Question

Identify the INCORRECT statement.

• A. At $273\text{ K}$, for the transition $\text{Ice}(s) \rightarrow \text{Water}(l)$, $\Delta G = 0$
• B. Entropy is an extensive property and state function
• C. For spontaneous process $(\Delta H_{\text{system}} - T\Delta S_{\text{system}}) < 0$
• D. A process will always be spontaneous at all temperatures, if $T\Delta S$ is positive

Hint:

To ensure spontaneity ($\Delta G < 0$) at all possible temperatures, a process must be exothermic ($\Delta H = -\text{ve}$) and result in an increase in disorder ($\Delta S = +\text{ve}$). Relying solely on a positive $T\Delta S$ term can fail at low temperatures if $\Delta H$ is positive.

Answer 1

The Correct Option is D

Concept: The spontaneity of a thermodynamic process is governed by the change in standard Gibbs Free Energy ($\Delta G$), defined by the equation: \[ \Delta G = \Delta H - T\Delta S \] For a process to be spontaneous, the overall value of $\Delta G$ must be strictly negative ($\Delta G < 0$).

Step 1: Evaluate Statement (D).
The spontaneity of a reaction depends on both the enthalpy change ($\Delta H$) and the entropy term ($-T\Delta S$). If $T\Delta S$ is positive, it favors spontaneity because it makes the $-T\Delta S$ term negative. However, if the reaction is highly endothermic ($\Delta H > 0$) and its value exceeds $T\Delta S$, then $\Delta G$ will be positive ($\Delta G > 0$), making the process non-spontaneous. Therefore, a positive $T\Delta S$ value alone does not guarantee spontaneity at all temperatures—the sign and magnitude of $\Delta H$ must be considered. This makes statement (D) incorrect, and thus the correct answer.

Step 2: Verify why the other options are correct statements.

• Statement (A) is correct: $273\text{ K}$ ($0^\circ\text{C}$) is the exact equilibrium melting point of ice at standard pressure. At any phase equilibrium point, $\Delta G = 0$.
• Statement (B) is correct: Entropy depends on the total quantity of matter in the system (extensive) and its value is determined solely by the current state variables (state function).
• Statement (C) is correct: The term $(\Delta H - T\Delta S)$ is the definition of $\Delta G$, which must be less than zero ($< 0$) for a process to be spontaneous.