At a particular temperature and atmospheric pressure, the solid and liquid phases of a pure substance can exis

NCERT Exemplar · Q21

Q. At a particular temperature and atmospheric pressure, the solid and liquid phases of a pure substance can exist in equilibrium. Which of the following term defines this temperature? (Note: more than one of the given options may be correct.)

(i) Normal melting point

(ii) Equilibrium temperature

(iii) Boiling point

(iv) Freezing point

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Concept understanding — Phase Equilibrium

Phase Equilibrium: From Intuition to Precision

Imagine a glass of ice water on a warm day. The ice cubes are melting, but the water around them stays cold. If you wait long enough, the ice stops melting — not because the room got colder, but because the system has reached a balance. The ice and water coexist without any net change. That balance is phase equilibrium.

The Intuition: A Tug-of-War Between Two Tendencies

Every substance wants to exist in the phase (solid, liquid, or gas) that has the lowest energy under the given conditions. But there's a catch: nature also loves disorder (entropy). A solid is low-energy but highly ordered; a gas is high-energy but very disordered. At a specific temperature and pressure, these two opposing drives — minimising energy and maximising disorder — exactly cancel each other out. The result? Two phases can coexist peacefully, with molecules constantly jumping between them but no net change in the amount of each phase.

Think of it as a tug-of-war. On one side, molecules in the solid phase are tightly bound and low in energy. On the other side, molecules in the liquid phase have more freedom and higher entropy. At the melting point, the rope doesn't move — the rates of melting and freezing are equal.

The Precise Statement

Phase equilibrium is the condition in which two or more phases of a substance coexist in thermodynamic equilibrium, with no net transfer of mass between phases. For a pure substance, this occurs at a unique temperature for a given pressure (or vice versa), defined by the equality of the chemical potential (or Gibbs free energy per mole) in all phases.

In simpler terms: at equilibrium, the driving force for a molecule to move from phase A to phase B is exactly the same as the driving force to move from B to A. The system is dynamic — molecules are still crossing the boundary — but macroscopically static.

The Key Condition: Equal Chemical Potential

The rigorous condition for phase equilibrium in a pure substance is:

\mu_{\text{solid}} = \mu_{\text{liquid}} = \mu_{\text{gas}}

where $\mu$ (mu) is the chemical potential — the Gibbs free energy per mole. When chemical potentials are equal, no phase has a "preference" to grow at the expense of another.

Important

For a pure substance, phase equilibrium occurs only along specific lines on a phase diagram (the melting curve, boiling curve, and sublimation curve). At the triple point, all three phases coexist.

A Concrete Example: Water at 0°C

At 1 atm pressure and 0°C, ice and liquid water are in equilibrium. Here's what's happening at the molecular level:

Water molecules at the surface of the ice are vibrating. Some gain enough energy to break free and enter the liquid.
Simultaneously, water molecules in the liquid near the ice surface lose energy and attach to the ice crystal.
The rates of these two processes are equal. So the amount of ice and the amount of liquid water remain constant — even though individual molecules are constantly switching sides. …

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When the solid and liquid phases of a pure substance coexist in equilibrium at atmospheric pressure, this temperature is known as the normal melting point — equivalently, the freezing point. The correct options are (i), (ii), and (iv).

When a pure substance exists in both its solid and liquid phases simultaneously, and there is no net change in the amount of either phase, the system is said to be in phase equilibrium. This specific condition occurs at a characteristic temperature for a given pressure.

Here's why this approach works:

The transition between solid and liquid phases is reversible. When a solid melts, it absorbs heat and turns into a liquid. When a liquid freezes, it releases heat and turns into a solid. At the equilibrium temperature, the rate of melting is exactly equal to the rate of freezing. This means that if you have both solid and liquid present at this temperature, their relative amounts will remain constant over time, provided no heat is added or removed from the system.

Understanding Phase Equilibrium:

For a pure substance, the solid and liquid phases can coexist in equilibrium only at a specific temperature for a given pressure. At this temperature, the Gibbs free energy of the solid phase is equal to the Gibbs free energy of the liquid phase ( $G_{solid} = G_{liquid}$ ). This is the condition for phase equilibrium.
Defining Melting Point and Freezing Point:
- The melting point is the temperature at which a solid changes into a liquid.
- The freezing point is the temperature at which a liquid changes into a solid. For a pure substance, the melting point and freezing point are identical. For example, pure water melts at $0^\circ\text{C}$ and freezes at $0^\circ\text{C}$ at standard atmospheric pressure.
Evaluating Option (i) Normal melting point:

The term "normal" refers to the condition of standard atmospheric pressure (typically 1 atmosphere or 101.325 kPa). The problem explicitly states "at a particular temperature and atmospheric pressure," and that "the solid and liquid phases of a pure substance can exist in equilibrium." This perfectly matches the definition of the normal melting point.
Evaluating Option (ii) Equilibrium temperature:

Since the solid and liquid phases are in equilibrium at this temperature, it is, by definition, an equilibrium temperature. This is a broader term that applies to any temperature at which a system is in equilibrium, including phase equilibrium.
Evaluating Option (iii) Boiling point: …

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Q.At a particular temperature and atmospheric pressure, the solid and liquid phases of a pure substance can exist in equilibrium. Which of the following term defines this temperature? (Note: more than one of the given options may be correct.)

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