Solid State and Solutions
Solid State and Solutions
This domain tests crystal lattices, packing, defects and the quantitative treatment of solutions: Raoult's law, deviations, azeotropes and colligative properties.
Core rules
- Unit-cell contents: primitive 1, bcc 2, fcc 4 atoms. Packing efficiency: 52.4%, 68%, 74%.
- Radius relations: sc r=a/2; bcc r=√3a/4; fcc r=a/(2√2).
- Density d = zM/(a³N_A); use a in cm.
- Schottky defect: paired vacancies, density falls. Frenkel: ion displaced to an interstitial site, density unchanged.
- Colligative properties depend on particle number: ΔTb=Kb·m·i, ΔTf=Kf·m·i, π=iCRT. van't Hoff factor i>1 for dissociation, <1 for association.
Worked example Copper crystallises fcc with a=361 pm and M=63.5 g mol⁻¹. z=4; a=3.61×10⁻⁸ cm. d = 4×63.5 / [(3.61×10⁻⁸)³×6.022×10²³] = 254 / 28.3 = 8.97 g cm⁻³. The result is close to the measured 8.96, confirming fcc.
Traps
- Converting pm to cm incorrectly (1 pm = 10⁻¹⁰ cm).
- Saying the Frenkel defect lowers density.
- Forgetting i: benzoic acid dimerises in benzene, so i≈0.5 and ΔTf is halved.
- Positive deviation means A–B forces are weaker than A–A/B–B; the mixture has higher vapour pressure.