Statement I: E_cell should have a positive value for the cell to function

Statement II: \(E_{cathode} < E_{anode}\)

Statement I is correct but Statement II is false

The correct answer is option 3. Statement I is correct but Statement II is false.

In an electrochemical cell (such as a galvanic or voltaic cell), the cell potential (\( E_{\text{cell}} \)) is the driving force for the electrochemical reaction. It is defined as the difference between the electrode potentials of the cathode and the anode:

\(E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}}\)

Statement I: \(E_{cell}\) should have a positive value for the cell to function

The given statement is correct. For the cell to function spontaneously, \( E_{\text{cell}} \) must be positive. This means the overall redox reaction is spontaneous, and the cell can generate electrical energy. When \( E_{\text{cell}} \) is positive, it indicates that the Gibbs free energy change (\( \Delta G \)) is negative (\( \Delta G = -nFE_{\text{cell}} \)), which corresponds to a spontaneous reaction.

Statement II: \(E_{cathode} < E_{anode}\)

The given statement is incorrect.  This statement implies that the potential of the cathode is less than the potential of the anode, which would lead to a negative cell potential (\( E_{\text{cell}} < 0 \)). For \( E_{\text{cell}} \) to be positive, the potential of the cathode must be greater than the potential of the anode:

\(E_{\text{cathode}} > E_{\text{anode}} \)

Correct Relationship for Spontaneous Cell:

To have a functioning (spontaneous) electrochemical cell, the reduction potential at the cathode must be higher than at the anode, making \( E_{\text{cell}} \) positive. This can be summarized as:

\(E_{\text{cathode}} > E_{\text{anode}}\)

Conclusion:

Statement I is correct because a positive \( E_{\text{cell}} \) indicates that the cell can function and drive a spontaneous reaction. Statement II is false because for the cell to function (\( E_{\text{cell}} \) to be positive), \( E_{\text{cathode}} \) must be greater than \( E_{\text{anode}} \), not less.

Therefore, the correct evaluation of the statements is: Statement I is correct but Statement II is false.