The cell potential, denoted as \(E_{cell}\) or electromotive force, represents the electrical voltage generated by a spontaneous chemical reaction within an electrochemical cell. This potential is the driving force that pushes electrons from one half of the cell to the other, creating an electrical current. Determining the cell potential allows scientists and engineers to predict the efficiency and power output of electrochemical devices, such as batteries and fuel cells.
Understanding the Cell Components
An electrochemical cell (galvanic or voltaic cell) converts chemical energy into electrical energy. It is composed of two half-cells, each containing an electrode submerged in an electrolyte solution. The system separates the oxidation and reduction processes, forcing electrons to travel through an external circuit.
The electrode where oxidation (loss of electrons) occurs is the anode, which is negative in a galvanic cell. Conversely, the electrode where reduction (gain of electrons) occurs is the cathode, the positive terminal. A salt bridge connects the two electrolyte solutions to maintain electrical neutrality by allowing ion migration. The cell potential arises from the difference in the substances’ tendencies at the anode and cathode to lose or gain electrons.
Determining Potential Under Standard Conditions
Calculating cell potential begins by defining standard conditions: \(25^circtext{C}\) (\(298 text{ K}\)), \(1 text{ M}\) concentration for all dissolved species, and \(1 text{ atm}\) pressure for any gases. Under these conditions, the cell potential is designated as \(E^circ_{cell}\). This standard potential is determined by referencing tabulated values known as Standard Reduction Potentials (\(E^circ_{red}\)).
Standard Reduction Potentials are measured against the Standard Hydrogen Electrode (SHE), which is assigned a potential of zero volts. The resulting table indicates the tendency of a species to be reduced, with higher positive values showing a greater tendency for reduction. To calculate \(E^circ_{cell}\), one must identify which half-reaction occurs at the cathode (reduction) and which occurs at the anode (oxidation).
The calculation is a simple subtraction: the standard reduction potential of the species undergoing reduction (at the cathode) minus the potential of the species undergoing oxidation (at the anode). The relationship is \(E^circ_{cell} = E^circ_{cathode} – E^circ_{anode}\). Always use the tabulated reduction potentials for both terms, avoiding the mistake of reversing the sign for the oxidation potential.
For example, in a zinc/copper cell, the copper reduction half-reaction has a higher positive potential and occurs at the cathode, while the zinc half-reaction has a lower potential and occurs at the anode. Substituting these values yields the standard potential for the entire cell. This calculated \(E^circ_{cell}\) provides the maximum theoretical voltage the cell can produce under standard \(1 text{ M}\) and \(1 text{ atm}\) conditions.
Determining Potential Under Non-Standard Conditions
Electrochemical cells rarely operate under the standard conditions of \(1 text{ M}\) concentrations and \(25^circtext{C}\). Changes in reactant and product concentrations, as well as temperature variations, significantly influence the reaction’s driving force and the measurable cell potential. As concentrations shift away from standard, the equilibrium position of the redox reaction is altered, causing the cell potential to deviate from \(E^circ_{cell}\).
To calculate the potential under non-standard conditions, the Nernst equation is employed as a correction factor. This equation links the standard cell potential to the actual cell potential based on current concentration and temperature. It explains that increasing reactant concentration or decreasing product concentration tends to increase the cell potential, driving the reaction forward.
A central component of the Nernst equation is the reaction quotient, \(Q\). This is a ratio of the actual product concentrations to the reactant concentrations, each raised to the power of their stoichiometric coefficients. The value of \(Q\) provides an instantaneous snapshot of the system’s composition, indicating how far the reaction is from equilibrium. If the reactant concentration is much higher than the products, \(Q\) is small, and the calculated cell potential will be higher than the standard potential.
The Nernst equation uses the previously calculated standard potential, \(E^circ_{cell}\), as a reference point and then modifies it based on the logarithmic term involving \(Q\) and the temperature. This allows for precise calculation of the cell potential for any given set of non-standard concentrations and temperatures. This ability to model potential changes based on concentration makes the Nernst equation an indispensable tool in electrochemistry and battery design.
Practical Measurement of Cell Potential
While theoretical calculations provide a precise value, the actual potential generated by an operating cell must be measured empirically. This measurement is accomplished using a high-impedance voltmeter or a specialized potentiometer. These instruments measure the electrical potential difference, or voltage, between the anode and the cathode.
To obtain an accurate reading, the voltmeter must be connected directly across the two electrodes, completing the electrical circuit. The positive terminal connects to the cathode, and the negative terminal connects to the anode. The measuring device must draw a negligible amount of current, as excessive current disrupts the chemical equilibrium and causes the measured voltage to drop. A high-impedance meter minimizes this disturbance, providing a reading that approximates the maximum open-circuit voltage.