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GATE 2026 CY – Question 44

Physical Chemistry · Phase Equilibria: Phase rule. Clausius- Clapeyron equation. Phase diagram of one component system: CO2, H2O, S; two component systems: liquid-vapor, liquid-liquid and solid-liquid systems. Fractional distillation. Azeotropes and Eutectics. · 2 marks · Multiple choice

For $2\mathrm{Pb_3O_4}(s)\rightleftharpoons6\mathrm{PbO}(s)+\mathrm O_2(g)$, the correct numbers of phases P, components C and degrees of freedom F are

Solid Pb3O4 decomposes reversibly to solid PbO and oxygen gas.
  1. P = 3, C = 2, F = 1
  2. P = 3, C = 3, F = 2
  3. P = 2, C = 3, F = 3
  4. P = 2, C = 2, F = 2

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Correct answer: (A) P = 3, C = 2, F = 1

Explanation

$$2\,\text{Pb}_3\text{O}_4(s)\rightleftharpoons6\,\text{PbO}(s)+\text{O}_2(g)$$

**Phases ($P$).** There are three distinct phases: solid $\text{Pb}_3\text{O}_4$, solid $\text{PbO}$ and gaseous $\text{O}_2$ (the two solids are different phases), so $P=3$.

**Components ($C$).** There are 3 chemical species and 1 independent chemical reaction relating them, so
$$C=S-R=3-1=2 .$$

**Degrees of freedom** from the Gibbs phase rule:
$$F=C-P+2=2-3+2=1 .$$

So $P=3$, $C=2$, $F=1$ (option A). (Physically: at a given temperature the oxygen pressure is fixed.)