The standard oxidation potentials, , for the half reactions are as follows :
`Zn rightarrow Zn^(2+) + 2e^(-)` ,` E^(@) = +0.76V`
`Fe rightarrow Fe^(2+)+ 2e^(-), E^(@) = + 0.41 V`
The EMF for the cell reaction,
`Fe^(2+) + Zn rightarrow Zn^(2+) + Fe`

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 by:

\[ \text{Fe}^{2+} + \text{Zn} \rightarrow \text{Zn}^{2+} + \text{Fe} \]

we will follow these steps:

### Step 1: Identify the half-reactions and their standard potentials
The half-reactions and their standard oxidation potentials are given as:
1. Oxidation:
\[ \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^{-} \quad E^{\circ} = +0.76 \, \text{V} \]
2. Reduction:
\[ \text{Fe}^{2+} + 2e^{-} \rightarrow \text{Fe} \quad E^{\circ} = +0.41 \, \text{V} \]

### Step 2: Determine which species is oxidized and which is reduced
- **Oxidation** occurs at the anode: Zinc (Zn) is oxidized to Zinc ions (\( \text{Zn}^{2+} \)).
- **Reduction** occurs at the cathode: Iron ions (\( \text{Fe}^{2+} \)) are reduced to Iron (Fe).

### Step 3: Write the cell notation
The overall cell reaction can be represented as:
\[ \text{Zn} + \text{Fe}^{2+} \rightarrow \text{Zn}^{2+} + \text{Fe} \]

### Step 4: Calculate the EMF of the cell
The standard EMF of the cell (\( E^{\circ}_{\text{cell}} \)) can be calculated using the formula:
\[ E^{\circ}_{\text{cell}} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}} \]

Where:
- \( E^{\circ}_{\text{cathode}} \) is the standard reduction potential for the reduction half-reaction (Fe).
- \( E^{\circ}_{\text{anode}} \) is the standard oxidation potential for the oxidation half-reaction (Zn).

Substituting the values:
- \( E^{\circ}_{\text{cathode}} = +0.41 \, \text{V} \)
- \( E^{\circ}_{\text{anode}} = +0.76 \, \text{V} \)

Thus,
\[ E^{\circ}_{\text{cell}} = 0.41 \, \text{V} - 0.76 \, \text{V} \]
\[ E^{\circ}_{\text{cell}} = -0.35 \, \text{V} \]

### Step 5: Conclusion
The EMF for the cell reaction is:
\[ E^{\circ}_{\text{cell}} = -0.35 \, \text{V} \]