The \(E^{\circ}\) value of one cell reaction is positive and that of another cell reaction is negative. Which cell reaction will proceed toward the formation of more products at equilibrium?

The standard cell potential, denoted as \( E^{\circ} \), is a crucial concept when studying electrochemical cells. It is the measure of the potential difference between two half-cells in an electrochemical cell when both electrodes are in their standard states at 25°C (298 K), with a 1 M concentration for solutions and at 1 atm pressure for gases.

The standard cell potential dictates the direction and magnitude of an electrochemical reaction. A positive \( E^{\circ} \) value suggests that a cell reaction is capable of occurring spontaneously under standard conditions, thus favoring the conversion of reactants to products. On the other hand, a negative \( E^{\circ} \) value implies that a cell reaction is non-spontaneous and would require an external energy source to proceed. It’s essential to understand that the standard cell potential is dependent on the inherent properties of the materials involved and their interactions but does not take concentration or gas pressure into account, other than the specified standard conditions.

Spontaneous reactions in electrochemistry refer to processes that occur naturally without the need for additional energy input from the outside. These reactions are driven by a positive standard cell potential, \( E^{\circ} > 0 \), suggesting that the overall Gibbs free energy change, \( \Delta G^{\circ} \), is negative, which is a thermodynamic requirement for spontaneity.

Understanding whether a reaction is spontaneous helps predict the behavior of electrochemical cells. When analyzing two cell reactions, the one with a positive \( E^{\circ} \) value will proceed toward the formation of products without external intervention. Conversely, if \( E^{\circ} \) is negative, the reaction is non-spontaneous, indicating that it is unfavorable under standard conditions unless influenced by an external voltage or by changing the reaction conditions.

Equilibrium in an electrochemical cell is achieved when the rates of the forward and reverse reactions are equal, leading to no net change in the concentration of reactants and products over time. The standard cell potential is related to the equilibrium constant, \( K \), of the cell reaction through the Nernst equation, which demonstrates how the cell potential varies with changes in concentration, temperature, and pressure.

At equilibrium, the net cell potential, \( E_{cell} \), is zero, indicating that no more work can be extracted from the cell as an energy source. The relation between \( E^{\circ} \) and \( K \) helps determine the position of equilibrium. A large positive \( E^{\circ} \) corresponds to a large \( K \), signifying that the reaction heavily favors the formation of products, whereas a negative \( E^{\circ} \) leads to a \( K < 1 \), favoring reactants at equilibrium.