Question

\( E^0_{\text{Fe}^{2+}/\text{Fe}} \) / Fe = x volts, \( E^0_{\text{Fe}^{3+}/\text{Fe}^{2+}} \) = y volts.
Calculate \( E^0_{\text{Fe}^{2+}/\text{Fe}^{3+}} \) in volts.

• A. \( 3x - 2y \)
• B. \( 3y - 2x \)
• C. \( 2x - 3y \)
• D. \( 2y - 3x \)

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem involves calculating the standard reduction potential of a redox couple from two other related redox couples using the concept of Gibbs free energy.
Step 2: Key Formula or Approach:
Potentials are not additive, but Gibbs free energy is: $\Delta G^\circ = -nFE^\circ$.
The target reaction can be represented as a combination of given half-reactions.
Step 3: Detailed Explanation:
(i) $Fe^{+2}(aq) + 2e^- \rightarrow Fe(s) \quad \Delta G_1^\circ = -2Fx$
(ii) $Fe^{+3}(aq) + 3e^- \rightarrow Fe(s) \quad \Delta G_2^\circ = -3Fy$
(iii) Target reaction: $Fe^{+2}(aq) \rightarrow Fe^{+3}(aq) + e^- \quad \Delta G_3^\circ = -1FE_3^\circ$

By observing the reactions, we can see that reaction (iii) = reaction (i) - reaction (ii).
$Fe^{+2} + 2e^- - (Fe^{+3} + 3e^-) \rightarrow Fe - Fe$
$Fe^{+2} - Fe^{+3} - e^- \rightarrow 0 \implies Fe^{+2} \rightarrow Fe^{+3} + e^-$

Therefore, $\Delta G_3^\circ = \Delta G_1^\circ - \Delta G_2^\circ$
$-FE_3^\circ = -2Fx - (-3Fy)$
$-E_3^\circ = -2x + 3y$
$E_3^\circ = 2x - 3y$
Step 4: Final Answer:
The value of $E^\circ_{Fe^{+2}/Fe^{+3}}$ is $2x - 3y$.