Editing Nernst equation (section)

===General form with chemical activities===

When an oxidized species ({{Math|Ox}}) accepts a number ''z'' of electrons ({{e-}}) to be  converted in its reduced form ({{Math|Red}}), the half-reaction is expressed as: 

: <chem>Ox + ze-  ->  Red</chem>

The [[reaction quotient]] (''{{Math|Q<sub>r</sub>}}''), also often called the ion activity product (''IAP''), is the ratio between the [[chemical activity|chemical activities]] (''a'') of the reduced form (the [[reductant]], {{Math|a<sub>Red</sub>}}) and the oxidized form (the [[oxidant]], {{Math|a<sub>Ox</sub>}}). The chemical activity of a dissolved species corresponds to its true thermodynamic concentration taking into account the electrical interactions between all ions present in solution at elevated concentrations. For a given dissolved species, its chemical activity (a) is the product of its [[activity coefficient]] (γ) by its [[Molar concentration|molar]] (mol/L solution), or [[Molality|molal]] (mol/kg water), [[concentration]] (C): a = γ C. So, if the concentration (''C'', also denoted here below with square brackets [ ]) of all the dissolved species of interest are sufficiently low and that their [[activity coefficient]]s are close to unity, their chemical activities can be approximated by their [[concentration]]s as commonly done when simplifying, or idealizing, a reaction for didactic purposes: 

: <math>Q_r = \frac{a_\text{Red}}{a_\text{Ox}} = \frac{[\operatorname{Red}]}{[\operatorname{Ox}]}</math>

At [[chemical equilibrium]], the ratio ''{{Math|Q<sub>r</sub>}}'' of the activity of the reaction product (''a''<sub>Red</sub>) by the reagent activity (''a''<sub>Ox</sub>) is equal to the [[equilibrium constant]] ''{{Math|K}}'' of the half-reaction: 

: <math>K = \frac{a_\text{Red}}{a_\text{Ox}}</math>

The standard thermodynamics also says that the actual [[Gibbs free energy]] {{math|Δ''G''}} is related to the free energy change under [[standard state]] {{math|Δ''G''{{su|p=<s>o</s>}}}} by the relationship:
<math display="block">\Delta G = \Delta G^{\ominus} + RT\ln Q_r</math>
where {{math|''Q''<sub>r</sub>}} is the [[reaction quotient]] and R is the [[gas constant|universal ideal gas constant]].
The cell potential {{mvar|E}} associated with the electrochemical reaction is defined as the decrease in Gibbs free energy per coulomb of charge transferred, which leads to the relationship <math display="block">\Delta G = -zFE.</math> The constant {{mvar|F}} (the [[Faraday constant]]) is a unit conversion factor {{math|1=''F'' = ''N''<sub>A</sub>''q''}}, where {{math|''N''<sub>A</sub>}} is the [[Avogadro constant]] and {{mvar|q}} is the fundamental [[electron]] charge. This immediately leads to the Nernst equation, which for an electrochemical half-cell is
<math display="block">E_\text{red} = E^\ominus_\text{red} - \frac{RT}{zF} \ln Q_r=E^\ominus_\text{red} - \frac{RT}{zF} \ln\frac{a_\text{Red}}{a_\text{Ox}}.</math>
For a complete electrochemical reaction (full cell), the equation can be written as
<math display="block">E_\text{cell} = E^\ominus_\text{cell} - \frac{RT}{zF} \ln Q_r</math>

where:
* {{math|''E''<sub>red</sub>}} is the half-cell [[reduction potential]] at the temperature of interest,
* {{math|''E''{{su|p=<s>o</s>|b=red}}}} is the [[standard electrode potential|''standard'' half-cell reduction potential]],
* {{math|''E''<sub>cell</sub>}} is the cell potential ([[electromotive force]]) at the temperature of interest,
* {{math|''E''{{su|p=<s>o</s>|b=cell}}}} is the [[standard cell potential]] in volts,
* {{mvar|R}} is the [[gas constant|universal ideal gas constant]]: {{math|1=''R'' = {{val|8.31446261815324|u=J K<sup>−1</sup> mol<sup>−1</sup>}}}},
* {{mvar|T}} is the temperature in [[kelvin]]s<!-- pluralized – see Kelvin#Usage conventions -->,
* {{mvar|z}} is the number of [[electron]]s transferred in the cell reaction or [[half-reaction]],
* {{mvar|F}} is Faraday's constant, the magnitude of charge (in [[coulomb]]s) per [[mole (unit)|mole]] of electrons: {{math|1=''F'' = {{val|96485.3321233100184|u=C mol<sup>−1</sup>}}}},
* {{math|''Q''<sub>r</sub>}} is the reaction quotient of the cell reaction, and,
* {{mvar|a}} is the chemical [[activity (chemistry)|activity]] for the relevant species, where {{math|''a''<sub>Red</sub>}} is the activity of the reduced form and {{math|''a''<sub>Ox</sub>}} is the activity of the oxidized form.