Page 360 - Physical Chemistry

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The programs MINTEQA2 (www.epa.gov/ceampubl/mmedia/minteq/index.htm; Section 11.7
see also www.lwr.kth.se/English/oursoftware/vminteq), PHREEQC (wwwbrr.cr.usgs. Temperature and Pressure Dependences
of the Equilibrium Constant
gov/projects/GWC_coupled/phreeqc), and MINEQL (www.mineql.com) are com-
putationally similar programs for calculations on natural and laboratory aqueous sys-
tems of ionic strength less than 0.5 mol/kg. Ion activity coefficients are estimated
from the Debye–Hückel formula (10.57) with a term proportional to I added, using
m
parameters fitted for each species. If these parameters are not available, the Davies
equation is used. Activity coefficients for uncharged solute species are estimated from
the formula
log g 0.11I >m°2
m
10
i
The experimentally determined activity coefficients of several uncharged solutes in
aqueous solution have been found to fit the equation log g b (I /m°), where b i
m
i
10 i
differs for different species. For several species in water at 25°C, b is roughly 0.1.
i
PHREEQC can also use the Pitzer method for activity coefficients.
The program EQS4WIN (www.mathtrek.com) solves multiple-equilibria prob-
lems that can involve several phases but no activity or fugacity coefficients are used,
the phases being assumed to be ideal. A free demonstration version is available.
ChemSage [www.esm-software.com/chemsage/; G. Eriksson and K. Hack, Metal-
lurg. Trans. B, 21B, 1013 (1990)] is a general-purpose DOS program that does nonideal
chemical equilibrium calculations in multiphase systems at temperatures up to 6000 K
and pressures to 1 Mbar. For nonideal gases, fugacity coefficients are found using the
virial equation. For aqueous electrolyte solutions, the Pitzer equations are used. For
nonelectrolyte solutions, the user can choose from several models for estimating activ-
ity coefficients. FactSage (www.factsage.com) is a Windows successor to ChemSage.
HSC Chemistry (www.esm-software.com/hsc/ and www.hsc-chemistry.net) is a
Windows program for multiphase chemical equilibrium calculations. Gases are as-
sumed ideal and the user must specify activity coefficients for species in solution.
The programs Equilib-Web (www.crct.polymtl.ca/equiweb.html) and Aqualib-
Web (www.crct.polymtl.ca/aquaweb.html) do online calculations for ideal-gas sys-
tems or ideally dilute aqueous solutions and are limited to systems with no more than
three reactants and five elements.

11.7 TEMPERATURE AND PRESSURE DEPENDENCES
OF THE EQUILIBRIUM CONSTANT

From G° RT ln K° [Eq. (11.4)], we have
ln K° ¢G°>RT (11.31)
where G° n m° is the standard change in Gibbs energy (all species in their stan-
i
i
i
dard states). For gases and for pure liquids and solids, we chose a fixed-pressure stan-
dard state (P° 1 bar), so here G° and hence K° are independent of pressure and
depend only on T. For liquid and solid solutions, we chose a variable-pressure stan-
dard state, with standard-state pressure equal to the actual pressure of the solution, so
here G° and K° are functions of both T and P.
Differentiation of (11.31) with respect to T gives

0 ln K° ¢G° 10¢G°>0T 2 P ¢G° ¢S° ¢G° T ¢S°
a b
0T P RT 2 RT RT 2 RT RT 2
0 ln K° ¢H°
a b (11.32)*
0T P RT 2