UPSC Civil Services (Mains), Chemistry optional · 2017 · Paper I

Q1(d)(i). Four phases of sulfur cannot coexist

Question

(i) Four-phase sulphur system (in equilibrium) is impossible. Explain.

For one component, F=C-P+2=1-4+2=-1. A negative number of degrees of freedom is impossible, so at most three phases (a triple point) can coexist.

rhombic solid, monoclinic solid, liquid and vapour, but only one component.
F=C-P+2. Two phases: F=1 (a line); three phases: F=0 (a point, invariant).
F=1-4+2=-1. This would need more equations than variables (T, p), so no T and p satisfy all of them.
The sulfur diagram has three stable triple points (A: rhombic–monoclinic–vapour; B: monoclinic–liquid–vapour; C: rhombic–monoclinic–liquid), but no point where four phases meet.

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

Sulfur has four phases: rhombic solid, monoclinic solid, liquid and vapour, but only one component.
Gibbs phase rule: F=C-P+2. Two phases: F=1 (a line); three phases: F=0 (a point, invariant).
Four phases: F=1-4+2=-1. This would need more equations than variables (T, p), so no T and p satisfy all of them.
The sulfur diagram has three stable triple points (A: rhombic–monoclinic–vapour; B: monoclinic–liquid–vapour; C: rhombic–monoclinic–liquid), but no point where four phases meet.

Practising this answer? Write it in a Mains test and get it checked by VKC. Civil Services Mains test series · Telegram