in entropy. Although salt will dissolve in polar
solutions such as water, it will not dissolve in other
liquids such as oil (a nonpolar solution), because
there are interactions that stabilize the ions in a
soluble form. For example, water is very polar and
can always align itself in such a way that the more
positive hydrogen ions are pointing at the chlo-
ride ions and the more negative oxygen ions are
pointing at the sodium ions (Figure 6.7). This
realignment of the water dipoles lowers the Gibbs
energy of the system, making it possible for the chloride anions and sodium
cations to separate in a stable configuration in solution. Due to the electro-
static interactions among the ions, the solutions have nonideal properties,
as ions of opposite charge will be attracted to each other, resulting in
clusters of an ion surrounded by ions of the opposite charge. These inter-
actions were modeled by Peter Debye and Erich Hückel in 1923 in what
is now described as the Debye–Hückel theoryof ionic solutions. These inter-
actions are sometimes parameterized by the use of activity coefficients
that decrease from the ideal value of one due to nonideal behavior.
Any experimental evaluation of the thermodynamic properties of an
ion will necessarily involve consideration that the solution contains both
the ion and the accompanying cation or anion in solution. Although a
property, such as the Gibbs energy, for a pair of ions can be determined
experimentally, application of the observed results usually requires deter-
mination of the property for only one of the ions. To separate the two
contributions, the convention is adopted of using the hydrogen ion as a
standard with zero standard enthalpy and Gibbs energy at all temperatures.
The enthalpy and Gibbs energy for other ions are then defined relative
to the hydrogen ion. For example, when hydrogen chloride is dissolved
in water, hydrogen and chloride ions are formed with a change ΔGf°in
theGibbs energy of formation:
H 2 (gas) + Cl 2 (gas) ↔H+(aqueous) +Cl−(aqueous) (6.10)
ΔG°(HCl) =−131.23 kJ mol−^1
By convention, the Gibbs energy of formation for the hydrogen ion is
zero; hence the Gibbs energy for hydrogen chloride is equal to that for
the chloride alone:
ΔG°(HCl) =ΔG°f(H+) +ΔG°f(Cl−) =ΔG°f(Cl−) =−131.23 kJ mol−^1 (6.11)
since ΔG°f(H+) = 0
Knowing ΔGf°(Cl−), the Gibbs energy of formation of sodium, ΔGf°(Na+),
can be determined by dissolving sodium chloride in solution, forming Na+
1
2
1
2
CHAPTER 6 REDOX REACTIONS AND BIOENERGETICS 121
Cl
H
O
H
O
H
H
O
H
Na H
O
H
H
H O
H
Figure 6.7In water,
salt will dissolve and
the resulting Na+
and Cl−ions will be
stabilized by the
rearrangements of
the orientations of
the dipoles of the
surrounding water
molecules.
