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The Nernst equation relates the reduction potential of a half-cell (or the total voltage of an electrochemical cell) to the standard electrode potential, temperature, and the activities (often approximated by concentrations) of the chemical species undergoing redox. The equation is [latex]E = E^{\circ} – \frac{RT}{nF} \ln Q[/latex], where Q is the reaction quotient.
The Nernst equation is a cornerstone of electrochemistry, providing a quantitative link between thermodynamics and cell potential. In the formula [latex]E = E^{\circ} – \frac{RT}{nF} \ln Q[/latex], [latex]E[/latex] is the cell potential under specific conditions, and [latex]E^{\circ}[/latex] is the standard cell potential, measured when all species are at unit activity. [latex]R[/latex] is the universal gas constant, [latex]T[/latex] is the absolute temperature, [latex]n[/latex] is the number of moles of electrons transferred, and [latex]F[/latex] is the Faraday constant.
The term [latex]Q[/latex], the reaction quotient, uses non-equilibrium concentrations. For a generic reaction [latex]aA + bB \rightleftharpoons cC + dD[/latex], [latex]Q = \frac{\{C\}^c \{D\}^d}{\{A\}^a \{B\}^b}[/latex], where {X} denotes activity. This equation shows that cell potential decreases as the reaction proceeds towards equilibrium (Q increases). At equilibrium, [latex]Q = K[/latex] (the equilibrium constant) and [latex]E = 0[/latex], meaning the battery is ‘dead’. The equation is crucial for understanding how concentration changes affect battery voltage and the potential across biological membranes, such as in neurons, where ion concentration gradients create membrane potentials essential for nerve signaling.
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