Thermodynamic Quantities for the Ionization Reactions of Buffers

234 GOLDBERG, KISHORE, AND LENNEN
absence of experimental values for these activity coefficients,
we have used the extended Debye–Hückel equation
ln iA mz i 2 I 1/2 /1BI 1/2 13
to estimate the needed values of the activity coefficients and
then the ratio m in Eq. 4. Here A m is the Debye–Hückel
constant, 16 z i is the charge number of the species, and B is an
empirical constant sometimes referred to as an ‘‘ion size’’
parameter which we have taken to equal 1.6 kg 1/2 mol 1/2 .
This value has been selected following prior usage of this
value in the treatment of biochemical reactions 17,18 and earlier
usage by Vasil’ev 19 and Vanderzee and Dawson. 20 Based
upon the activity coefficient model, Eq. 13, the Debye–
Hückel expressions for the excess enthalpy H i ex and heat capacity
C i ex of species i are
H i ex RT 2 Am /T pz i 2 I 1/2 /1BI 1/2 . 14
C i ex RT 2 2 Am /T 2 pz i 2 I 1/2 /1BI 1/2
2RTA m /T pz i 2 I 1/2 /1BI 1/2 . 15
Analogously, we have used these expressions to adjust values
of enthalpy and heat-capacity changes determined at finite
ionic strengths to I0. The parameter B has also been
maintained at the same constant value of 1.6 kg 1/2 mol 1/2 .It
should be noted that for charge symmetric reactions e.g., the
deprotonation reaction of amines, the model used in this
paper predicts corrections of zero for the adjustment of pK,
rH°, and rC p values to I0. In the light of existing data
e.g., the study of Cox et al. 21 on the ionization reactions of
alkyl ammonium ions it is clear that the above equations are
approximations. Thus, additional terms can and have been
added to Eqs. 13–15 or to similar type equations. 22,23
These terms serve to extend the model to higher molalities
and ionic strengths by accounting for specific interactions.
However, due to a general lack of the needed interaction
parameters for the systems and actual solutions of interest,
we have used Eqs. 13–15 and the assumed value of the
parameter B. Thus, in our evaluations, we have relied, insofar
as possible, on the results of experiments where the data
have been more rigorously adjusted to the standard state.
However, such results do not exist for several buffers and in
these situations, it is estimated that the use of the above
equations could cause errors in the standard value of the pK
of about 0.05 to 0.10. Also, if the results are adjusted
from high ionic strengths (I0.1 mol dm 3 )toI0, the errors
could be substantially larger.
A significant fraction of the buffers considered herein undergo
multiple ionizations. In such cases, it is also possible
to consider the various microscopic ionization constants that
can arise. The determination of values for these microscopic
ionization constants requires an experimental method e.g.,
nuclear magnetic resonance NMR that can distinguish the
pertinent species. In this paper, we have limited the scope to
the macroscopic ionization constants that are determined by
using the usual methods. All thermodynamic quantities given
herein pertain to the macroscopic ionization reactions.
J. Phys. Chem. Ref. Data, Vol. 31, No. 2, 2002
3. Presentation of Data
Tables 7.1–7.68 contain the following information on each
of the buffers considered in this review: 1 the chemical
names and CAS registry number; 2 the structure, empirical
formula, and molecular weight; 3 the selected values of
thermodynamic quantities pK, rG°, rH°, and rC p for
the ionization reactions at T298.15 K and for the molality
standard state see Sec. 2. The remainder of each table gives
the basis for the selected values, namely a summary of values
of thermodynamic quantities pK, rH°, and rC p from
the literature; and finally values of pK, rH°, and rC p that
have been adjusted from the reported conditions to T
298.15 K and to the standard state, which has been denoted
as ‘‘I0.’’ In constructing these tables, we have generally
recalculated the values of rH° and rC p from the pK values
which have been determined at several temperatures.
This has been done by using the model given in Eq. 12.
Values of rH° and rC p are given only when they were
statistically significant. In no case did we select values for
( rC p /T) p , although such values are generally noted.
Since the molality standard state is the preferred one in this
paper, all selected values for pK and for rG° are on this
basis. For simplicity of expression, we have used ‘‘pK’’
rather than the more exact notation ‘‘pK m’’ in these tables.
We have attempted to make our survey of the literature
essentially complete for most of the buffers considered
herein. One exception is the omission of a substantial fraction
of studies from the very early literature where the results
were often very approximate. Also, for 17 of the buffers, the
extent of the literature is sufficiently large that practical considerations
mitigated against the desire for completeness.
This has been noted in the comments section for each of
these 17 buffers. Nevertheless, in each such case we attempted
to include all studies that involved any of the following
features: the use of an electrochemical cell without a
liquid junction; results that had been extrapolated to I0;
calorimetric measurements, and pKs that had been measured
at several temperatures. Additionally, the existing evaluations
for three substances carbonate, sulfate, and sulfite appeared
to be sufficiently thorough as to make it doubtful that an
additional evaluation would provide any real improvement in
the values of the selected thermodynamic quantities.
Except for the calculation of values of rH° and rC p
from values of ionization constants reported at several temperatures
we have, for the most part, not recalculated the
values of the thermodynamic quantities reported in the various
studies cited herein. However, in some cases we have
extrapolated reported pK and rH° values to I0, recalculated
calorimetric results by using evaluated ‘‘best’’
values 24 for rH° and rC p for the ionization of water, and,
when necessary, converted values of basicity constants to
ionization constants. Such recalculations have, as a rule,
been noted in the tables. In almost all of the studies performed
by means of potentiometric titrations, only the summary
results are reported and a recalculation of the data is
not possible. However, in the studies based on electrochemi-