Deduce from the following `E^(c-)` values of half cells, what combination of two half cells would results in a cell with the largest potential?
`{:(I. , A+e(-) rarr A^(c-),,,,E^(c-)=-0.24V),(II., B^(c-)+e^(-)rarr B^(2-),,,,E^(c-)=+1.25V),(III.,C^(c-)+2e^(-) rarr C^(3-),,,,E^(c-)=-1.25V),(IV. , D+2e^(c-)rarr D^(2-),,,, E^(c-)=+0.68V):}`

Options

A. (i) and (iii)
B. (i) and (ii)
C. (ii) and (iv)
D. (iii) and (iv)

Answer

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

### Step 1: Identify the half-cell potentials
We are given the following half-cell reactions and their standard electrode potentials (E°):

1. \( A^+ + e^- \rightarrow A \), \( E° = -0.24 \, V \)
2. \( B^{2+} + 2e^- \rightarrow B \), \( E° = +1.25 \, V \)
3. \( C^{3+} + 2e^- \rightarrow C \), \( E° = -1.25 \, V \)
4. \( D + 2e^- \rightarrow D^{2-} \), \( E° = +0.68 \, V \)

### Step 2: Determine the best cathode and anode
To maximize the cell potential (E_cell), we need to select the half-cell with the highest E° as the cathode and the half-cell with the lowest E° as the anode.

- The highest E° value is for half-cell II (B), which is +1.25 V.
- The lowest E° value is for half-cell III (C), which is -1.25 V.

### Step 3: Calculate the cell potential
The cell potential (E_cell) can be calculated using the formula:
\[ E_{cell} = E_{cathode} - E_{anode} \]

Substituting the values:
\[ E_{cell} = E_{B} - E_{C} = 1.25 \, V - (-1.25 \, V) = 1.25 \, V + 1.25 \, V = 2.50 \, V \]

### Step 4: Check other combinations
Now, we will check the other combinations to ensure that we have the largest potential:

- **Combination of I and II**:
\[ E_{cell} = E_{B} - E_{A} = 1.25 \, V - (-0.24 \, V) = 1.25 \, V + 0.24 \, V = 1.49 \, V \]

- **Combination of II and IV**:
\[ E_{cell} = E_{B} - E_{D} = 1.25 \, V - 0.68 \, V = 0.57 \, V \]

- **Combination of III and IV**:
\[ E_{cell} = E_{D} - E_{C} = 0.68 \, V - (-1.25 \, V) = 0.68 \, V + 1.25 \, V = 1.93 \, V \]

### Conclusion
The combination of half-cell II (B) and half-cell III (C) gives the largest cell potential of 2.50 V.

Thus, the combination of two half-cells that results in a cell with the largest potential is:
**B and C (II and III)**.

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