Complete the following table. State whether the cell reaction is spontaneous, nonspontaneous, or at equilibrium. $$ \begin{array}{c|c|c} \boldsymbol{E} & \boldsymbol{\Delta} \boldsymbol{G} & \text { Cell Reaction } \\\ \hline > 0 & & \\ \hline & > 0 & \\ \hline=0 & & \\ \hline \end{array} $$

The cell potential, often denoted as \(E\), is a measure of the electromotive force (emf) of an electrochemical cell. Think of it as a way to quantify the ability of a cell's chemical reaction to drive an electric current. A positive cell potential represents a spontaneous reaction, meaning that the electrons will flow through an external circuit from the anode (the electrode where oxidation occurs) to the cathode (the electrode where reduction occurs) naturally.

An example of this is a standard alkaline battery that you might put into a flashlight. Once the circuit is complete, the reaction proceeds spontaneously, lighting the bulb. Conversely, a negative cell potential indicates a nonspontaneous reaction; external energy would be required to drive the reaction forward. This is seen in the process of electrolysis, where electricity is used to drive a chemical reaction. Understanding cell potential is crucial for predicting the direction of electron flow in electrochemical cells.

Gibbs free energy, denoted by \(\Delta G\), is a thermodynamic quantity associated with the spontaneity of a reaction at constant temperature and pressure. A negative \(\Delta G\) indicates a spontaneous process, one that can occur without any continuous input of energy. In contrast, a positive \(\Delta G\) suggests a nonspontaneous reaction, meaning you'd have to provide energy for the reaction to proceed.

For students, remembering which sign of \(\Delta G\) corresponds to which type of reaction can be challenging, but an easy trick is to think of spontaneity as a ball rolling downhill (negative \(\Delta G\)) and nonspontaneity as the need to push a ball uphill (positive \(\Delta G\)). In terms of electrochemistry, \(\Delta G\) is directly related to the cell potential by the equation \(\Delta G = -nFE\), where \(n\) represents the number of moles of electrons transferred, \(F\) is Faraday's constant, and \(E\) is the cell potential.

Electrochemical cell equilibrium is the state in which the cell potential \(E\) equals zero, and there is no net change in the Gibbs free energy (\(\Delta G = 0\)). At this state, the forward and reverse reactions occur at equal rates, and there is no net cell reaction occurring over time. This is akin to reaching a balance on a seesaw where neither side is heavier, and the seesaw is level.

The equilibrium state has practical applications: it's integral to a battery's discharge. As a battery is used, it slowly moves towards equilibrium, eventually reaching a point where it can no longer provide electrical work. This is the stage at which your remote control stops working because the batteries can no longer sustain the chemical reactions required to produce electricity. Understanding this concept helps one gauge the capacity and shelf-life of electrochemical cells and batteries.