Page 316 - MODERN ELECTROCHEMISTRY

252 CHAPTER 3

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In this expression, is the concentration of the solute in mole fraction units, and
is its chemical potential in the standard state, i.e., when assumes a standard or
normalized value of unity

when

Since the solute particles in a solution of a nonelectrolyte are uncharged, they do
not engage in long-range Coulombic interactions. The short-range interactions arising
from dipole–dipole or dispersion forces become significant only when the mean
distance between the solute particles is small, i.e., when the concentration of the solute
is high. Thus, one can to a good approximation say that there are no interactions
between solute particles in dilute nonelectrolyte solutions. Hence, if Eq. (3.52) for the
chemical potential of a solute in a nonelectrolyte solution (with noninteracting parti-
cles) is used for the chemical potential of an ionic species i in an electrolytic solution,
then it is tantamount to ignoring the long-range Coulombic interactions between ions.
In an actual electrolytic solution, however, ion–ion interactions operate whether one
ignores them or not. It is obvious therefore that measurements of the chemical potential
of an ionic species—or, rather, measurements of any property that depends on the
chemical potential—would reveal the error in Eq. (3.52), which is blind to ion–ion
interactions. In other words, experiments show that even in dilute solutions,

In this context, a frankly empirical approach was adopted by earlier workers not
yet blessed by Debye and Hückel’s light. Solutions that obeyed Eq. (3.52) were
characterized as ideal solutions since this equation applies to systems of noninteracting
solute particles, i.e., ideal particles. Electrolytic solutions that do not obey the equation
were said to be nonideal. In order to use an equation of the form of Eq. (3.52) to treat
nonideal electrolytic solutions, an empirical correction factor was introduced by
Lewis as a modifier of the concentration term 6

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The value of in the case of an electrolyte derives from the number of moles of ions of species i actually
present in solution. This number need not be equal to the number of moles of i expected of dissolved
electrolyte; if, for instance, the electrolyte is a potential one, then only a fraction of the electrolyte may
react with the solvent to form ions, i.e., the electrolyte may be incompletely dissociated.
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The standard chemical potential has the same significance here as in Eq. (3.52) for ideal solutions. Thus,
can be defined either as the chemical potential of an ideal solution in its standard state of or as
the chemical potential of a solution in its state of and No real solution can have
when so the standard state pertains to the same hypothetical solution as the standard state of
an ideal solution.