Page 142 - Mechanism and Theory in Organic Chemistry

Strengths of Weak Br~lnsted Bases 131

etc.), A to the free base form, S to some base present in the solvent (H,O mole-
cules or HS04- ions), and SH+ to the conjugate acids of these species (H30+,
H2S04). Note that the nature of S and SH+ is not well defined, since in mixed
solvents each consists of more than one species; however, the proton-donating
ability of SH+ and the proton-accepting ability of S, whatever they may be,
together determine the effectiveness of the particular solvent mixture in pro-
tonating the base A, and so are characteristic of that solvent mixture. It is this
"protonation effectiveness" that Hammett and Deyrup first set out to measure.
The next step is to choose a series of bases, A,, A,, A,. . ., A,, . . ., each
weaker than the previous one. We also require that these substances absorb light
in the visible or ultraviolet region, and that the absorption spectra of the free
bases differ from the spectra of their respective conjugate acids. The reason for
this latter requirement is that we must have some means of determining the
concentrations [A] and [AH+] for each of the base-conjugate acid pairs; the
visible-ultraviolet spectrophotometric method is convenient and is the one that
has been employed most frequently, although there are other methods. Hammett
and Deyrup picked as their series of bases various substituted anilines with in-
creasing numbers of electron-withdrawing substituents to provide successively
weaker bases. It is essential to the method that the first base, A,, be sufficiently
strong that the acid dissociation constant of its conjugate acid can be determined
in pure water. In dilute aqueous solution, SH+ in Equation 3.28 is H,O+, S is
H,O, and the activity coefficients approach unity, so the problem reduces to the
relatively straightforward one discussed in Section 3.1. We next go to a solvent
containing a small amount of sulfuric acid, for example 10 percent of H,SO,, in
which the base A, will still give appreciable concentrations of both the conjugate
acid and conjugate base forms, and that will also allow measurements to be made
on the weaker base A,, which is too weak to give measurable amounts of A,H+
in pure water.
We may now write two equations of the type 3.30 describing the behavior
of our two bases in the new solvent :

Note that KaAIH+ is known from the measurements in dilute water solution; we
have defined the quantities in the equations in such a way that the K,'s are truly
constants (at constant temperature and pressure), and all nonideal behavior
resulting from changing the solvent is incorporated into the activities. Further-
more, the concentrations [A,], [A,H +], [A,], [A,H +] are directly measurable
spectrophotometrically. If we divide Equation 3.31 by Equation 3.32, we obtain
Equation 3.33 :

In Equation 3.33 all quantities are known or measurable except KaAz,+ and the
ratio involving activity coefficients.