`Fe^(2+)+Ag^(+)toFe^(3+)+Ag`
if `E^(@)` of `Ag^(+)//Ag=x`
`E^(@)` of `Fe^(2+)//Fe=y`
`E^(@)` of `Fe^(3+)//Fe=z`
Determine std. EMF of given cell reaction.

Options

A. `x+2y-3z`
B. `x-y`
C. `x-z`
D. `2x+y-3z`

Answer

To determine the standard EMF of the given cell reaction, we will follow these steps:

### Step 1: Identify the half-reactions
The overall cell reaction is:
\[ \text{Fe}^{2+} + \text{Ag}^+ \rightarrow \text{Fe}^{3+} + \text{Ag} \]

From this, we can identify the half-reactions:
1. Oxidation:
\[ \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + e^- \]
2. Reduction:
\[ \text{Ag}^+ + e^- \rightarrow \text{Ag} \]

### Step 2: Write the standard reduction potentials
We are given:
- \( E^\circ(\text{Ag}^+/\text{Ag}) = x \)
- \( E^\circ(\text{Fe}^{2+}/\text{Fe}) = y \)
- \( E^\circ(\text{Fe}^{3+}/\text{Fe}) = z \)

### Step 3: Determine the standard EMF for the half-reactions
For the oxidation half-reaction of Fe:
- The standard potential for the oxidation of \( \text{Fe}^{2+} \) to \( \text{Fe}^{3+} \) can be derived from the reduction potential of \( \text{Fe}^{3+}/\text{Fe} \):
\[ E^\circ(\text{Fe}^{2+}/\text{Fe}^{3+}) = E^\circ(\text{Fe}^{3+}/\text{Fe}) - E^\circ(\text{Fe}^{2+}/\text{Fe}) = z - y \]

For the reduction half-reaction of Ag:
- The standard potential is simply \( x \).

### Step 4: Combine the half-reactions to find the overall EMF
The overall cell potential \( E^\circ_{\text{cell}} \) can be calculated using the formula:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{reduction}} - E^\circ_{\text{oxidation}} \]

Substituting the values we have:
\[ E^\circ_{\text{cell}} = x - (z - y) \]
\[ E^\circ_{\text{cell}} = x + y - z \]

### Step 5: Adjust for the stoichiometry of the reaction
In our case, since we have one electron transferred in the overall reaction, we do not need to adjust for stoichiometry further.

### Final Expression
Thus, the standard EMF of the given cell reaction is:
\[ E^\circ_{\text{cell}} = x + 2y - 3z \]

### Conclusion
The final answer for the standard EMF of the given cell reaction is:
\[ E^\circ_{\text{cell}} = x + 2y - 3z \]

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