18.6
The Nernst Equation
Nonstandard Reaction Conditions
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free en…
A zinc-copper galvanic cell at standard conditions has a cell potential of +1.10 V and a ΔG value of −212 kJ, indicating that it operates spontaneously. However, as the reactant’s concentration changes during the cell’s discharge, it leads to a gradual decrease of cell potential until the reaction stops completely.
Conditions like these are called nonstandard. Here, the established standard values of cell potential, Gibbs free energy, and the equilibrium constant are no longer valid.
Nonstandard conditions are prevalent in many reactions ranging from redox reactions to ion gradients in neuronal membranes. But how is an accurate cell potential determined in such systems?
If the concentration of a reactant is greater, and the concentration of a product is smaller compared to standard conditions, then Le Châtelier’s Principle is used to determine the reaction’s direction qualitatively; however, it cannot be used for quantifying the deviating cell potential.
Thus, this necessitates establishing a relationship between the cell potentials for cells under standard and nonstandard conditions. Recall that the free energy changes under standard and nonstandard conditions are related.
Substituting the equation of change in free energy with the cell potential results in a modified equation known as the Nernst equation. The Nernst equation determines how the cell potential differs from its standard value depending on the number of electrons transferred, temperature, and reaction composition.
The reaction quotient, Q, accounts for the change in free energy due to the difference in the reaction mixtures’ composition. If reactants are solid, Q is omitted.
Under standard state conditions, the value of Q is unity and the concentration of reactants and products is equal. The logarithm of one is zero, so the cell potential equals the standard cell potential.
A Q value less than one indicates a higher concentration of reactants compared to products, which shifts the equilibrium to the right, increasing the cell potential.
A Q value greater than one indicates a higher product to reactant concentration, driving the reaction to the left and lowering the cell potential.
At equilibrium, the Q value is equal to K, and the cell potential becomes zero.
The Nernst equation explains why electrochemical batteries “die” post-discharge: as the reactant concentration decreases, the cell approaches equilibrium conditions and its potential decreases to zero
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Q1: What is the Nernst equation and why is it important?
The Nernst equation determines how cell potential differs from its standard value under nonstandard conditions, accounting for changes in electron transfer, temperature, and reaction composition. It relates standard cell potential to actual cell potential using the reaction quotient Q, enabling accurate predictions of electrochemical behavior when reactant and product concentrations deviate from 1 M standard conditions.
Q2: How does the reaction quotient Q affect cell potential?
The reaction quotient Q accounts for composition changes in the reaction mixture. When Q is less than one, reactant concentration exceeds product concentration, shifting equilibrium rightward and increasing cell potential above standard value. When Q exceeds one, product concentration dominates, driving the reaction leftward and decreasing cell potential below the standard value.
Q3: Why do batteries lose potential during discharge?
As a battery discharges, reactant concentration decreases while product concentration increases, causing the reaction quotient Q to approach the equilibrium constant K. This drives the cell toward equilibrium, where Q equals K and cell potential becomes zero, explaining why batteries eventually die and can no longer drive current.
Q4: What happens to cell potential at equilibrium?
At equilibrium, the reaction quotient Q equals the equilibrium constant K, and the cell potential becomes zero. This indicates the reaction has no tendency to proceed in either direction, representing the point where the electrochemical driving force is completely dissipated and no net electron transfer occurs.
Q5: How does temperature affect the Nernst equation?
Temperature is a key variable in the Nernst equation, influencing how significantly the reaction quotient Q affects cell potential. The equation incorporates temperature in kelvin to account for thermal effects on the system's electrochemical behavior, with higher temperatures generally increasing the logarithmic term's contribution to potential changes.
Q6: When is the cell potential equal to the standard cell potential?
Under standard state conditions, the reaction quotient Q equals one because reactant and product concentrations are equal at 1 M. Since the logarithm of one is zero, the Nernst equation simplifies and cell potential equals standard cell potential, making standard electrode potentials direction spontaneous redox predictions valid.
Q7: How does Le Châtelier's Principle relate to the Nernst equation?
Le Châtelier's Principle qualitatively predicts reaction direction when concentrations deviate from standard conditions, but cannot quantify the resulting potential change. The Nernst equation provides the quantitative relationship needed, using the reaction quotient Q to calculate exact cell potential values under nonstandard conditions where Le Châtelier alone is insufficient.