GATE 2025 CY – Question 46

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

The phase diagram of a single component system is given below. The option with the correct number of degrees of freedom corresponding to the labelled points i, j, and k, respectively, is

One-component pressure–temperature phase diagram with i at the triple point, j on a coexistence line and k in a single phase.

0, 1, 2
3, 2, 1
2, 0, 1
0, 2, 1

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Correct answer: (A) 0, 1, 2

Explanation

The **Gibbs phase rule** for a one-component system ($C=1$) is
$$F=C-P+2=3-P,$$
where $P$ is the number of phases in equilibrium.

**i, the triple point:** three phases ($P=3$), so $F=0$ (an invariant point).
**j, on a coexistence line:** two phases ($P=2$), so $F=1$ (we can change either $T$ or $P$ and the other follows).
**k, inside a single-phase region:** one phase ($P=1$), so $F=2$ (both $T$ and $P$ can be varied).

Answer **0, 1, 2** (option A).