Question

What is the value of $E^\circ(\text{Fe}^{3+}/\text{Fe}^0)$?
(The standard reduction potential values are $E^\circ(\text{Fe}^{3+}/\text{Fe}^{2+}) = 0.77\text{ V}$, and $E^\circ(\text{Fe}^{2+}/\text{Fe}^0) = -0.44\text{ V}$)}

• A. $-0.04\text{ V}$
• B. $0.33\text{ V}$
• C. $0.11\text{ V}$
• D. $-0.11\text{ V}$

Hint:

Never add $E^\circ$ values directly!
Always use the formula:
\[ E^\circ_{\text{net}} = \frac{n_1 E^\circ_1 + n_2 E^\circ_2}{n_1 + n_2} \]
Plugging in:
\[ E^\circ_{\text{net}} = \frac{1(0.77) + 2(-0.44)}{3} = \frac{0.77 - 0.88}{3} = -0.037\text{ V} \]

Answer 1

The Correct Option is A

Step 1 : Understanding the Question:
The question asks us to calculate the standard reduction potential for the reduction of $\text{Fe}^{3+}$ to metallic iron ($\text{Fe}^0$) using the given standard reduction potentials of the individual steps ($\text{Fe}^{3+}/\text{Fe}^{2+}$ and $\text{Fe}^{2+}/\text{Fe}^0$).

Step 2 : Key Formulas and Approach:
Standard reduction potentials ($E^\circ$) are intensive properties and cannot be added directly.
We must convert them to standard Gibbs free energy changes ($\Delta G^\circ$), which is an extensive property, using the formula:
\[ \Delta G^\circ = -nFE^\circ \]
We will set up the thermodynamic cycle:
\[ \Delta G^\circ_3 = \Delta G^\circ_1 + \Delta G^\circ_2 \]

Step 3 : Detailed Explanation:
Let us write down the half-cell reactions and their corresponding parameters:

• First step: Reduction of $\text{Fe}^{3+}$ to $\text{Fe}^{2+}$
\[ \text{Fe}^{3+} + \text{e}^- \rightarrow \text{Fe}^{2+} \quad (n_1 = 1, \, E_1^\circ = 0.77\text{ V}) \]
\[ \Delta G^\circ_1 = -1 \cdot F \cdot (0.77) = -0.77F \]

• Second step: Reduction of $\text{Fe}^{2+}$ to $\text{Fe}^0$
\[ \text{Fe}^{2+} + 2\text{e}^- \rightarrow \text{Fe}^0 \quad (n_2 = 2, \, E_2^\circ = -0.44\text{ V}) \]
\[ \Delta G^\circ_2 = -2 \cdot F \cdot (-0.44) = +0.88F \]

• Target step: Reduction of $\text{Fe}^{3+}$ to $\text{Fe}^0$
\[ \text{Fe}^{3+} + 3\text{e}^- \rightarrow \text{Fe}^0 \quad (n_3 = 3, \, E_3^\circ = ?) \]
\[ \Delta G^\circ_3 = -3 \cdot F \cdot E_3^\circ \]
Now, adding the first two reactions gives the target reaction:
\[ \Delta G^\circ_3 = \Delta G^\circ_1 + \Delta G^\circ_2 \]
\[ -3FE_3^\circ = -0.77F + 0.88F \]
\[ -3E_3^\circ = 0.11 \]
\[ E_3^\circ = -\frac{0.11}{3} \approx -0.0367\text{ V} \]
Rounding this value to two decimal places gives $-0.04\text{ V}$.

Step 4 : Final Answer:
The standard reduction potential $E^\circ(\text{Fe}^{3+}/\text{Fe}^0)$ is $-0.04\text{ V}$.
This corresponds to Option (A).