Electrochemical Cell Basics
An electrochemical cell is a device that facilitates the conversion between chemical energy and electrical energy. It consists of two distinct parts, known as half-cells, each containing an electrode immersed in an electrolyte solution. These cells are designed to either produce an electric current from a chemical reaction or to drive a chemical reaction using an electric current.
Within an electrochemical cell, specific chemical processes called half-reactions occur at each electrode. The anode is the electrode where oxidation takes place, meaning that atoms or ions lose electrons during the reaction. Conversely, the cathode is the electrode where reduction occurs, with atoms or ions gaining electrons.
The movement of electrons from the anode to the cathode through an external circuit generates an electric current. This flow is driven by an inherent difference in the electron-attracting tendencies of the chemical species involved in each half-reaction. This difference in potential, often measured in volts, is what powers devices such as batteries.
Calculating Standard Cell Potential
The standard cell potential, denoted as E°cell, quantifies the voltage an electrochemical cell can generate under specific standard conditions. These conditions are defined as a temperature of 25°C (298.15 K), a concentration of 1 Molar for all dissolved species, and a partial pressure of 1 atmosphere for all gases involved. E°cell provides a baseline for a cell’s maximum potential output.
To determine E°cell, a table of standard reduction potentials (E°red) for various half-reactions is used. Each value in this table represents the tendency of a species to gain electrons under standard conditions. The half-reaction with the more positive E°red value will act as the cathode, undergoing reduction. The other half-reaction, with a less positive E°red, acts as the anode, undergoing oxidation.
Once the anode and cathode are identified, the standard cell potential is calculated using a straightforward formula: E°cell = E°cathode – E°anode. For example, consider a cell made of zinc and copper. If the standard reduction potential for Cu²⁺/Cu is +0.34 V and for Zn²⁺/Zn is -0.76 V, copper would be the cathode and zinc the anode. Therefore, E°cell = (+0.34 V) – (-0.76 V) = +1.10 V.
Calculating Cell Potential Under Non-Standard Conditions
While standard cell potential is a useful reference, electrochemical cells rarely operate under ideal standard conditions. Changes in temperature, reactant or product concentrations, or gas pressures directly influence the cell’s potential. To calculate the cell potential under these non-standard conditions, the Nernst equation is employed.
The Nernst equation is expressed as: Ecell = E°cell – (RT/nF)lnQ. Ecell is the cell potential under non-standard conditions, and E°cell is the standard cell potential. R is the ideal gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin. The variable ‘n’ denotes the number of moles of electrons transferred in the balanced redox reaction.
The Faraday constant (F) is 96,485 C/mol, representing the charge of one mole of electrons. Q, the reaction quotient, describes the relative amounts of products and reactants. It is calculated using concentrations of aqueous species and partial pressures of gases.
For a hypothetical reaction aA + bB ⇌ cC + dD, the reaction quotient Q would be ([C]c[D]d) / ([A]a[B]b), where brackets indicate molar concentrations or partial pressures. For example, if a cell reaction is Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s) and the concentrations are [Cu²⁺] = 0.1 M and [Zn²⁺] = 1.0 M at 298 K, and E°cell is +1.10 V, then Q = [Zn²⁺]/[Cu²⁺] = 1.0/0.1 = 10. With n = 2 (for two electrons transferred), the Nernst equation would be Ecell = 1.10 V – ((8.314 J/(mol·K) 298 K) / (2 mol 96485 C/mol)) ln(10).
What Cell Potential Reveals
Ecell indicates the spontaneity of an electrochemical reaction. A positive Ecell indicates that the reaction is spontaneous under the given conditions. This characterizes a galvanic (voltaic) cell, which produces electrical energy from a chemical reaction, like in a battery.
Conversely, a negative Ecell value signifies that the reaction is non-spontaneous. Such a reaction requires an external electrical energy input. This is the principle of an electrolytic cell, where electricity drives a non-spontaneous chemical change, such as electroplating or battery recharging.
When the Ecell is exactly zero, the electrochemical system has reached equilibrium. At this point, there is no net electron flow, and reaction rates are equal. A positive Ecell corresponds to a negative change in Gibbs Free Energy (ΔG), the thermodynamic criterion for spontaneity.