Page 153 - Thermodynamics of Biochemical Reactions

8.7 Equilibrium Distribution of Carbon Dioxide 151

Table 8.2 Standard Formation Properties of Species
at 298.15 K

AfHo/kJ mol-' AfGo/kJ mol-'

CO,(SP) -413.81 - 385.97
co; -(sP) - 677.14 - 527.81
HCO,(SP) -691.99 - 586.77
H,CO,(~P) - 694.91 - 606.33

Reprinted with permission from R. A. Alberty, J. Phys.
Chem., 99, 11028 (1995). Copyright 1995 American Chemi-
cal Society.

The acid dissociation constant for the species H,CO, is given by

H,CO,(sp) = H+(~o) + HCO,(sp) K(H,CO,) = K, (lK:') = 1.668 x lop4
~
(8.7-3)

where K = 4.300 x lo-'. Knowing this equilibrium constant makes it possible to
make a table of thermodynamic properties of species (Alberty, 1995b), as shown
in Table 8.2.
Thus there are four terms in the calculation of A,Go(iso) and A,H'"(iso) for
TotCO,, which is the sum of the four species. Table 8.2 make it possible to
calculate the standard transformed Gibbs energies of formation and standard
transformed enthalpies of formation of the equilibrium mixture of species of
carbon dioxide in dilute aqueous solution as a function of pH and ionic strength
by the methods discussed earlier in Section 3.4. The standard transformed Gibbs
energies of formation are given as a function of pH and ionic strength in Table 8.3.
Later this table was also calculated using equilibrium constants (Alberty,
1997). A third way to calculate this table is to use the properties of H2C0,(ao),
HCO,(ao), and COi-(ao) directly from the NBS Tables (Alberty, 199%). The
reason is that when only dilute aqueous solutions are considered, the ther-
modynamic properties of TotCO, are independent of the value of K,.
The values of A,Go(TotCO,) make it possible to calculate the apparent
Henry's law constant for carbon dioxide as a function of pH and ionic strength.
This constant is the equilibrium constant for the reaction
P(CO,, g)
TotCO,(aq) = CO,(g) + H,O K' - (8.7-4)
" - [TotCO,]
where P(CO,, g) is in bars. The H,O on the right-hand side is required to balance
oxygen atoms. As the pH is decreased, the apparent Henry's law constant
approaches the equilibrium constant for the reaction

(8.8.5)

Table 8.3 A,G"(TotCO,) in kJ mol-' in Dilute
Aqueous Solution at 298.15 K

5 - 566.19 - 565.28 - 564.67
6 - 555.56 - 554.93 - 554.55
7 - 547.39 - 541.24 -547.16
8 - 541.23 -541.23 -541.24
9 - 535.58 - 535.70 - 535.85