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Question #44177

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The Question

Consider the gaseous tetrahedral molecule $X_4(g)$ which undergoes dissociation into two diatomic molecules $X_2(g)$ at $300 \text{ K}$ . The $X-X$ single bond energy in $X_4$ is $160 \text{ kJ mol}^{-1}$ and the $X=X$ double bond energy in $X_2$ is $420 \text{ kJ mol}^{-1}$ . The standard entropy change for the dissociation reaction is $\Delta S^\circ = 450 \text{ J K}^{-1} \text{ mol}^{-1}$ . Which of the following correctly represents the standard enthalpy ( $\Delta H^\circ$ ), standard Gibbs free energy ( $\Delta G^\circ$ ) of the reaction, and the thermodynamic stability of $X_4(g)$ at $300 \text{ K}$ ?

Options

A.
+120 \text{ kJ mol}^{-1}, -15 \text{ kJ mol}^{-1}, \text{Unstable}
B.
+120 \text{ kJ mol}^{-1}, +106.5 \text{ kJ mol}^{-1}, \text{Stable}
C.
-200 \text{ kJ mol}^{-1}, -335 \text{ kJ mol}^{-1}, \text{Unstable}
D.
+540 \text{ kJ mol}^{-1}, +405 \text{ kJ mol}^{-1}, \text{Stable}

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Bond Energy vs Bond Length|Gibbs Energy and Spontaneity|Entropy of Phase Change

Why This Question Is Tricky

Common Mistakes

This problem tests the critical distinction between kinetic stability (high total bond energy) and thermodynamic stability ( $\Delta G < 0$ ).

Students often fall into the trap of assuming that a molecule with a massive total bond dissociation energy must be thermodynamically stable.

The 'Hidden Variable' is the entropy dominance ( $\Delta S$ ) which drives the endothermic dissociation process spontaneously at room temperature.

Additionally, it tests structural geometry knowledge: a common trap is assuming a tetrahedral cluster has 4 bonds instead of 6 (Option C), or forgetting the stoichiometric coefficient of the products (Option D), or making a decimal error in the entropy unit conversion (Option B).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Bonding and Molecular Structure - Class 11 Part 1
Concept	Bond Energy vs Bond Length
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free