Surface Chemistry & States of Matter

Adsorption: Accumulation of molecules on a surface (adsorbent = surface, adsorbate = substance adsorbed). Physical adsorption (physisorption): weak van der Waals forces, reversible, low enthalpy (20-40 kJ/mol), multilayer, not specific, increases with pressure, decreases with temperature. Chemical adsorption (chemisorption): chemical bond formation, irreversible, high enthalpy (80-240 kJ/mol), monolayer, specific, may increase then decrease with temperature. All gases adsorb more at low temperature and high pressure. Activated adsorption = chemisorption requiring activation energy.

Adsorption Isotherms: Freundlich isotherm: x/m = kP^(1/n) where 1/n is between 0 and 1 (usually ~0.1-0.5). Log form: log(x/m) = log k + (1/n) log P. Linear plot: log(x/m) vs log P gives slope 1/n and intercept log k. Fails at very high pressure. Langmuir isotherm: x/m = aP/(1+bP). Assumes monolayer, all sites equivalent, no interaction between adsorbed molecules. At low P: x/m is proportional to P. At high P: x/m approaches maximum (surface saturated). BET isotherm extends to multilayer adsorption.

Catalysis: Catalyst changes reaction rate without being consumed. Homogeneous: same phase (acid catalysis, enzyme catalysis in solution). Heterogeneous: different phase (solid catalyst, gaseous reactants). Mechanism of heterogeneous catalysis: (1) Diffusion to surface. (2) Adsorption. (3) Surface reaction. (4) Desorption. (5) Diffusion away. Catalyst provides alternative pathway with lower activation energy. Does NOT change equilibrium position or $\delta_{G}$ — only increases rate of both forward and reverse reactions equally. Selectivity: different catalysts can give different products from same reactants.

Colloids: Particle size 1-1000 nm (between true solutions < 1 nm and suspensions > 1000 nm). Classification: sol (solid in liquid), emulsion (liquid in liquid), foam (gas in liquid), aerosol (liquid/solid in gas). Lyophilic (solvent-loving): reversible, stable, low viscosity change (starch, gum, gelatin, proteins). Lyophobic (solvent-fearing): irreversible, unstable, needs stabilising agent (metal sols: Au, Ag, Fe(OH)₃, As₂S₃). Preparation methods: chemical (reduction, oxidation, double decomposition), Bredig's arc (metals), peptisation (adding electrolyte to precipitate).

Colloidal Properties: Tyndall effect: scattering of light by colloidal particles (distinguishes from true solutions). Brownian motion: random zig-zag due to molecular collisions (proves kinetic nature). Electrophoresis: migration of charged particles under electric field. Electroosmosis: movement of dispersion medium under electric field. Coagulation (flocculation): destabilisation by adding electrolyte — Hardy-Schulze rule: higher the valence of the ion opposite in charge to colloid, greater the coagulating power. For negatively charged colloid (As₂S₃): $Al^{3}$+ > $Ba^{2}$+ > Na+. For positively charged colloid (Fe(OH)₃): $PO4^{3}$- > $SO4^{2}$- > Cl-.

Emulsions: Oil-in-water (O/W): oil dispersed in water, stabilised by Na-stearate (milk, vanishing cream). Water-in-oil (W/O): water dispersed in oil, stabilised by long-chain alcohols (butter, cold cream). Emulsifier prevents coalescence by forming a film at interface.

Sodium stearate — O/W emulsifier (soap), hydrophilic head + hydrophobic tail Demulsification: breaking emulsion by heating, centrifuging, or adding demulsifier.

Ideal Gas: PV = nRT. Assumptions: point particles, no intermolecular forces, elastic collisions, random motion.
KE = ($\frac{3}{2}$)kT per molecule = ($\frac{3}{2}$)RT per mole.
Root mean square speed: $u_{rms}$ = $\sqrt{3RT/M}$.
Average speed: $u_{avg}$ = $\sqrt{8RT/(piM}$).
Most probable speed: $u_{mp}$ = $\sqrt{2RT/M}$.
Ratio: $u_{mp}$ : $u_{avg}$ : $u_{rms}$ = 1 : 1.128 : 1.224. Maxwell-Boltzmann distribution: at higher T, curve flattens and shifts right (higher speeds, broader distribution).

Real Gas and van der Waals Equation: (P + $\frac{an^{2}}{V^{2}}$)(V - nb) = nRT. 'a' corrects for intermolecular attractions (higher a = more attraction = easier to liquefy). 'b' corrects for molecular volume (excluded volume, b = 4 x actual molecular volume per mole). Boyle temperature $T_{B}$ = a/(Rb): above this, gas behaves nearly ideally. Compressibility factor Z = PV/(nRT). Ideal: Z = 1. Z < 1: attractive forces dominate (gas more compressible). Z > 1: repulsive forces dominate (gas less compressible). At very high pressure: Z > 1 for all gases (volume exclusion dominates). H₂ and He: Z > 1 at all pressures (very weak attractions).

Critical Constants: $T_{c}$ = 8a/(27Rb), $P_{c}$ = a/($27b^{2}$), $V_{c}$ = 3b. At the critical point: liquid and gas become indistinguishable. Above $T_{c}$: gas cannot be liquefied by pressure alone (called supercritical fluid).
$Z_{c}$ = $P_{cV_c}$/($\text{RT}_{c}$) = $\frac{3}{8}$ = 0.375 (van der Waals prediction). Actual $Z_{c}$ values are typically 0.2-0.3 (deviations from van der Waals).

Liquefaction of Gases: Requirements: cool below $T_{c}$, then apply pressure. Methods: Linde's process (Joule-Thomson effect: cooling on expansion through porous plug), Claude's process (adiabatic expansion against piston). Joule-Thomson effect: for real gases, expansion below inversion temperature causes cooling.
Inversion temperature $T_{i}$ = 2a/(Rb) = $2T_{B}$. Most gases have $T_{i}$ well above room temperature, but H₂ and He must be pre-cooled before liquefaction.