorption-desorption equilibrium towards desorption, decreasing the amount adsorbed. / भौतिक अधिशोषण ऊष्माक्षेपी है, अतः ल शातेलिए सिद्धांत के अनुसार ताप वृद्धि अधिशोषण-विशोषण साम्य को विशोषण की ओर विस्थापित करती है, जिससे अधिशोषित मात्रा घटती है।

  5. Derive the linear form of the Langmuir isotherm used to find monolayer capacity. / एकपरत क्षमता ज्ञात करने हेतु लैंगम्यूर समतापी का रैखिक रूप व्युत्पन्न कीजिए।
    Show answer

    From x/m = (a·b·P)/(1+b·P), taking reciprocal and rearranging gives P/(x/m) = 1/(a·b) + P/a; a plot of P/(x/m) vs P is linear with slope 1/a (giving monolayer capacity a) and intercept 1/(a·b). / x/m = (a·b·P)/(1+b·P) से व्युत्क्रम लेकर पुनर्व्यवस्थित करने पर P/(x/m) = 1/(a·b) + P/a; P/(x/m) बनाम P का आलेख रैखिक है जिसका ढाल 1/a (एकपरत क्षमता a देता है) तथा अंतःखंड 1/(a·b) होता है।

  6. How does surface area of the adsorbent affect the extent of adsorption? / अधिशोषक का पृष्ठ क्षेत्रफल अधिशोषण की मात्रा को किस प्रकार प्रभावित करता है?
    Show answer

    A larger surface area provides more active sites, so adsorption increases; that is why finely divided or porous adsorbents like activated charcoal and silica gel are highly effective. / अधिक पृष्ठ क्षेत्रफल अधिक सक्रिय स्थल प्रदान करता है, अतः अधिशोषण बढ़ता है; इसीलिए सूक्ष्म विभाजित या सरंध्र अधिशोषक जैसे सक्रिय चारकोल व सिलिका जेल अत्यधिक प्रभावी होते हैं।

  7. Give two important applications of adsorption with the adsorbent used. / प्रयुक्त अधिशोषक सहित अधिशोषण के दो महत्वपूर्ण अनुप्रयोग दीजिए।
    Show answer

    Gas masks use activated carbon to adsorb toxic gases; desiccant silica gel adsorbs water vapour to keep products dry (other uses: chromatography, water purification). / गैस मास्क विषैली गैसों के अधिशोषण हेतु सक्रिय कार्बन का उपयोग करते हैं; शुष्कक सिलिका जेल जल वाष्प का अधिशोषण कर उत्पादों को शुष्क रखता है (अन्य उपयोग: वर्णलेखन, जल शुद्धिकरण)।

  8. Explain the molecular origin of surface tension and write its capillary-rise relation. / पृष्ठ तनाव के आण्विक मूल को समझाइए तथा इसका केशिका-उन्नयन संबंध लिखिए।
    Show answer

    Surface molecules experience a net inward cohesive force as they have fewer neighbours, giving extra surface energy that makes the surface contract; capillary rise is h = (2γ cosθ)/(ρgr). / पृष्ठीय अणुओं में पड़ोसी कम होने से शुद्ध अंतर्मुखी संसंजक बल लगता है जो अतिरिक्त पृष्ठ ऊर्जा देता है तथा पृष्ठ को संकुचित करता है; केशिका उन्नयन h = (2γ cosθ)/(ρgr) है।

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