Q. 22 The standard reduction potential (E°) for the conversion of Cr2O72− to Cr3+ at 25°C in an aqueous solution of pH 3.0 is 1.33 V. The concentrations of Cr2O72− and Cr3+ are 1.0 × 10−4M and 1.0 × 10−3M, respectively. Then the potential of this half-cell reaction is (Given: Faraday constant = 96500 C mol−1, Gas constant R = 8.314 J K−1 mol−1)
(A) 1.04 V (B) 0.94 V (C) 0.84 V (D) 0.74 V
The reduction of dichromate ions to chromium(III) ions is a classic electrochemistry
problem frequently asked in competitive exams. In this article, we calculate the
non-standard reduction potential at pH = 3 using the Nernst equation,
identify the correct option, and explain why the other choices are incorrect.
Given Half-Reaction
The balanced reduction half-reaction in acidic medium is:
Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O
Given data:
- Standard reduction potential, E° = 1.33 V
- pH = 3 → [H⁺] = 10−3 M
- [Cr₂O₇²⁻] = 1.0 × 10−4 M
- [Cr³⁺] = 1.0 × 10−3 M
- Number of electrons transferred, n = 6
Nernst Equation Setup
At 25°C (298 K), the Nernst equation is:
E = E° − (0.059 / n) log Q
The reaction quotient for the given half-reaction is:
Q = [Cr³⁺]² / ( [Cr₂O₇²⁻] [H⁺]¹⁴ )
Substitution of Values
Q = (10−3)² / (10−4 × (10−3)¹⁴)
Q = 10−6 / 10−46 = 1040
So,
log Q = 40
Step-by-Step Potential Calculation
Calculate the correction term:
(0.059 / 6) × 40 = 0.3933 V
Now calculate the actual electrode potential:
E = 1.33 − 0.3933 = 0.9367 V ≈ 0.94 V
(B) 0.94 V
Why Other Options Are Incorrect
| Option | Value (V) | Why It Is Incorrect |
|---|---|---|
| (A) | 1.04 V | Underestimates the effect of the large [H⁺]¹⁴ term; log Q is taken too small. |
| (B) | 0.94 V | Correct. Matches the exact Nernst equation calculation. |
| (C) | 0.84 V | Overestimates the correction term, possibly using an incorrect electron count. |
| (D) | 0.74 V | Subtracts too much from E°, often due to ignoring proper stoichiometry. |
Key Takeaways for Electrochemistry Exams
- Always balance the half-reaction to confirm the correct value of n.
- At low pH, powers of
[H⁺]dominate the reaction quotient. - Use
0.059 / nfor quick MCQ calculations at 298 K. - Large
Qvalues significantly lower the electrode potential fromE°.
