# Nernst Equation

The standard electrochemical potential defines the voltage between a redox reaction under standard conditions (1 molar for aqueous solutions, 1 atmosphere for gases). The voltage also depends on the concentration (for liquids) or pressure (for gaseous reactants) of the components in the redox reaction since the average energy of the components will be altered by changes in concentration or pressure. The voltage under conditions other than 1 M for solutions and 1 atm for gasses is given by the Nernst equation.

## Nernst Equation

$E={E}^{0}-\frac{RT}{nF}×\mathrm{ln}\left(Q\right)$

where R is the universal gas constant (8.3145 J/mol K), T is temperature, and F is Faraday’s constant ( 96,484.6 C mol-1), and n is the number of moles of electrons exchanged between the redox and oxidation reaction. Q is the reaction coefficient and for a reaction of the form

## Standard Redox

$aA+bB\to cC+dD$

is given by:

## Reaction Coefficient

$Q=\frac{{\left[D\right]}^{d}{\left[C\right]}^{c}}{{\left[A\right]}^{a}{\left[B\right]}^{b}}$

where [X] refers to the concentration or pressure of the material X (ie [D] is the concentration of the compound D in the reaction). For a solid, this corresponds to 1, which means that battery systems which have all solid components do not have a concentration dependence of their voltage.

A key implication of the Nernst equation is that the voltage of a battery is not necessarily constant, but varies as it is charged or discharged as the concentration of the components of the electrolyte changes.

The concentration dependence of the potential means that for battery systems in which the components are not all solids and change their concentration, the potential changes as the battery charges or discharges. This is shown below for a lead acid battery. However, for a battery in which all the components of the redox reactions are solids and hence do not change their concentration, their ideal battery voltage calculated from equilibrium conditions is constant.