NOTES
1787
.:
Common Scaling of the Hammett and
(gR1
-
- aRDaH4)
d/(‘JR1CsH4
= pXi,Xz/PCsH&Xz
(5)
Taft Equations
Hence, introducing by Peter R. Wells
(Q*RiCsH4
Department of Chemistry, University of Queensland, Brisbane, Australia (Receivtsd January 4, 1966)
+ RzGXz
RiGXz
+ RzGXi
(1)
in which R1 and Rz are substituents and the reaction is represented by X1 -+ Xz. G is some linking group. (Equation 1 is simply a generalized expression for the relative reactivities correlated by the Hammett and Taft equations.) When G is the CsH4CHz group, the reaction series may be correlated by the Hammett or Taft equations so that log K1 =
(QR1
-- ‘JRz)PCHZXI,XZ =
(c*RdeH4
*X1,Xz
= PCH&,Xz(URi
(URiCaH4
-
=
- ‘JRz)/(u*RiCaH4 - a*RCsH4)
CeH4eC6H4
aR1CeH3PXiIX1 = (URi
-
-
aRzCaH4)
(6)
P*XiXz
=
PCHzXiXn
x
PX~XZ/PCIHIX~XZ
(7)
PX,XJ~~H~X,X is, simply a relay factor ( L Y C ~ H for ~ ) the C6H4 group. The only reliable data from which this can be calculated are for the saponification of XCeH4C6H4C02C2Hs in 88.7% aqueous ethanol at 40°8 (pea, = 0.589 0.01). After correction to 30°, ~ c ~= H 0.608. ~ (Note that ester saponifications are found to be isoentropic so that p ~ / p z= Tz/T1with high precision.) Using p = 2.545,Iait is found that
*
w a ~=40.608/2.545 -N 0.25 Berliner and Bloomers4have also reported pKavalues for RCaH4C02H and RCeH4C6H4C02H in 50% Butyl Cellosolve. Unfortunately, the Hammett correlations do not have high precision. However, these data give W~H, 0.3 in support of the more reliable estimate above. Aliphatic reaction parameters may now be calculated through eq. 7 on the same scale as the aromatic parameters
-
Reaction
Conditions
PCRzXlXz P*XlXZ
(a) COZHe COZ(b) COZCZES OH-
HzO at 25” 88% aq. EtOH at 30”
0.562 2 . 2 5 0.824 3 . 3
+
The assumption that p*b = 2.48 should lead to a value P*a =
2.25 X 2.48/3.3 = 1.7
which is indeed the value reported (1.72) so that this reaction series is in no way abnormal. The validity of the Taft equation and the precision of the correlations are in no way affected by these modifications. For a common scaling, however, Taft’s list of a*-values must be multiplied by a factor 2.48/ 3.3 = 0.74, i.e., reduced by ca. 25%.
(2) (3)
However, when G
(URiCeH4
-
U*RICsH4) P*Xi,X*
P
U*RZCEHI)
which is the condition for a common scaling of the u*and U-values, one obtains
It is attractive to consider that the Hammett equation provides measures of substituent inductive and resonance polar effects while the Taft equation yields measures of inductive effects alone. If this were SO, a separation of the total substituent polar effect into two components might be possible. Some progress has been made along these 1ines.l An outstanding problem for this approach is the fact that before comparisons can be made, the two sets of substituent parameters must be placed on the same scale. Taft2 attempted to achieve this, a t least approximately, by assuming the p- and p*-values for the saponification of ethyl esters (substituted benzoates and acetates, respectively) to be equal (2.48). This sets the scale for the a*-vaIues, and leads to a p*value of 1.72 for the dissociation of the substituted acetic acids in water at 25”. Clearly, had this reaction series been employed to define the u*-values, a set all 1.72 times as large would have been obtained. This arises because the corresponding p-value is by deiinition unity. Although it has been recognized that p*values “are seldom exactly the same as” the p-values,lc this assumption is implicit in the quantitative separation of inductive and resonance effects. A common scaling can, however, be achieved as follows. Consider the exchange reaction RIGXI
-
~Rz)PC~H&,XZ
(4)
(1) For references, discussion, and criticism see: (a) P. R. Wells, Chern. Rev., 63,171 (1963); (b) s. Ehrenson, Progr. Phys. Org. Chem., 2, 195 (1964); (c) C.D.Ritchie and W. F. Sager, ibid.,2, 323 (1964). (2) R. W. Taft, Jr., J . Am. Chem. SOC.,74, 2729, 3120 (1952); 75, 4231 (1953). (3) E.Berliner and L.-H; Lui, ibid., 75, 2417 (1953). (4) E. Berliner and E. A. Bloomers, ibid., 73, 2479 (1951).
Volume 69,Number 6 M a y 1966
