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Question #44070

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The Question

Consider the formation of tetracarbonylnickel(0) in the Mond process at temperature $T$ :

$\ce{Ni(s) + 4CO(g) <=> Ni(CO)4(g)}$

Due to strong intramolecular $\pi$ -backbonding (synergic effect), the $\ce{Ni(CO)4}$ molecule possesses a highly polarizable electron cloud, leading to significant intermolecular Van der Waals attractions. Assume $\ce{CO(g)}$ behaves as an ideal gas. For $\ce{Ni(CO)4(g)}$ , the repulsive volume parameter is negligible ( $b \approx 0$ ), but the attractive parameter ' $a$ ' is significant.

Let the partial pressure of $\ce{Ni(CO)4(g)}$ at equilibrium be $p$ . The compressibility factor of $\ce{Ni(CO)4(g)}$ is $Z = 1 - x$ , and its fugacity coefficient is $\phi = e^{-x}$ , where $x = \frac{ap}{(RT)^2}$ .

If $K_f$ is the true thermodynamic equilibrium constant defined in terms of fugacity, which of the following correctly expresses the apparent concentration-based equilibrium constant $K_c$ ?

Options

A.
$\frac{K_f (RT)^3}{e^{-x}(1-x)}$
B.
$K_f (RT)^{-3} e^{-x}(1-x)$
C.
$\frac{K_f (RT)^3}{e^x(1+x)}$
D.
$K_f (RT)^3 e^{-x}(1-x)$

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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

Relationship between Kp and Kc|Internal Energy of Real Gases|Synergic Bonding in Carbonyls

Why This Question Is Tricky

Common Mistakes

This problem tests the intersection of Coordination Chemistry and Real Gas Thermodynamics.

Students typically memorize the ideal relationship $K_p = K_c(RT)^{\Delta n}$ .

The 'Hidden Variable' here is the non-ideality of $\ce{Ni(CO)4}$ induced by its highly polarizable electron cloud (a consequence of intramolecular synergic $\pi$ -backbonding).

This requires deriving the equilibrium constant from first principles using fugacity ( $f = \phi p$ ) and the real gas law ( $p = ZCRT$ ).

The trap is failing to account for both the fugacity coefficient $\phi$ in the thermodynamic constant and the compressibility factor $Z$ in the concentration conversion, leading to incorrect algebraic manipulations.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Relationship between Kp and Kc
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free