Solid State and Surface Chemistry
This domain tests crystal lattices and unit cells, density calculations, point defects, semiconductors, adsorption isotherms, catalysis and colloids.
Unit cells and packing
Simple cubic: Z = 1, packing efficiency 52.4%, coordination number 6. BCC: Z = 2, 68%, coordination number 8. FCC/CCP: Z = 4, 74%, coordination number 12 (HCP is also 74%). Density d = ZM/(a³N_A), with a in cm.
Defects and semiconductors
Schottky defect: equal numbers of cations and anions missing, so density falls (NaCl, KCl). Frenkel defect: an ion leaves its site for an interstitial position, so density is unchanged (AgCl, ZnS). Metal excess defects with F-centres colour crystals (yellow NaCl). Doping silicon with P or As (group 15) gives n-type; with B, Al or Ga (group 13) gives p-type.
Adsorption and catalysis
Physisorption: van der Waals forces, ΔH about 20–40 kJ mol⁻¹, multilayer, reversible, decreases with temperature. Chemisorption: chemical bonds, ΔH about 80–240 kJ mol⁻¹, monolayer, often irreversible. Freundlich isotherm x/m = k·p^(1/n); Langmuir predicts a saturation plateau. Promoters raise catalytic activity, poisons destroy it.
Colloids
Particle size 1–1000 nm; Tyndall scattering, Brownian motion, electrophoresis. Coagulation by electrolytes follows the Hardy–Schulze rule: the ion of opposite charge with the higher valency is most effective, Al³⁺ > Ca²⁺ > Na⁺.
Worked example
Copper is FCC with a = 361 pm and M = 63.5 g mol⁻¹. Find the density. a = 3.61 × 10⁻⁸ cm, so a³ = 4.70 × 10⁻²³ cm³ and Z = 4. d = (4 × 63.5)/(4.70 × 10⁻²³ × 6.022 × 10²³) = 254/28.3 = 8.96 g cm⁻³.
Traps that cost marks
- Using Z = 1 for every cubic cell.
- Saying Schottky defects leave density unchanged.
- Reversing the n-type and p-type dopants.
- Forgetting to convert picometres to centimetres before substituting into the density formula.