RELATIVE STRENGTHS OF m- AND o-SUBSTITUTED BENZOIC ACIDS IN TOLUENE
469
1
2
(
see Table 1) and even in the gas phase. This must be due
Plots of the left-hand side of equation (11) vs log [HA] were
found to be linear for all the acids selected. LogkϪ1
(intercept) and f (slope) obtained by the least-squares
to the stabilization of the conjugate base, the salicylate
anion by the same strong intramolecular hydrogen bonding
involving the phenolic hydrogen and the carboxylate anion
in all the three media. Thus, the overall effect of an o-
substituent on proton transfer from the —COOH group in a
benzoic acid molecule is contributed to by field-inductive,
resonance, steric, cheltion (in both the undissociated acid
and its conjugate base), solvation and possibly other less
significant factors.
method and logk and r calculated using equations (9) and
1
(10), respectively, are given in Table 1.
The strength of an acid in an apolar aprotic solvent as
determined in terms of its association constant (K) with a
dye carbinol (when the n values do not differ widely) is thus
due to the interplay of at least four parameters, k , k , f
1
Ϫ1
and r.
Kinetic results
Individual acid exponents (f, r)
The toluene-phase reaction between a substituted benzoic
acid (HA) and the carbinol base (D) of Crystal Violet
The acid exponent f for the forward step can be interpreted
as the mean aggregation number of HA species, HA,
[
equation (2)] under the conditions employed, CHA ӷC (see
D
H(A · · · HA), H[A · · · (HA) ], etc., reacting with the dye
2
Experimental), follows first-order kinetics:
carbinol in the forward step, the acid reacting effectively as
an f-mer, (HA) . The f values, as expected, are generally
f
greater than unity and non-integral (see Table 1). Further,
the magnitude of f (1·4–2·2) shows an upward trend with
increase in the strength of HA.
The acid exponent r for the reverse step is much smaller
(0·3–0·9) (see Table 1) and can be interpreted as the number
2
·303
Xe
k=
log
(6)
ͩ
ͪ
Ϫ
t
X ϪXt
e
where k is the rate constant and X and Xt are the
e
+
absorbances of the ion associate (DH A ) at equilibrium
and at time t. The rate constant (k), however, depends upon
CHA , the total acid concentration. In an apolar aprotic
solvent, a carboxylic acid (HA) exists as an equilibrium
mixture of the monomer acid, HA, and the stronger
homoconjugate acid–acid anion complex acids,
H(A · · · HA), H[A · · · (HA) ], etc., the proportion of the
latter increasing with increase in CHA . Thus, the overall
proton-donating power of a carboxylic acid solution in such
solvents increases with increase in CHA . On the assumption
that both the forward and reverse steps of the equilibrium
of HA molecules released from the f-mer, (HA) , after the
f
equilibrium of its reaction with the dye carbinol has been
attained. The degree of homoconjugation in the ion
+
Ϫ
associate DH [A · · · (HA)nϪ1 ] (where n is the overall
+
Ϫ
acid exponent) symbolized as DH A would depend on the
Ϫ
+
relative affinity of the base A between the acids DH and
1
2
HA and differ from f. In fact, when HA is considerably
+
stronger than DH (the conjugate acid of the dye carbinol),
5–7, 11
n could exceed f and r and may even become negative.
Individual rate constants (k , k
)
Ϫ1
1
[
equation (2)] are influenced by the acid, equation (2) can be
As can be seen from Table 1, the magnitude for the rate
expressed as
constant of the forward step, k , is much greater than the
+
Ϫ
1
*
D+fHA)DH A +rHA
(7)
rate constant for the reverse step, kϪ1 , and both the
parameters vary considerably over the set of acids. How-
+
Ϫ
where DH A symbolizes the coloured ion associate
irrespective of the number of HA molecules associated with
a D molecule and f and r are the individual acid exponents
for the forward and reverse steps of the equilibrium,
respectively. If k and k represent the rate constants for the
ever, compared with kϪ1 , k for an acid is significantly more
1
sensitive to the strength of the acid. Further, the magnitudes
of k and f and also those of k and r follow a similar trend
1
Ϫ1
(
see Table 1), pointing to the catalytic role of the acid in
both the forward and reverse steps of the equilibrium
equation (2)].
1
Ϫ1
forward and reverse steps, respectively, it follows that
[
f
r
k=k [HA] +kϪ1[HA]
(8)
(9)
1
Log k scale of toluene-phase acidities
1
k1
K=
kϪ1
An acidity scale in terms of logk would be meaningful only
1
if the acids do not have significantly different f values. This
scale would be of greater intrinsic value than that in terms
of logK as the latter depends on the interplay of at least four
parameters (k , k , f and r) as against two (k and f) for the
former. The variation observed in f over the different acids
is ±0·42. However, it seems justifiable to infer that
neglecting the variation would not invalidate the general
n=fϪr
(10)
Algebraic manipulations of equations (8), (9) and (10)
lead to the relationship
1
Ϫ1
1
k
log
=f log [HA]+logkϪ1
(11)
ͩ
Ϫn
ͪ
conclusions reached on the basis of the logk
1
scale of
K+[HA]
acidities. As can be seen from Table 1, the logk acidity
1
©
1997 by John Wiley & Sons, Ltd.
JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, VOL. 10, 466–471 (1997)