Statement I: Current stops flowing when \(E_{cell} = 0\)

Statement II: Equilibrium of the cell reaction is attained.

Statement I is correct but Statement II is false

The correct answer is option 1. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I.

Let us delve deeper into each statement and their relationship:

Statement I: Current stops flowing when \( E_{\text{cell}} = 0 \)

In an electrochemical cell, \( E_{\text{cell}} \) (the cell potential or electromotive force) represents the driving force that pushes electrons through the external circuit from the anode to the cathode. Here's how this statement holds true:

Cell Potential \( E_{\text{cell}} \): When \( E_{\text{cell}} > 0 \), the cell is in a non-equilibrium state, indicating that the cell reactions are spontaneous and capable of driving an electric current. Electrons flow from the anode (where oxidation occurs) to the cathode (where reduction occurs) through the external circuit.

Equilibrium Condition: As the cell operates and the reactions proceed, the concentrations of reactants and products change. Eventually, the rates of the forward and reverse reactions reach equilibrium. At this point, \( E_{\text{cell}} = 0 \), indicating that there is no longer any potential difference between the two electrodes. Without this potential difference, there is no driving force for electrons to move, hence current stops flowing through the external circuit.

Statement II: Equilibrium of the cell reaction is attained

Equilibrium in the Cell: This statement refers to the point where the rates of oxidation and reduction reactions within the cell become equal. At equilibrium, the cell potential (\( E_{\text{cell}} \)) reaches zero because the forward and reverse reactions occur at the same rate, leading to no net change in the concentrations of reactants and products over time.

Explanation of Statement I: Statement II explains why Statement I is true. When the cell reaches equilibrium, \( E_{\text{cell}} = 0 \), indicating that the electrochemical processes have balanced out. At this point, there is no longer any driving force (potential difference) to sustain the flow of electrons through the external circuit. Therefore, current stops flowing because there is no longer a potential difference to maintain electron movement.

Conclusion:

Both statements are correct in their own right:

Statement I correctly identifies that current stops flowing when \( E_{\text{cell}} = 0 \).

Statement II correctly states that this occurs when equilibrium of the cell reaction is attained, leading to \( E_{\text{cell}} = 0 \).

Statement II provides the explanatory framework for Statement I, as it clarifies that the cessation of current flow is directly linked to the equilibrium condition where \( E_{\text{cell}} = 0 \).

Therefore, the correct option is: 1. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I.