Question

Which of following reactions has a positive entropy change ($\Delta S^{\circ}$)?

• A. $H_{2}O(l) \rightarrow H_{2}O(s)$
• B. $2SO_{2}(g) + O_{2}(g) \rightarrow 2SO_{3}(g)$
• C. $N_{2}(g) + 3H_{2}(g) \rightarrow 2NH_{3}(g)$
• D. $CaCO_{3}(s) \rightarrow CaO(s) + CO_{2}(g)$

Hint:

Look for reactions where the number of moles of gas increases; these almost always have a positive $\Delta S$.

Answer 1

The Correct Option is D

Step 1: Concept
Entropy ($S$) measures the degree of randomness or disorder in a system. A positive entropy change ($\Delta S > 0$) indicates an increase in disorder.

Step 2: Phase and Molecule Analysis
In (A), a liquid becomes a solid (more ordered). In (B) and (C), the number of gas molecules decreases (3 to 2 and 4 to 2 respectively), leading to less disorder.

Step 3: Analysis of Option D
In the decomposition of $CaCO_{3}$, a solid reactant produces both a solid and a gas. Since gases have much higher entropy than solids, the production of $CO_{2}$ significantly increases the system's disorder.

Step 4: Conclusion
The reaction $CaCO_{3}(s) \rightarrow CaO(s) + CO_{2}(g)$ results in a positive entropy change. Final Answer: (D)