Solid State and Surface Chemistry
Solid State and Surface Chemistry links the geometry of crystals to bulk density, defects and the behaviour of surfaces. The exam asks you to convert unit-cell data, identify packing and defects, and apply adsorption and colloid models.
Crystal lattices
A unit cell is described by a, b, c and alpha, beta, gamma. For cubic cells, Z is 1 (simple), 2 (body-centred) and 4 (face-centred). Packing efficiencies are 52.4%, 68% and 74% for sc, bcc and fcc/hcp. Density is d = ZM/(a^3 N_A), with a in cm. Bragg's law is n lambda = 2d sin theta.
Defects and surfaces
Schottky defect removes one cation and one anion; Frenkel moves an ion to an interstitial site. An F-centre is an anion vacancy holding an electron. Physisorption is weak, multilayer and low enthalpy; chemisorption is strong, monolayer and high enthalpy. Freundlich isotherm: x/m = k p^(1/n), with 1/n between 0 and 1. Colloids show Tyndall scattering, Brownian motion and electrophoresis; coagulating power rises with ionic charge.
Worked example
NaCl is fcc with Z = 4, M = 58.5 g/mol and a = 564 pm = 5.64 x 10^-8 cm. Then a^3 = 1.794 x 10^-22 cm^3. d = (4 x 58.5)/(1.794 x 10^-22 x 6.022 x 10^23) = 234/108.0 = 2.17 g/cm^3. The reasoning is to convert pm to cm before using N_A.
Traps
Using Z = 1 for fcc, leaving a in pm, confusing adsorption with absorption, and writing 1/n > 1 in Freundlich all lose marks.