Question

What is the cell potential of a galvanic cell when the cell reaction has reached equilibrium?

Short answer

The cell potential of a galvanic cell at equilibrium is 0 volts.

Step-by-step solution

Understanding Electrochemical Cell Equilibrium

An electrochemical or galvanic cell reaches equilibrium when there is no net cell reaction occurring. At equilibrium, the cell can no longer produce an electrical current and the concentrations of reactants and products remain constant.

Relating Cell Potential to Equilibrium

The cell potential, also known as the electromotive force (EMF), is the measure of the voltage output of the cell. At equilibrium, the forward and reverse reactions occur at the same rate, meaning there is no net cell potential. This is described by the Nernst equation at equilibrium where the cell potential is equal to zero.

Conclusion

Since the cell potential is the driving force for the cell reaction and a cell at equilibrium has no net reaction, the cell potential at equilibrium is zero volts.

Key concepts

Electrochemical Cell

An electrochemical cell is a device that generates electrical energy from chemical reactions or facilitates chemical reactions through the introduction of electrical energy. There are two main types of electrochemical cells: galvanic (or voltaic) cells, which convert chemical energy into electrical energy, and electrolytic cells, which use electrical energy to drive chemical reactions.

In a galvanic cell, two different metals or metal ions are connected by a conductive path, consisting of a wire and an electrolyte. Each metal or metal ion forms an electrode, with one being the anode (where oxidation occurs) and the other being the cathode (where reduction happens). These reactions at the electrodes create a flow of electrons through the wire, generating an electric current.

When discussing equilibrium in the context of electrochemical cells, it refers to the state where the cell can no longer produce electrical current because the chemical reactions have reached a balance. At this point, the concentrations of reactants and products are constant, and there is no driving force to move electrons from the anode to the cathode.

Cell Potential

Cell potential, also known as electromotive force (EMF), is a fundamental characteristic of an electrochemical cell that measures the cell's ability to drive an electric current through an external circuit. It is the difference in potential energy per unit charge between the two electrodes. The unit of measurement for cell potential is volts (V).

The cell potential is determined by the specific metals or metal ions that compose the electrodes and the concentrations of the electrolytes within the cell. The standard cell potential is measured under standard conditions, which include all soluble substances at 1 M concentration, gases at 1 atm pressure, and a temperature of 25°C (298 K).

As a galvanic cell operates and the chemical reactions proceed, the concentrations of reactants and products change, potentially altering the cell's potential. However, at equilibrium, there is no net movement of electrons, and therefore no cell potential, which will be further explained through the Nernst equation.

Nernst Equation

The Nernst equation is a mathematical expression that allows us to calculate the cell potential of an electrochemical cell under non-standard conditions. It links the standard cell potential to the actual cell potential when concentrations or pressures of the reactants and products are not at standard conditions. The equation is stated as follows:

\[ E = E^0 - \frac{RT}{nF} \ln(Q) \]
where \(E\) is the actual cell potential, \(E^0\) is the standard cell potential, \(R\) is the universal gas constant, \(T\) is the temperature in kelvin, \(n\) is the number of moles of electrons exchanged, \(F\) is the Faraday's constant, and \(Q\) is the reaction quotient, which represents the ratio of concentrations of products to reactants.

At equilibrium, the value of \(Q\) will equal the equilibrium constant, \(K\), for the cell reaction, and the cell potential (\(E\)) drops to zero, since the system is in a state where no further work can be done. This is why, at equilibrium, the Nernst equation simplifies to show that the EMF of the cell is zero.

Electromotive Force (EMF)

Electromotive force, commonly abbreviated as EMF, refers to the voltage generated by an electrochemical cell when no current is flowing; it is the maximum potential difference between two electrodes. The EMF is essentially the 'driving force' behind the movement of electrons from one electrode to another when an external circuit is connected.

It's important to note that EMF is not a force but rather a potential energy difference—a kind of 'pressure' that pushes electrons through the circuit. The value of the EMF depends on the specific chemical reactions occurring at the electrodes and can be influenced by temperature, pressure, and the concentration of reactants.

However, when the electrochemical cell reaches equilibrium and the electrical current stops flowing, the EMF is no longer present. In this case, as noted from the Nernst equation, the cell potential is zero, indicating that the chemical reactions have reached a point where they do not proceed spontaneously in either direction to create an electrical current.