Page 46 - Thermodynamics of Biochemical Reactions

40 Chapter 3 Chemical Equilibrium in Aqueous Solutions

for G has three Maxwell equations.
dArG
= (-IjP. = -Ars (3.2-6)

(3.2-7)

(3.2-8)

ArS is the reaction entropy and A,V is the reaction volume. The Legendre
transforms H = U + PV and G = U + PI/ - TS lead to G = H - TS, and so
ArG = ArH - TArS (3.2-9)
The relation for the entropy of reaction ArS can be derived from equation
3.2-1 and equation 3.2-2. Equation 3.2-6 shows that
8Ar G N,
= viAfSi = A.,So - RInQ (3.2- 10)
P,< i=l
where ArSi is the entropy of formation of species i and ArSo is the standard entropy
of reaction at a specified ionic strength. Thus

(3.2-1 1)

where AfSY is the standard entropy of formation of species i. According to the third
law of thermodynamics, absolute values of molar entropies of species can be
determined, but we will be primarily concerned with the entropies of formation
that can be calculated from the temperature derivative of the Gibbs energy of
formation or from a combination of data on equilibrium constants and enthalpies
of reaction.
The enthalpy of reaction can be calculated using the Gibbs-Helmholtz
equation 2.5-18. Since A,H = A,G + TA,S (equation 3.2-9), the enthalpy of
reaction is given by
?Ar G ' ArGIT)
ArH = A,G - T __ (3.2-12)
( (7T ),= -T2 ('( 6T
Substituting A,G = C viAfGi yields
N,
ArH = C viAfHi (3.2- 13)
i= 1
where AfHi is the enthalpy of formation of species i. Since H = G + 7S, it is
evident that
AfHi = AfGi + TA,S, (3.2-14)
and
A~H; = A,G; + TAJ; (3.2-15)

where AfHO is the standard enthalpy of formation of species i.
Taking the derivative of the enthalpy of reaction with respect to temperature
yields the heat capacity of reaction at a constant pressure Arcp:
N, N.
(3.2- 1 6)
i= 1 i= 1
A, C,"(i) is the standard heat capacity of formation of species i at constant pressure
and C;,(i) is the standard molar heat capacity of species i at constant pressure.
Equation 3.2-12 can be written in the form
BlnK A,Ho
RT2
(;l)p (3.2- 17)
=