The Nernst Equation Effect of Concentration on Half-Cell Potential

The Nernst Equation Effect of Concentration on Half-Cell Potential (Ref 3, 6) 

One of the most significant equations derived from chemical thermodynamics permits calculation of the change in the GFE for this reaction at constant total pressure and temperature as a function of AGf of the reactant and product species in their standard states and the concentrations ofthose species with concentrations that can be varied. The equation is  

In this equation, AG°eact is the change in the GFE for the reaction as written for reactants and products in their standard states it is calculated from Eq 2.20. The a s are the activities of the species indicated by the subscripts each activity is raised to a power equal to the stoichiometric coefficient of the species as it appears in the reaction. The activity is frequently called the effective concentration of the species because it naturally arises as a function of the concentration, that is necessary to satisfy the changes in the thermodynamic functions (here, the GFE). In electrochemical systems, the activity is usually related to the molality of the species (moles per 1000 g of solvent) by the following equation  

The standard state for reactants and products in reaction 2.62 is pure solid for solid species, one atmosphere pressure for gas species, and unit activity (approximately unit molality) for ionic species. The activity is unity in each of these standard states, and if these conditions are substituted into Eq 2.63, AGreact will equal AG cact this must follow if the derivation of this equation is examined. If, under the actual conditions of the reaction, one or more species are solids, or a gas exists at one atmosphere pressure, then unit activity for each of these species is substituted in Eq 2.63, which effectively removes these activities from the log term. Also, the activity of water can usually be set equal to unity because its concentration changes insignificantly in most reactions in aqueous solution. Thus, taking M and X as solids, Eq 2.63 reduces to  

From the convention relating the cell reaction to the cell representation (Table 2.2), the cell potentials are written as  

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