Again, as expected, the equivalent conductance changes with concentra-
tion. However, it was noted by early investigators that for dilute (less than
about 0.1 normal) solutions,varied with the square root of the concentra-
tion, and the y-intercept of the straight line ofversus N was a value of
that was characteristic of the ionic solute. This characteristic, infinitely diluted
value is given the symbol 0. Various values of 0 are listed in Table 8.4.
Mathematically, the relationship between the equivalent conductance versus
concentration can be expressed as
0 K N (8.66)
where Kis a proportionality constant that relates the slope of the straight line.
Equation 8.66 is called Kohlrausch’s lawafter Friedrich Kohlrausch, a German
chemist who first proposed it in the late 1800s after a detailed study of the elec-
trical properties of ionic solutions. Debye and Hückel, and later the Norwegian
chemist Lars Onsäger, derived an expression for K:
K
(60.32 0.2289 0 ) (8.67)
When combined, equations 8.66 and 8.67 are called the Onsäger equationfor
the conductance of ionic solutions.8.9 Summary
Ions play a key role in many thermodynamic systems. Because ionic solutions
can carry a current, chemical changes not considered in previous chapters
might occur spontaneously. Some of those changes are very useful, because we
can extract electrical work from those systems. Some of these changes are
spontaneous but not inherently useful. For example, corrosion is one electro-
chemical process that is by definition an undesirable process. We can undo or
reverse these undesirable processes, of course—but the second law of thermo-
dynamics says that each of those processes will be inefficient to some degree.
The laws of thermodynamics do allow us to determine how much energy we
can get from (or must put into) a process, and we have been able to define
standard electrochemical potentials to aid in those calculations.
The application of thermodynamics to electrochemical systems also helps
us understand potentials at nonstandard conditions and gives us a relationship
with the equilibrium constant and reaction quotient. However, we understand
now that concentration is not necessarily the best unit to relate to the proper-
ties of a solution. Rather, activity of ions is a better unit to use. Using Debye-
Hückel theory, we have ways of calculating the activities of ions so we can more
precisely model the behavior of nonideal solutions.8.9 Summary 237Table 8.4 Some values of 0 for ionic salts
Salt 0 (cm^2 /normalohm)
NaCl 126.45
KCl 149.86
KBr 151.9
NH 4 Cl 149.7
CaCl 2 135.84
NaNO 3 121.55
KNO 3 144.96
Ca(NO 3 ) 2 130.94
HCl 426.16
LiCl 115.03
BaCl 2 139.98