The standard reductino potentials `E^(c-)` for the half reactinos are as follows`:`
`ZnrarrZn^(2+)+2e^(-)" "E^(c-)=+0.76V`
`FerarrFe^(2+)+2e^(-) " "E^(c-)=0.41V`
The `EMF` for the cell reaction
`Fe^(2+)+Znrarr Zn^(2+)+Fe`
is

Options

A. `-0.35V`
B. `+0.35V`
C. `+1.17V`
D. `-1.17V`

Explanation

To find the EMF (Electromotive Force) for the cell reaction given in the question, we will follow these steps:

### Step 1: Identify the half-reactions and their standard reduction potentials
The half-reactions provided are:
1. For zinc:
\[ \text{Zn}^{2+} + 2e^- \rightarrow \text{Zn} \quad E^\circ = +0.76 \, \text{V} \]
2. For iron:
\[ \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \quad E^\circ = +0.41 \, \text{V} \]

### Step 2: Determine which species is oxidized and which is reduced
In the cell reaction:
\[ \text{Fe}^{2+} + \text{Zn} \rightarrow \text{Zn}^{2+} + \text{Fe} \]
- **Oxidation** occurs at zinc (Zn is oxidized to Zn²⁺).
- **Reduction** occurs at iron (Fe²⁺ is reduced to Fe).

### Step 3: Write the oxidation and reduction half-reactions
- Oxidation half-reaction (for zinc):
\[ \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^- \]
- Reduction half-reaction (for iron):
\[ \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \]

### Step 4: Calculate the standard oxidation potential for zinc
The oxidation potential is the negative of the reduction potential:
\[ E^\circ_{\text{oxidation}} (\text{Zn}) = -E^\circ_{\text{reduction}} (\text{Zn}) = -0.76 \, \text{V} \]

### Step 5: Calculate the standard cell potential (E_cell)
The standard cell potential can be calculated using the formula:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \]
Where:
- \(E^\circ_{\text{cathode}} = E^\circ_{\text{reduction}} (\text{Fe}) = +0.41 \, \text{V}\)
- \(E^\circ_{\text{anode}} = E^\circ_{\text{oxidation}} (\text{Zn}) = -0.76 \, \text{V}\)

Substituting the values:
\[ E^\circ_{\text{cell}} = 0.41 \, \text{V} - (-0.76 \, \text{V}) = 0.41 \, \text{V} + 0.76 \, \text{V} = 1.17 \, \text{V} \]

### Step 6: Conclusion
The EMF for the cell reaction is:
\[ \text{E}_{\text{cell}} = 1.17 \, \text{V} \]