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):}`
1) `II,IV`
2) `II,III`
3) `III,IV`
4) `I,II`

Options

A. `II,IV`
B. `II,III`
C. `III,IV`
D. `I,II`

Explanation

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

### Step 1: Identify the half-cell potentials
We are given the following half-cell reactions and their standard reduction 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. \( D^{2+} + 2e^- \rightarrow D \), \( E° = +0.68 \, V \)

### Step 2: Determine the combinations of half-cells
We will evaluate the combinations provided in the options:

1. **Option 1: II and IV**
- Cathode: \( B^{2+} + 2e^- \rightarrow B \) (E° = +1.25 V)
- Anode: \( D^{2+} + 2e^- \rightarrow D \) (E° = +0.68 V)
- \( E°_{cell} = E°_{cathode} - E°_{anode} = 1.25 - 0.68 = 0.57 \, V \)

2. **Option 2: II and III**
- Cathode: \( B^{2+} + 2e^- \rightarrow B \) (E° = +1.25 V)
- Anode: \( C^{3+} + 2e^- \rightarrow C \) (E° = -1.25 V)
- \( E°_{cell} = E°_{cathode} - E°_{anode} = 1.25 - (-1.25) = 1.25 + 1.25 = 2.50 \, V \)

3. **Option 3: III and IV**
- Cathode: \( D^{2+} + 2e^- \rightarrow D \) (E° = +0.68 V)
- Anode: \( C^{3+} + 2e^- \rightarrow C \) (E° = -1.25 V)
- \( E°_{cell} = E°_{cathode} - E°_{anode} = 0.68 - (-1.25) = 0.68 + 1.25 = 1.93 \, V \)

4. **Option 4: I and II**
- Cathode: \( B^{2+} + 2e^- \rightarrow B \) (E° = +1.25 V)
- Anode: \( A^+ + e^- \rightarrow A \) (E° = -0.24 V)
- \( E°_{cell} = E°_{cathode} - E°_{anode} = 1.25 - (-0.24) = 1.25 + 0.24 = 1.49 \, V \)

### Step 3: Compare the cell potentials
Now we can summarize the calculated cell potentials for each combination:
- Option 1: \( 0.57 \, V \)
- Option 2: \( 2.50 \, V \)
- Option 3: \( 1.93 \, V \)
- Option 4: \( 1.49 \, V \)

### Conclusion
The combination that results in the largest cell potential is **Option 2: II and III**, with a cell potential of \( 2.50 \, V \).

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