If `E_(Fe^(2+))^(@)//Fe = -0.441 V`
and `E_(Fe^(3+))^(@)//Fe^(2+) = 0.771 V`
The standard `EMF` of the reaction
`Fe+2Fe^(3+) rarr 3Fe^(2+)`
will be:

Options

A. 0.111 V
B. 0.330 V
C. 1.653 V
D. 1.212 V

Explanation

To find the standard EMF of the reaction \( \text{Fe} + 2 \text{Fe}^{3+} \rightarrow 3 \text{Fe}^{2+} \), we can follow these steps:

### Step 1: Identify the half-reactions and their standard reduction potentials.

1. The first half-reaction involves the reduction of \( \text{Fe}^{3+} \) to \( \text{Fe}^{2+} \):
\[ \text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+} \quad (E^\circ = 0.771 \, \text{V}) \]

2. The second half-reaction involves the oxidation of \( \text{Fe} \) to \( \text{Fe}^{2+} \):
\[ \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \quad (E^\circ = -0.441 \, \text{V}) \]

### Step 2: Adjust the half-reactions for the overall reaction.

To combine these half-reactions, we need to multiply the first half-reaction by 2 to match the number of electrons transferred in the second half-reaction:

- Multiply the first half-reaction by 2:
\[ 2 \text{Fe}^{3+} + 2e^- \rightarrow 2 \text{Fe}^{2+} \quad (E^\circ = 0.771 \, \text{V}) \]

### Step 3: Reverse the second half-reaction.

Since we are looking for the oxidation of \( \text{Fe} \), we reverse the second half-reaction:
\[ \text{Fe} \rightarrow \text{Fe}^{2+} + 2e^- \quad (E^\circ = +0.441 \, \text{V}) \]

### Step 4: Combine the half-reactions.

Now we can add the two half-reactions together:
\[ 2 \text{Fe}^{3+} + 2e^- + \text{Fe} \rightarrow 2 \text{Fe}^{2+} + 2e^- \]
Simplifying gives:
\[ 2 \text{Fe}^{3+} + \text{Fe} \rightarrow 3 \text{Fe}^{2+} \]

### Step 5: Calculate the standard EMF of the overall reaction.

The standard EMF of the overall reaction can be calculated using the formula:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{reduction}} - E^\circ_{\text{oxidation}} \]
Substituting the values:
\[ E^\circ_{\text{cell}} = 0.771 \, \text{V} - (-0.441 \, \text{V}) = 0.771 \, \text{V} + 0.441 \, \text{V} = 1.212 \, \text{V} \]

### Final Answer:
The standard EMF of the reaction \( \text{Fe} + 2 \text{Fe}^{3+} \rightarrow 3 \text{Fe}^{2+} \) is **1.212 V**.

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