Page 139 - Mechanism and Theory in Organic Chemistry

defined by Equations 3.25 and 3.26, and has been carefully measured at various
temperatures.

2Hz0 H30+ + OH- (3.25)

It has the value 10-14.00 at 25"CeQ From Equations 3.22, 3.24, and 3.26, it is easy
to verify that the relation between K, of a substance and Ka of its conjugate acid
is Equation 3.27:
K,Kb = Kw (3.27)
es,
customary
In order to avoid proliferation of ta w to report only one constant
is
1
for each conjugate acid-conjugate base pair. The reader may easily verify th-1
acid A is a stronger - giid-Mrl B. the conjugate base of A will be a weaker
----
base than t w n
The Leveling Effect
We are now in a position to consider the experimental problems involved in
measuring equilibrium constants for acids of differing strengths. One may use
any of a number of methods of determining the concentrations of the various
species involved in the reaction; the most common procedure for aqueous solu-
tions is to use the glass electrode, which allows a convenient and accurate deter-
mination of hydrogen ion activity over a wide range.1° Other possibilities include
spectrophotometric determinations of acid and conjugate base, and conducti-
metric measurement of ion concentrations.
It generally happens that the range of acidity that can be determined in a
given solvent is limited by the acid-lase reactions of the solvent itself. Consider,
for example, the hypothetical situation of two acids, HA, and HA,, with dis-
sociation constants of lo+, and respectively,(pKa = - 2 and - 3, respec-
tively) .ll If we add enough of each of these acids to water to give solutions 0.1 M
in total acid, the solutions will be respectively 0.09990 M and 0.09999 M in
hydrogen ion, a difference of only 0.0004 pH unit. This difference is too small to
measure; the most one can say is that both substances, being stronger acids than
H,O +, behave as strong acids in water, and are essentially completely dissociated.
Note that, if the two acids are again separated by one pK unit, but this time have
dissociation constants of 1 0-4 and 1 0-5 (pKa = + 4 and + 5), the pH of the two
solutions will differ by an easily measurable 0.5 unit. Similar difficulties arise
with very weak acids; in this case the amount of H30 + produced by dissociation
of the acid is less than the amount present by virtue of the ionization of water
itself (Equation 3.25) and so cannot be determined. As a rough rule we can state
that in water solution i t m e to m easure strengths only of tllx a_cids tzt
-__
_-
are stronger tlian ..- watey -- _and weak~ than-hydronium ion; by the same token,
--
-.
H. S. Harned and R. A. Robinson, Trans. Faraday Soc., 36, 973 (1940).
lo See, for example, H. H. Willard, L. L. Merritt, Jr., and J. A. Dean, Instrumental Methods of Analysis,
4th ed., Van Nostrand Reinhold, New York, 1965, p. 589.
l1 pK, is defined by the equation:
pK, = -log K,
A pK difference of one unit thus corresponds to a factor of ten difference in K,.