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Question #44658

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The Question

The spectroscopic bond dissociation energy ( $D_0$ ) of a homonuclear diatomic molecule \ce{X2(g)} at $0\text{ K}$ is $240.00\text{ kJ mol}^{-1}$ . At $300\text{ K}$ , the vibrational contribution to the internal energy ( $U_{vib}$ ) of \ce{X2(g)} is $0.735\text{ kJ mol}^{-1}$ . Assuming ideal gas behavior for all species, calculate the standard bond enthalpy ( $\Delta_{bond}H^\circ$ ) of \ce{X2(g)} at $300\text{ K}$ .

[Given: Universal gas constant $R = 8.3\text{ J K}^{-1}\text{ mol}^{-1}$ ]

Options

A.
$243.00\text{ kJ mol}^{-1}$
B.
$242.49\text{ kJ mol}^{-1}$
C.
$240.00\text{ kJ mol}^{-1}$
D.
$238.02\text{ kJ mol}^{-1}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Dimensional Consistency of Constants|Bond Enthalpy Pitfall|State vs Path Functions

Why This Question Is Tricky

Common Mistakes

Students often conflate the spectroscopic bond dissociation energy at $0\text{ K}$ ( $D_0$ ) with the standard bond enthalpy at a given temperature $T$ .

A common trap is to either assume they are identical (Option C) or to only apply the ideal gas expansion work correction $\Delta n_g RT$ (Option B), ignoring the heat capacity differences ( $\Delta C_p$ ) arising from translational, rotational, and vibrational degrees of freedom.

This question tests the dimensional consistency of thermodynamic states, requiring the application of the equipartition theorem to bridge microscopic energy states with macroscopic state functions.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Dimensional Consistency of Constants
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free