Question

A: Entropy of a perfect crystalline solid at absolute zero approaches zero.
B: For spontaneity of a reaction, T\(\Delta\)S>\(\Delta\)H.
Among the two statements given above, identify the correct answer from the options given below.

• A. Both 'A' and 'B' are true
• B. 'A' is true but 'B' is false
• C. Both 'A' and 'B' are false
• D. 'A' is false but 'B' is true

Hint:

Remember the key thermodynamic principles:

• \textbf{Third Law:} S \(\rightarrow\) 0 as T \(\rightarrow\) 0 K for a perfect crystal.
• \textbf{Spontaneity (Gibbs Free Energy):} A reaction is spontaneous if \(\Delta\)G<0. Always start from the fundamental equation \(\Delta G = \Delta H - T\Delta S\) to derive the conditions for spontaneity.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Evaluate statement A using the Third Law of Thermodynamics and statement B using the Gibbs Free Energy criterion for spontaneity.
Step 2: Key Formula or Approach:
Third Law of Thermodynamics: $S \rightarrow 0$ as $T \rightarrow 0$ K.
Gibbs Free Energy Equation: $\Delta G = \Delta H - T\Delta S$. Spontaneity strictly requires $\Delta G<0$.
Step 3: Detailed Explanation:
1. Statement A: This is the formal definition of the Third Law of Thermodynamics. At absolute zero ($0$ K), there is no thermal motion, and perfectly ordered crystalline solids have zero disorder. Hence, their entropy is exactly zero. (Statement A is True)

2. Statement B: For a reaction to be spontaneous at constant temperature and pressure, the change in Gibbs free energy ($\Delta G$) must be negative ($\Delta G<0$).
Using the equation: $\Delta H - T\Delta S<0$.
Rearranging this inequality gives:
$\Delta H<T\Delta S$
Which is exactly the same as: $T\Delta S>\Delta H$.
This mathematical condition ensures that the negative entropy term overcomes any positive enthalpy term, leading to a spontaneous process. (Statement B is True)
Step 4: Final Answer:
Both statements 'A' and 'B' are true.