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Question #44093

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The Question

A $1.0 \text{ L}$ aqueous solution at $298 \text{ K}$ contains $0.01 \text{ mol}$ of $\ce{FeSO4}$ and $0.1 \text{ mol}$ of $\ce{KCN}$ . The solution is buffered at $\text{pH} = 2.2$ . Given the acid dissociation constant of $\ce{HCN}$ is $K_a = 10^{-9.2}$ and the overall formation constant of $\ce{[Fe(CN)6]^{4-}}$ is $\beta_6 = 10^{35}$ . Assuming no volume change and no precipitation of any solid species, what is the spin-only magnetic moment (in Bohr Magnetons) and the Crystal Field Stabilization Energy (CFSE) of the predominant iron complex in the solution? (Ignore pairing energy, $\Delta_o$ is the octahedral splitting energy for the predominant complex).

Options

A.
$4.90 \text{ BM}, -0.4 \Delta_o$
B.
$0 \text{ BM}, -2.4 \Delta_o$
C.
$5.92 \text{ BM}, 0 \Delta_o$
D.
$1.73 \text{ BM}, -2.0 \Delta_o$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Buffer Capacity and pH Range|Complex Ion Oxidation States|Crystal Field Splitting (Octahedral)

Why This Question Is Tricky

Common Mistakes

This question tests the concept of the 'Conditional Formation Constant'.

Students often see a massive formation constant ( $\beta_6 = 10^{35}$ ) and immediately assume the strong-field complex $\ce{[Fe(CN)6]^{4-}}$ forms quantitatively, leading them to incorrectly choose the low-spin $d^6$ configuration ( $0 \text{ BM}$ , $-2.4 \Delta_o$ ).

However, they fail to account for the pH dependency of the ligand.

In a highly acidic buffer, the cyanide ion is almost entirely protonated to $\ce{HCN}$ , drastically reducing the free $\ce{CN^-}$ concentration.

The 6th power dependence on $\ce{[CN^-]}$ in the equilibrium expression completely overrides the large $\beta_6$ , causing the coordination sphere to collapse back to the weak-field hexaaqua complex.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Buffer Capacity and pH Range
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free