Answer: \(F'=C-P+1\) (pressure fixed). In the Pb–Ag system the two freezing curves meet at the eutectic point (2.6% Ag, 303 °C), where \(F'=2-3+1=0\); this is the basis of Pattinson's process for desilverisation of lead.
Condensed (reduced) phase rule. For solid–liquid systems the gas phase is absent and the effect of pressure is negligible, so the experiment is done at constant (atmospheric) pressure. One degree of freedom is used up:
\[F'=C-P+1\]
Phase diagram (described): the x-axis gives composition, from 100% Pb (left) to 100% Ag (right); the y-axis gives temperature.
- Point A (left axis, 327 °C) is the melting point of Pb; point B (right axis, 961 °C) is the melting point of Ag.
- Curve AO: freezing-point curve of Pb. Adding Ag lowers the freezing point of Pb. Along AO, solid Pb ⇌ liquid: \(F'=2-2+1=1\) (univariant).
- Curve BO: freezing-point curve of Ag; adding Pb lowers it. Along BO, solid Ag ⇌ liquid, \(F'=1\).
- Point O (eutectic): where AO and BO meet, at 2.6% Ag and 303 °C. Solid Pb, solid Ag and liquid coexist: \(F'=2-3+1=0\) (invariant). It is the lowest temperature at which a liquid can exist in this system.
- Areas: above AOB, a single liquid phase, \(F'=2-1+1=2\) (bivariant). Area AOC (below AO): solid Pb + liquid. Area BOD (below BO): solid Ag + liquid. Below the horizontal eutectic line COD: solid Pb + eutectic (left of O) and solid Ag + eutectic (right of O).
Application – Pattinson's process (desilverisation of lead): argentiferous lead containing a very small amount of Ag (well below 2.6%, i.e. on curve AO side) is melted and cooled slowly. Pure Pb separates out first and is removed with ladles, so the liquid becomes richer in Ag along AO. Cooling continues until the liquid reaches the eutectic point O (2.6% Ag); this enriched alloy is then treated (e.g. cupellation) to recover silver.
