Page 151 - Thermodynamics of Biochemical Reactions

8.6 Effects of Electric Potentials on Molar Properties of Ions 149

where 4% = 0. Integration at constant values of intensive variables yields

G = 1 Piznia + 1 Pionia + 4PQ (8.6-2)
The entropy of the system can be obtained by use of the following derivative:

(8.6-3)

Taking this derivative of G yields

(8.6-4)
S = 1 MiaSmia + 1 MipSrnio
where Smi is the molar entropy of i. Substituting pi = + Fz,~~ in equation 8.6-2
yields
G = 1 &,ni, + 1 &finio + ‘$a C Zinio + 4oQ (8.6-5)

Taking the derivative in equation 8.6-3 yields
S = 1 + 1 njsS;ill (8.6-6)

where Ski is the transformed molar entropy of i. Comparing this equation with
equation 8.6-4 shows that the molar entropy if a species is not affected by the
electric potential of a phase, thus Smi = Ski and S = S’.
The corresponding molar enthalpy is obtained by use of the Gibbs-Helmholtz
equation: H = - T2[(d(G/T)/dT],. Applying the Gibbs-Helmholtz equation to
equations 8.6-2 and 8.6-5 yields

H = niaffmia + C nioffmio + 4oQ (8.6- 7)
where Hmi is the molar enthalpy of i, and

H = C niaHbiz + 1 nioHdiP + F4b C zini + 4oQ (8.6-8)
where Hki is the transformed molar enthalpy. Comparing equation 8.6-7 and 8.6-8
shows that

Hmi = Hki + FZi& (8.6-9)
Thus the molar enthalpy of an ion is affected by the electric potential of the phase
in the same way as the chemical potential.
In 1974 IUPAC (Parsons, 1974) recommended that the electrochemical
potential jii be defined by

j& = pj + FZi4 (8.6-10)
where pi was referred to as the chemical potential. There are several problems
with this recommendation. The electrochemical potential is actually the chemical
potential defined by equation 8.4-6. The quantity represented by pi on the
right-hand side of equation 8.6-1 0 is the transformed chemical potential pI defined
by equation 8.5-5. According to the equations presented here, the chemical
potential for an ion should be defined by equation 8.3-8, rather than by equation
8.6- 10. Guggenheim (1 967) wrote

pi = RTIn 1; + RTln ai + FZ,~~ (8.6-11)
and pointed out that 1: is independent of the electric potential of a phase. Thus
his equation is the same as equation 8.3-8 with a different symbol for the constant
term. Physicists consider that the chemical potential pi of an electron in a metal
includes a contribution due to the electrostatic energy of the electron and is
constant throughout the system, so their use of the chemical potential pi is the
same as that recommended here.