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Question #44260

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The Question

The standard enthalpy of atomization of solid Chromium, $\ce{Cr(s)}$ , at $298\text{ K}$ is $397\text{ kJ mol}^{-1}$ . The ground state electronic configuration of gaseous Chromium is an Aufbau exception. The energy required to excite the gaseous Chromium atom from its true ground state to the expected (but incorrect) Aufbau configuration $[Ar] 3d^4 4s^2$ is $96\text{ kJ mol}^{-1}$ .

A theoretical model calculates the mean $\ce{Cr-Cl}$ bond dissociation enthalpy in $\ce{CrCl_3(g)}$ to be $350\text{ kJ mol}^{-1}$ . However, this model mistakenly defines the bond dissociation relative to the gaseous Chromium atom in the $[Ar] 3d^4 4s^2$ state.

Given that the standard enthalpy of formation of $\ce{Cl(g)}$ is $121\text{ kJ mol}^{-1}$ , calculate the true standard enthalpy of formation ( $\Delta H^\circ_f$ ) of $\ce{CrCl_3(g)}$ at $298\text{ K}$ .

Options

A.
$-194\text{ kJ mol}^{-1}$
B.
$-290\text{ kJ mol}^{-1}$
C.
$-386\text{ kJ mol}^{-1}$
D.
$-436\text{ kJ mol}^{-1}$

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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

Aufbau Principle Exceptions|Standard State Conditions|Hess's Law Application

Why This Question Is Tricky

Common Mistakes

This problem tests the intersection of quantum mechanical electron configurations and macroscopic thermodynamics via Hess's Law.

Students often memorize Aufbau exceptions (like Cr being $3d^5 4s^1$ ) but fail to realize that standard thermodynamic values (like $\Delta H^\circ_{at}$ ) inherently reference this true ground state.

The primary trap (Option B) catches students who ignore the Aufbau exception, assuming $3d^4 4s^2$ is the ground state and thus omitting the $96\text{ kJ mol}^{-1}$ excitation energy from the cycle.

It forces a rigorous application of state functions and reference states.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Structure of Atom - Class 11 Part 1
Concept	Aufbau Principle Exceptions
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free