Page 337 - Physical Chemistry

lev38627_ch10.qxd 3/14/08 1:07 PM Page 318

318
Chapter 10 experimental activity coefficient data, so the values of these parameters implicitly
Nonideal Solutions incorporate the effects of ion pairing. Some workers have used the Pitzer equations
together with explicit allowance for ion pairing to obtain better results than given by
the Pitzer equations with ion pairing ignored [see Pitzer (1991), pp. 294, 306, 307].
When this is done, the Pitzer parameters are modified from their usual values.
The Pitzer and Meissner equations do not explicitly consider ion pairing and so
one calculates I in these equations by assuming each strong electrolyte is present
m
solely as ions, and these equations are designed to yield the experimentally observed
†
activity coefficient g .
A review of ion pairing concluded that “ion pairs can be treated as real species in
the solution” and that “when at least one of the ion partners has a charge larger than
1, ion pairing can be a reality in most solvents” [Y. Marcus and G. Hefter, Chem. Rev.,
106, 4585 (2006)].

10.9 STANDARD-STATE THERMODYNAMIC PROPERTIES
OF SOLUTION COMPONENTS
To deal with chemical equilibrium in solution, we want to tabulate standard-state ther-
modynamic properties of substances in solution. How are such properties determined?

Nonelectrolyte Solutions
For nonelectrolyte solutions where Convention I is used, the standard states are the
pure substances, and we know how to determine standard-state properties of pure sub-
stances (see Chapter 5).
For solid and gaseous solutes, the molality scale is most commonly used. The
standard Gibbs energy of formation and standard enthalpy of formation of substance
i in solution at temperature T are defined by
¢ G°1i, sln2 m° 1T, P°2 G° 1T2 (10.78)
f
elem
m,i
T

¢ H°1i, sln2 H° 1T, P°2 H° 1T2 (10.79)
m,i
T
f
elem

where i, sln indicates substance i in solution in some particular solvent, m° and H° m,i
m,i
are the molality-scale standard-state partial molar Gibbs energy and enthalpy of i in
solution, and G° elem and H° elem are the standard-state Gibbs energy and enthalpy of the
pure, separated elements needed to form 1 mole of i. One way to determine standard-
state molality-scale thermodynamic properties is from solubility data—the fact that m i
in a saturated solution equals m* enables us to relate properties in solution to pure-
i
substance properties. The following example shows how this is done.
EXAMPLE 10.4 Standard-state properties of a solute
The molality of a saturated solution of sucrose in water at 25°C and 1 bar is
6.05 mol/kg. Vapor-pressure measurements and the Gibbs–Duhem equation give
g (C H O ) 2.87 in the saturated solution. For pure sucrose at 25°C, G°
f
11
12
22
m
1544 kJ/mol, H° 2221 kJ/mol, and S° 360 J/(mol K). At 25°C and
m
f
1 bar, the differential heat of solution of sucrose in water at infinite dilution is

5.9 kJ/mol. Find G° , H° , and S° 298 for C H O (aq).
11
22
12
298
f
f
298
Using the phase-equilibrium condition of equality of chemical potentials, we
equate m of pure sucrose to m of sucrose in the saturated solution. m of sucrose in
solution is given by m m° RT ln (g m /m°) [Eq. (10.28)], and we have
i
i
m,i
m,i
G* 1T, P°2 m° 1T, P°2 RT ln 1g m,i,sat m i,sat >m°2 (10.80)
m,i
m,i