From the following `E^(o)` value of helf cells:
(i) `A+e^(-)rarr A ^(-) , E^(o) = -0.824 V`
(ii) `B^(-)+e^(-)rarr B ^(2-) , E^(o) = +1.25V`
(iii) `C^(-)+2e^(-)rarr C ^(3-) , E^(o) = -1.25V`
(iv) `D^(-)+2e^(-)rarr D ^(2-) , E^(o) = +0.68V`
What combination of two half cells would result is a cell with the largest cell potential?

Options

A. (ii)&(iii)
B. (ii)&(iV)
C. (i)&(iii)
D. (i)&(iv)

Answer

To determine the combination of two half-cells that results in the largest cell potential, we can follow these steps:

### Step 1: Identify the half-cell reactions and their standard reduction potentials (E°)
We have the following half-cell reactions and their respective standard reduction potentials:

1. \( A^+ + e^- \rightarrow A^- \), \( E^\circ = -0.824 \, \text{V} \)
2. \( B^- + e^- \rightarrow B^{2-} \), \( E^\circ = +1.25 \, \text{V} \)
3. \( C^- + 2e^- \rightarrow C^{3-} \), \( E^\circ = -1.25 \, \text{V} \)
4. \( D^- + 2e^- \rightarrow D^{2-} \), \( E^\circ = +0.68 \, \text{V} \)

### Step 2: Determine the best combination for maximum cell potential
The cell potential \( E^\circ_{\text{cell}} \) is calculated using the formula:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \]
To maximize \( E^\circ_{\text{cell}} \), we want the cathode (reduction) to have the highest positive potential and the anode (oxidation) to have the lowest (most negative) potential.

### Step 3: Identify the maximum positive and maximum negative potentials
- The maximum positive potential is from \( B^- \) with \( E^\circ = +1.25 \, \text{V} \).
- The maximum negative potential is from \( C^- \) with \( E^\circ = -1.25 \, \text{V} \).

### Step 4: Calculate the cell potential for the selected combination
Using \( B^- \) as the cathode and \( C^- \) as the anode:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = (+1.25 \, \text{V}) - (-1.25 \, \text{V}) \]
\[ E^\circ_{\text{cell}} = 1.25 \, \text{V} + 1.25 \, \text{V} = 2.50 \, \text{V} \]

### Step 5: Conclusion
The combination of half-cells \( B^- \) and \( C^- \) results in the largest cell potential of \( 2.50 \, \text{V} \).

### Final Answer
The combination of half-cells that results in the largest cell potential is:
- \( B^- + C^- \)

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