Q.Match the following :
Column I

Entropy Change Prediction

Concept: Matching thermodynamic quantities with their characteristic properties requires understanding entropy definitions, spontaneity criteria, state functions, and the first law under specific conditions.

Analysis:

(i) Entropy of vaporization is the entropy change when one mole of liquid converts to vapour at its boiling point: $\Delta S_{\text{vap}} = \frac{\Delta H_{\text{vap}}}{T_b}$ — and since vaporisation always increases disorder, it is always positive. → (b), (d)

(ii) Equilibrium constant $K$ for a spontaneous process: $\Delta G° = -RT \ln K$; for a spontaneous process $\Delta G° < 0$, so $\ln K > 0$ and $K > 1$ — in particular, $K$ is always positive. → (b) …

The heart of this matching exercise lies in understanding how entropy, spontaneity, and energy behave in different thermodynamic contexts. Each item in Column I represents a fundamental concept whose behavior or value follows from first principles.

Concept: Connecting Thermodynamic Quantities

Entropy measures disorder. Phase transitions, equilibrium positions, structural order, and energy changes all leave signatures in entropy and related quantities. The key is recognizing what each process or state implies about the underlying thermodynamics.

Step-by-Step Matching

1. Entropy of vaporization → (b) is always positive, and (d) $\Delta H_{\text{vap}}/T_b$

Vaporisation always increases disorder, so $\Delta S_{vap}$ is always positive — and its value at the boiling point is $\Delta H_{vap}/T_b$:

When a liquid vaporizes at its boiling point, the process occurs reversibly at constant temperature and pressure. The entropy change for this phase transition is:

This is Trouton's rule in its exact form. At the boiling point, the system is in equilibrium between phases, so the heat absorbed divided by the absolute temperature gives the entropy increase as molecules escape into the disordered gas phase.

2. $K$ for spontaneous process → (b) is always positive

The equilibrium constant $K$ is defined as:

For a spontaneous process under standard conditions, $\Delta G° < 0$, which means $\ln K > 0$, and therefore $K > 1$. But more fundamentally, $K$ itself—being a ratio of activities or concentrations raised to positive powers—is always a positive number by definition, regardless of whether the forward or reverse reaction is spontaneous. You cannot have a negative equilibrium constant; it would be physically meaningless.

3. Crystalline solid state → (c) lowest entropy

Entropy quantifies the number of accessible microstates. In a perfect crystalline solid at low temperature, atoms or molecules are locked into a highly ordered lattice with minimal positional or orientational freedom. This represents the state of minimum disorder for a substance. …