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Question #44876

Difficulty: 8/10 | 🟢 Free

The Question

A galvanic cell is constructed at 298 K: $\ce{Pt | Fe^{2+} (1.1 \times 10^{-3} M), Fe^{3+} (10^{-7} M) || Fe^{3+} (1.1 \times 10^{-3} M), Fe^{2+} (10^{-7} M) | Pt}$ The volumes of both half-cells are 1.0 L. The cell is allowed to discharge spontaneously through a resistor until the cell potential drops to 0.118 V, at which point the circuit is opened.

An aliquot of the solution from the left half-cell (anode compartment) is taken, and solid \ce{KSCN} is added to it such that the equilibrium concentration of free \ce{SCN^-} is 0.09 M. This forms the intensely red complex \ce{[Fe(SCN)]^{2+}} via Ligand-to-Metal Charge Transfer (LMCT).

Given the formation constant of \ce{[Fe(SCN)]^{2+}} is $K_f = 100 \text{ M}^{-1}$ and its molar absorptivity is $\epsilon = 5000 \text{ L mol}^{-1} \text{ cm}^{-1}$ at $\lambda_{max}$ .

Calculate the absorbance of this solution in a 1.0 cm cuvette. (Assume no volume change upon addition of \ce{KSCN}, and \ce{Fe^{2+}} does not complex with \ce{SCN^-}. Given: $\frac{2.303 RT}{F} = 0.059$ V)

Options

A.
0.45
B.
2.48
C.
0.50
D.
4.50

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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

Color and Charge Transfer|Nernst Equation Concentration Dependence|Concentration Cells

Why This Question Is Tricky

Common Mistakes

The problem tests the integration of electrochemistry (Nernst equation for a discharging concentration cell) with coordination chemistry and analytical chemistry (Beer-Lambert Law).

The primary trap is the assumption that the cell discharges completely to equilibrium ( $E_{cell} = 0$ ), which yields an incorrect extent of reaction ( $x = 5.5 \times 10^{-4}$ M, leading to $A = 2.48$ ).

Furthermore, students often forget that the formation of the complex consumes the metal ion, requiring the use of the mass balance equation ( $[\ce{Fe^{3+}}]_{free} = [\ce{Fe^{3+}}]_{total} - [\text{Complex}]$ ) rather than assuming 100% conversion (leading to $A = 0.50$ ) or ignoring mass balance entirely (leading to $A = 4.50$ ).

The problem also tests the correct formulation of the Nernst equation for a cell where both oxidized and reduced species are in solution, leading to a squared term in the reaction quotient $Q$ .

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	D and F Block Elements - Class 12
Concept	Color and Charge Transfer
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free