For the cell prepared from electrodes A and B,
Electrode A :`Cr_2O_7^(2-)//Cr^(3+),E_"red"^@=1.33 V` and Electrode B: `Fe^(3+)//Fe^(2+), E_"red"^@=0.77 V`
Which of the following statements is correct?

Options

A. The electrons will flow from B to A when connections are made.
B. The standard EMF of the cell will be 0.56 V.
C. A will be a positive electrode.
D. All of these.

Explanation

To solve the problem, we need to analyze the given electrochemical cell involving two half-reactions and their standard reduction potentials. We will determine which statements about the cell are correct based on the information provided.

### Step-by-Step Solution:

1. **Identify the Half-Reactions and Their Standard Reduction Potentials:**
- Electrode A: \( \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{e}^- \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O} \) with \( E^\circ_{\text{red}} = 1.33 \, \text{V} \)
- Electrode B: \( \text{Fe}^{3+} + \text{e}^- \rightarrow \text{Fe}^{2+} \) with \( E^\circ_{\text{red}} = 0.77 \, \text{V} \)

2. **Determine the Anode and Cathode:**
- The electrode with the higher reduction potential acts as the cathode, while the one with the lower reduction potential acts as the anode.
- Here, \( E^\circ_{\text{red}} \) for Electrode A (1.33 V) is greater than that for Electrode B (0.77 V).
- Therefore, Electrode A is the cathode and Electrode B is the anode.

3. **Calculate the Cell Potential (E_cell):**
- The cell potential can be calculated using the formula:
\[ E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}} \]
- Substituting the values:
\[ E_{\text{cell}} = 1.33 \, \text{V} - 0.77 \, \text{V} = 0.56 \, \text{V} \]

4. **Determine the Correct Statements:**
- Since Electrode A is the cathode and Electrode B is the anode, we can conclude that:
- Electrode A will undergo reduction (gain of electrons).
- Electrode B will undergo oxidation (loss of electrons).
- The positive value of \( E_{\text{cell}} \) indicates that the reaction is spontaneous.

5. **Conclusion:**
- Based on the analysis, the correct statement regarding the electrochemical cell is that Electrode A is the cathode, Electrode B is the anode, and the cell potential is positive.