The standard potentials in table 7.1 can be converted to standard free energies using Eq. 7.8 . What
if we are interested in the potentials at non-standard concentrations? We start with the relation
between standard Gibbs free energy and molar Gibbs free energy
The standard potentials in table 7.1 can be converted to standard free energies using Eq. 7.8 . What if we are interested in the potentials at non-standard concentrations? We start with the relation between standard Gibbs free energy and molar Gibbs free energy
Substituting Eq. 7.7 for ∆_r G_m and 7.8 for∆_r G^° :
Simplifying, we obtain the Nernst equation :
The reaction quotient is as defined previously ( Eq. 4.16 ). At 25°C, we can make use of the identity
that ln Q= In 10 log10 Q= 2.303 log10 Q , and substitute 298 K for T , to get the
useful rule of thumb:
The Nernst equation can be used to calculate the potential for any concentrations of reactants and
products in a cell. At equilibrium, ∆_r G=0 and therefore ε =0 , so the left hand side of
Eq. 7.11 is zero and we can substitute K for Q. Thus, the standard potential gives the equilibrium
constant for the reaction in the cell:
The standard potentials in table 7.1 can be converted to standard free energies using Eq. 7.8 . What if we are interested in the potentials at non-standard concentrations? We start with the relation between standard Gibbs free energy and molar Gibbs free energyThe standard potentials in table 7.1 can be converted to standard free energies using Eq. 7.8 . What if we are interested in the potentials at non-standard concentrations? We start with the relation between standard Gibbs free energy and molar Gibbs free energySubstituting Eq. 7.7 for ∆_r G_m and 7.8 for∆_r G^° :Simplifying, we obtain the Nernst equation :The reaction quotient is as defined previously ( Eq. 4.16 ). At 25°C, we can make use of the identitythat ln Q= In 10 log10 Q= 2.303 log10 Q , and substitute 298 K for T , to get theuseful rule of thumb:The Nernst equation can be used to calculate the potential for any concentrations of reactants andproducts in a cell. At equilibrium, ∆_r G=0 and therefore ε =0 , so the left hand side ofEq. 7.11 is zero and we can substitute K for Q. Thus, the standard potential gives the equilibriumconstant for the reaction in the cell:
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