NernstEquation

For the reaction

$$\text{rxn:}\ \ \sum\limits_{i}{{}}{{a}_{i~}}{{R}_{i~}}=~\underset{j}{\mathop \sum }\,{{b}_{j}}{{P}_{j}}$$

having reactants R_i with stoichiometric coefficients a_i and products P_j with stoichiometric coefficients b_j, the Nernst potential, E, is calculated as

$$E=~{{E}_{0}}-~\frac{RT}{zF}\text{ln}Q$$

where R is the universal gas constant, F is Faraday’s constant, z is the number [moles] of electrons transferred,

$$Q=~\frac{\mathop{\prod }_{j}{{\left[ {{P}_{j}} \right]}^{{{b}_{j}}}}}{\mathop{\prod }_{i}{{\left[ {{R}_{i}} \right]}^{{{a}_{i}}}}}$$

with [ denoting mole fraction, and

$${{E}_{0}}=~-\frac{\Delta {{G}_{\text{rxn }\!\!~\!\!\text{  }\!\!~\!\!\text{ }}}}{F}=~-\frac{\left( \Delta {{H}_{\text{rxn}}}-T\Delta {{S}_{\text{rxn}}} \right)}{F}$$

where

$$\Delta {{H}_{\text{rxn}}}~=~\underset{j}{\mathop \sum }\,{{b}_{j}}\Delta H\left( {{P}_{j}} \right)-\underset{i}{\mathop \sum }\,{{a}_{i}}\Delta H({{R}_{i}})$$
and

$$\Delta {{S}_{\text{rxn}}}~=~\underset{j}{\mathop \sum }\,{{b}_{j}}\Delta S\left( {{P}_{j}} \right)-\underset{i}{\mathop \sum }\,{{a}_{i}}\Delta S({{R}_{i}})$$
For species X,

$$\Delta H\left( X \right)=~\underset{{{T}_{0}}}{\overset{T}{\mathop \int }}\,{{C}_{p,X}}\left( T \right)dT$$
and,

$$\Delta S\left( X \right)=~\underset{{{T}_{0}}}{\overset{T}{\mathop \int }}\,\frac{{{C}_{p,X}}\left( T \right)dT}{T}$$
where T₀ and T are reference and ambient temperatures, respectively. Todd-Young polynomials for molar heat capacity are used to evaluate the and integrals, using polyToddYoung class functions polyInt and polyIntS, respectively.