Which Nernst equation is true to find out the potential of non-standard electrochemical cell from the following ?
`Fe(s)|Fe^(2+) (xM) || I^(-)(s) (Pt)`

Options

A. `E_(cell) = E_(cell)^(@) - (0.592)/(n) log_(10) [Fe^(2+)][I^(-)]^(2)`
B. `E_(cell) = E_(cell)^(@) - (0.0592)/(n) log_(10) [Fe^(2+)][I^(-)]^(2)`
C. `E_(cell) = E_(cell)^(@) - (0.0592)/(n) log_(10) [Fe^(2+)][I^(-)]`
D. `E_(cell) = E_(cell)^(@) - (0.0592)/(nF) log_(10) .([Fe^(2+)][I^(-)]^(2))/([Fe][I_(2)])`

Answer

To find the potential of the non-standard electrochemical cell represented by the notation `Fe(s)|Fe^(2+) (xM) || I^(-)(s) (Pt)`, we can use the Nernst equation. Here’s a step-by-step solution:

### Step 1: Identify the half-reactions
In the given cell, we have:
- Oxidation half-reaction:
\[ \text{Fe(s)} \rightarrow \text{Fe}^{2+} + 2e^- \]
- Reduction half-reaction:
\[ \text{I}_2 + 2e^- \rightarrow 2\text{I}^- \]

### Step 2: Write the overall cell reaction
Combining the half-reactions, we get the overall cell reaction:
\[ \text{Fe(s)} + \text{I}_2 \rightarrow \text{Fe}^{2+} + 2\text{I}^- \]

### Step 3: Write the Nernst equation
The Nernst equation relates the cell potential (E) to the standard cell potential (E°) and the concentrations of the reactants and products:
\[ E = E^\circ - \frac{0.0591}{n} \log Q \]
where:
- \(E\) = cell potential
- \(E^\circ\) = standard cell potential
- \(n\) = number of moles of electrons transferred (which is 2 in this case)
- \(Q\) = reaction quotient

### Step 4: Determine the reaction quotient (Q)
For the reaction:
\[ \text{Fe(s)} + \text{I}_2 \rightarrow \text{Fe}^{2+} + 2\text{I}^- \]
The reaction quotient \(Q\) is given by:
\[ Q = \frac{[\text{Fe}^{2+}]}{[\text{I}_2]} \]
Since the solid iron (Fe) does not appear in the expression, we only consider the aqueous ions.

### Step 5: Substitute values into the Nernst equation
Substituting the values into the Nernst equation:
\[ E = E^\circ - \frac{0.0591}{2} \log \left(\frac{[\text{Fe}^{2+}]}{[\text{I}_2]}\right) \]

### Final Nernst Equation
Thus, the Nernst equation to find the potential of the non-standard electrochemical cell is:
\[ E = E^\circ - 0.02955 \log \left(\frac{[\text{Fe}^{2+}]}{[\text{I}_2]}\right) \]