Page 152 - Thermodynamics of Biochemical Reactions

150 Chapter 8 Phase Equilibrium in Aqueous Systems

8.7 EQUILIBRIUM DISTRIBUTION OF CARBON
DIOXIDE BETWEEN THE GAS PHASE AND
AQUEOUS SOLUTION

The distribution of carbon dioxide between the gas phase and aqueous solution
is much more complex than the distributions of H,, O,, and N, because in the
aqueous phase, carbon dioxide is distributed between CO,( as), H,CO,. HCO,,
and COi-. This equilibrium can be treated with data in the NBS Tables (1982),
even though it only provides data on CO,(g), H,CO,(ao), HCO,(ao), and
CO: -(ao). The "ao" designates undissociated molecules in water.The standard
formation properties from the NBS Tables are given in Table 8.1. The entry for
H,CO,(ao) is simply the sum of the entries for CO,(ao) and H,O(ao). The
introductory material of the NBS Tables explains that some species in aqueous
solution are listed with two or more formulas that differ only in the number of
molecules of water contained in them. These forms are referred to as being
equivalent in the sense that the thermodynamic properties of each pair are
connected by the formal chemical equation

A(aq) + nH,O(l) = A. IzH,O(aq) (8.7-1)

for which A,Ho = A,Go = A,S" = 0 by convention. Thus the arbitrary convention
is that K = 1 at each temperature for this reaction. This convention is necessary
when there is no way to distinguish between A(aq) and A.nH,O(aq) in dilute
aqueous solutions. The number M of water molecules bound cannot be determined
by equilibrium measurements because the concentration of H,O cannot be
changed (Alberty, 2002b). This convention is also used in the NBS Tables (1982)
for SO, and H,SO,, NH, and NH,OH, Fe0;- and Fe(OH):-, and so on. Thus
the entry for H,CO,(ao) in the NBS Table is simply the sum of the entries for
COJao) and H,O(ao).
Dissolved carbon dioxide is different from species like SO, and NH, in
aqueous solutions in that the hydration reaction is slow enough (t, , = 15 seconds
at pH 7 and 298 K) so that the rate constants involved can be determined and
can be used to calculate the hydrolysis equilibrium constant (Edsall, 1969) at
298.15 K in terms of species for

CO,(sp) + H20(1) = H,CO,(sp) K,, = 2.584 x lo-, (8.7-2)

The slowness of this reaction leads to a fading end point when a solution
containing bicarbonate is titrated with sodium hydroxide using methyl orange as
an indicator. The rate of liberation of CO, from carbonate buffers in the neutral
range is so slow that this reaction has to be catalyzed in our lungs by carbonic
anhydrase.

Table 8.1 Standard Formation Properties at 298.15 K
from the NBS Tables (1 982)
'
A, N'lkJ in01 A[ GO, kJ inol~

CO,(g) - 373.51 - 394.36
CO,(ao) -413.80 ~ 385.98
CO:-(ao) -617.14 - 527.8 1
HCOi (ao) - 69 1.99 - 586.77
H,CO,(ao) - 699.63 - 623.08
H,O(ao) - 285.83 -237.1 3