Solvolysis of 2-chloro-2(3,4-disubstituted) phenylpropanes: Validity of Hammett-Brown σ+ constants in assessing additive effects of substituents

Article abstract of DOI:10.1002/kin.20617

The objective of this study is to test the suitability of the extended Hammett-Brown equation, log (k_XX/k_HH) = ρ⁺∑σ⁺, in depicting satisfactorily additive effects of electronegative atom-bearing substituents, which are known to possess diverse and multicomponent influences on the side chain reactions of polysubstituted benzenes. The equation has been used to correlate, for the first time, the additive effect of substituents in the specific rates of solvolysis of 2-chloro-2-phenylpropanes (3b-3f) having 3-F,4-Me, 3-Br,4-Me, 3-I,4-Me, 3-Me,4-Me, or 3-MeO,4-Me substituents. The rates were determined titrimetrically at 288, 298, and 308 K using 90% aqueous acetone as solvent. Measured additive effects of these substituents on the solvolysis rate and activation parameters of the parent cumyl chloride (2-chloro-2-phenylpropane) are found to be well correlated using the equation given above. Plots of log (k_XX/k _HH) of 3b-3f together with mainly di-, but also tri- and mono-substituted cumyl chlorides from previous studies against ∑σ⁺ give a linear correlation coefficient of 0.990 as a measure of the validity of the equation to depict such systems. The halogen substituents' extent of conformity with additivity reflected in their relative (k_obsd/k_calcd) rate ratios is found to correlate with the steric size of substituents. Plots of rate ratios against Taft's steric factor of each halogen give a linear correlation coefficient of 0.994 for the 3-halo substituents. The 3,4-dimethyl substituents' relative rate ratio of 1.03 shows excellent additivity, whereas the 3-methoxy-4-methyl ratio of 1.43 shows the methoxy group to be far less deactivating than predicted. Similar trends were found for the free energy of activation (δG? - δG ₀?) differences, which correlated linearly with a coefficient of 0.983 with Taft's steric factor of halogen atoms.

Full text of DOI:10.1002/kin.20617

Solvolysis of 2-Chloro-2(3,4-
disubstituted)
Phenylpropanes: Validity of
Hammett–Brown σ+
Constants in Assessing
Additive Effects of
Substituents
AHMED A. TAHA
Department of Chemistry, College of Science, University of Bahrain, Sakheer, Bahrain
Received 18 October 2010; revised 2 May 2011, 17 August 2011; accepted 18 August 2011
DOI 10.1002/kin.20617
Published online 21 March 2012 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: The objective of this study is to test the suitability of the extended Hammett–Brown
equation, log (kXX/kHH) = ρ+ꢀσ+, in depicting satisfactorily additive effects of electroneg-
ative atom-bearing substituents, which are known to possess diverse and multicomponent
influences on the side chain reactions of polysubstituted benzenes. The equation has been
used to correlate, for the first time, the additive effect of substituents in the specific rates of
solvolysis of 2-chloro-2-phenylpropanes (3b–3f) having 3-F,4-Me, 3-Br,4-Me, 3-I,4-Me, 3-Me,4-
Me, or 3-MeO,4-Me substituents. The rates were determined titrimetrically at 288, 298, and
308 K using 90% aqueous acetone as solvent. Measured additive effects of these substituents
on the solvolysis rate and activation parameters of the parent cumyl chloride (2-chloro-2-
phenylpropane) are found to be well correlated using the equation given above. Plots of log
(kXX/kHH) of 3b–3f together with mainly di-, but also tri- and mono-substituted cumyl chlo-
rides from previous studies against ꢀσ+ give a linear correlation coefficient of 0.990 as a
measure of the validity of the equation to depict such systems. The halogen substituents’
extent of conformity with additivity reflected in their relative (kobsd/kcalcd) rate ratios is found
to correlate with the steric size of substituents. Plots of rate ratios against Taft’s steric factor
of each halogen give a linear correlation coefficient of 0.994 for the 3-halo substituents. The
3,4-dimethyl substituents’ relative rate ratio of 1.03 shows excellent additivity, whereas the
Correspondence to: Ahmed A. Taha; e-mail: ahmedabd@
sci.uob.bh.
c
ꢀ
2012 Wiley Periodicals, Inc.

SOLVOLYSIS OF 2-CHLORO-2(3,4-DISUBSTITUTED)PHENYLPROPANES
515
3-methoxy-4-methyl ratio of 1.43 shows the methoxy group to be far less deactivating than
predicted. Similar trends were found for the free energy of activation (ꢁG‡ – ꢁG0‡) differences,
which correlated linearly with a coefficient of 0.983 with Taft’s steric factor of halogen atoms.
ꢀ
C
2012 Wiley Periodicals, Inc. Int J Chem Kinet 44: 514–523, 2012
pected to have an enhanced resonance demand and are
better correlated with Yukawa–Tsuno equation [7]:
INTRODUCTION
The Hammett equation [1]:
log(kX/kH) = ρ(σ+rꢀσ+R
)
(3)
log(kX/kH) = ρσ
(1)
where r is a parameter characteristic of a given reaction
and describes+the resonance demand of the transition
state, and rꢀσR is a substituent constant describing
resonance capacity of the substituent and is given by
is considered to be one of the most important structure–
activity relationships in organic chemistry. The equa-
tion was successful in describing specific rate constants
of substituted (kX) and unsubstituted (kH) benzenoid
systems in relation to a dual constant (ρσ). σ is a sub-
stituent constant varying with the type of substituent
(X), whereas ρ is a constant related to the particular
type of reaction involved. By applying the Hammett
equation to the solvolyses of substituted cumyl chlo-
rides, Brown and coworkers [2] found that the equation
is obeyed when ring substituents are meta to the reac-
tion center. The equation, however, fails to describe sat-
isfactorily solvolyses of para-substituted benzylic sys-
tem in which ππdelocalization of the cationic charge
into the benzene ring takes place. To be able to de-
scribe such systems satisfactorily, Brown used solvol-
ysis rates of meta-substituted cumyl chlorides in 90%
aqueous acetone–10% water (v/v) to derive a new set
of substituent constants (σ+) known as the Hammett–
Brown equation [2]:
σ
+ − σ. Correlation analyses of several solvolytic rate
data of cumyl derivatives using both single parameter
(the Hammett–Brown equation) and dual parameter
(the Yukawa–Tsuno equation) have been made [8–11].
The Hammett–Brown scale is expected to prevail in
solvolytic systems generating ordinary and relatively
stable benzylic carbocations, whereas the Yukawa–
Tsuno scale prevails in systems having r values larger
or smaller than unity.
Extension of the Hammett equation to polysubsti-
tuted benzenes was shown to be feasible by Jaffe´ [12].
Much later, following the work of Jaffe´ [12] and the
work of others [13], Benson [14] summarized the as-
sumptions of the additivity principle. The principle pre-
dicts that the contribution of each substituent on the
benzene ring is to be constant and simply additive. The
Hammett–Brown equation hence takes the following
extended form:
log(kX/kH) = ρ+σ+
(2)
log(kXY/kHH) = ρ+ꢁσ+
(4)
where σ+ is the substituent’s (X) contribution to
the rate constant kX and its ability to stabilize the
charged carbocation intermediate. Negative values of
the substituent constant σ+ indicate rate enhancement,
whereas positive values indicate deactivation by the
substituent. The reaction constant ρ+ gives a measure
of the sensitivity of the reaction to perturbation by
factors such as those pertaining to the substituent and
the solvent; kH is the rate constant of the parent (un-
substituted) cumyl chloride (3a). The Hammett–Brown
equation proved to be useful in correlating substituents’
effects in various substituted benzenes [3–5] irrespec-
tive of the substituent position in the ring (meta or
para), the type of carbocation formed, or the solvent
used [6]. In systems where strong deactivating groups
are attached to the carbocation intermediate, such as
the CF3 group, strong departures from the Hammett–
Brown linear plots take place. Such systems are ex-
where ꢁσ+ is the sum of the contributions of all sub-
stituents present. Apart from their classical area of ap-
plication in the structure–reactivity relationship [4], the
Hammett–Brown parameters or the Hammett equation
on which they are based have recently found appli-
cations in various fields such as environmental toxi-
cology, drug metabolism [15], chromatography [16],
oxidation studies [17], mechanistic studies [18], mass
spectrometry [19] to name but a few. Some earlier stud-
ies based on the original Hammett equation found dis-
ubstitution effects of various substituted benzoic acids
to be additive [20]. Additive effects were observed in
various other systems such as polyfluorinated trypto-
phans [21] and the electrostatic potentials of substi-
tuted benzoic acids [22].
Successful treatments of the rates of reactions
of polymethylbenzenes systems were reported for
International Journal of Chemical Kinetics DOI 10.1002/kin.20617

516
TAHA
mercuration, bromination, chlorination, and protodesi-
lylation and to a lesser extent in nitration reactions [23].
On the other hand, substituents with electronegative
atoms are known to possess diverse and multicompo-
nent influences on the side chain reactions of polysub-
stituted benzenes [24] and as such present a serious
challenge to the capabilities of linear free energy re-
lationship and to the additivity principle on which it
is based. The objective of this work was thus to test
the suitability of Hammett–Brown parameters for pre-
dicting additive behavior of such type of substituents.
This work therefore undertook to investigate the behav-
ior of the electronegative atom-bearing halogeno and
methoxy substituents in disubstituted cumyl chlorides
under the same conditions used by Brown for deriving
ρ+σ+ values. A fewer studies to the author’s knowl-
edge dealt with these effects of disubstitution [4,25]
in such systems studied by Brown. The compounds
chosen to be investigated were, namely the halogeno
3-flouro-4-methyl- (3b), 3-bromo-4-methyl- (3c), and
3-iodo-4-methyl- (3d) derivatives of cumyl chloride (2-
chloro-2-phenylpropane) together with the 3-methoxy-
4-methyl- (3e) and 3,4-dimethyl- (3f) derivatives. The
latter was chosen by a way of comparison, as pre-
vious studies indicated close adherence to additiv-
ity predictions [26]. The observed rate constants of
these disubstituted cumyl chlorides are then compared
with the calculated rate constants obtained from the
modified Hammett–Brown equation (4) as a mea-
sure of the additivity of substituent effects. Activa-
tion energy (Ea) is obtained utilizing the Arrhenius
equation:
over KMnO4 and then was distilled, dried (CaSO4),
and fractionated. 3-Substituted p-toluic acids, alkyl
halides, and acetophenone were purchased and used as
received. IR spectra were recorded using a Shimadzu
IR-435 spectrophotometer on KBr windows.
Compounds 1a–1f and 2a–2f were synthesized ac-
cording to standard procedures [27] and had elemental
analysis values and spectral data consistent with their
structures (Table I).
The parent alcohol (2a) was prepared in 80% yield
by the reaction between acetone and phenylmagne-
sium bromide [28,30]. The alcohols 2b–2e (Table I)
were prepared by reacting the corresponding meta-
substituted methyl p-toluate esters (1b–1e) with 2 mo-
lar equiv of methylmagnesium bromide or iodide [29].
The esters were prepared by refluxing the correspond-
ing acids in MeOH/H+. The alcohol 2f was prepared by
reacting 4-bromomagnesium-o-xylene with acetone.
The stock solvent for rate measurements was pre-
pared by mixing pure dry acetone (9 volumes) and
boiled, redistilled water (1 volume); this was adjusted
by adding small amounts of acetone or water to give a
value of k = (12.3 0.1) × 10−5 s−1 (0.999 correla-
tion coefficient) at 298 K for 2-chloro-2-phenylpropane
(3a) [30]. After adjustment, the solvent composition
was calculated to be 90.4:9.6% (v/v) acetone to wa-
ter. The rates were measured titrametrically following
the procedure of Brown et al. [30]. All reactions were
carried out under pseudo-first-order conditions. Rates
were determined at three different temperatures for
each chloride, and the activation parameters were eval-
uated. Temperature fluctuations were less than 0.05
K for the temperature range 288–308 K and less than
0.1 K for lower temperatures. Plots of log rate con-
stants against 1/T gave a straight line with a lin-
ear correlation. The activation parameters were eval-
uated from the slopes of these lines. Data obtained
were from duplicate runs within an experimental error
of 3.3%.
Synthesis of alcohol and its chloride. The alcohols
(2) were synthesized by the Grignard reaction of
MeMgBr or MeMgI with the ester of benzoic acid
(1) according to Scheme 1. The alcohol 2f was pre-
pared by the action of 3,4-dimethylphenylmagnesium
bromide upon Me2CO. Physical data and elemental
analysis values are given in Table I. The chlorides
R1R2-C6H4·CMe2Cl (3) were prepared from the al-
cohols by saturation with HCl gas in pentane. The
m-methoxy chloride was highly unstable and was pre-
pared at –20◦C in CH2Cl2. Purification of the chlorides
was not attempted and they were used directly in rate
measurements.
k = Ae−E /RT
(5)
a
and the observed and predicted dif‡ferences in the free
energy of activation (ꢀG‡ − ꢀG0) can be obtained
from the following equation:
ꢀ
‡ꢁ
ꢀG‡ − ꢀG0 = −2.303 RT log10 k/ko (6)
EXPERIMENTAL
General Remark, Synthesis of Alcohols,
and Rate Measurement
Boiling points and melting points were uncorrected.
Starting materials and solvents were of analytical
grade. Anhydrous solvents were obtained by prior dis-
tillation over a suitable drying agent and kept over
molecular sieves (type 4). Et2O was sodium-dried
grade. Acetone (used for preparation of stock solu-
tions of substrates) was purified by refluxing it first
Solvolysis rate. Following the procedure by Brown
et al. [31], the specific rates of solvolysis of the
International Journal of Chemical Kinetics DOI 10.1002/kin.20617

SOLVOLYSIS OF 2-CHLORO-2(3,4-DISUBSTITUTED)PHENYLPROPANES
517
Table I Physical Constants, Yields (%), and Elemental Analysis of Cumyl Alcohols (2) and Their Precursor Esters (1)
Melting
Boiling Point
Analysis C, H,
and Halogen
Compound
Point (◦C)
(◦C/mmHg (Lit.))s; IR
Yield (%)
80
2a
67–68/0.2(93/11) [30]; IR (liquid film,
cm–1): 3345 ν(O H); 2975 ν(C H);
1370–1365 ν( CMe2def)
–
1b
2b
1c
–
–
–
100/10; IR (liquid film, cm–1); 2975–2950
ν(C H); 1730–1715 ν(C O); 1275,
1125 ν(C O); 1110–1000 ν(C F)
55/0.05 [27]; IR (liquid film, cm–1): 3400
ν(O H); 2975–2950 ν(C H);
75
70
70
–
Calcd for C10H13OF
(Found): C: 71.44 (71.14);
H:7.74 (7.91)
Calcd for C9H9BrO2
(Found): C: 47.19 (47.34);
H: 3.91 (4.03); Br: 34.91
(34.73)
Calcd forC10H13BrO
(Found): C: 52.24 (52.43);
H: 5.68 (5.82), Br: 34.91
(34.80)
1370–1365 ν( CMe2 def)
119/0.75(138–40/10) [28]. IR (liquid film,
cm–1): 2975–2950 ν(C H); 1730–1715
ν(C O); 1280, 1125 ν(C O)
2c
48-49
90–91/0.04; IR (liquid film, cm−1): 3400
ν(O H); 2975–2950 ν(C H);
1370–1365 ν( CMe2 def)
87
1d
2d
1e
2e
2f
–
52
200/57(194/52) [29]; IR (liquid film,
cm−1): 2975–2950 ν(C H); 1730–1715
ν(C O); 1275,1125 ν(C O)
77
87
70
78
65
–
100–102/0.065; IR (liquid film, cm−1):
3400 ν(O H); 2975–2950 ν(C H);
1370–1365 ν( CMe2 def)
Calcd for C10H13OI (Found):
C: 43.49 (43.32); H: 4.71
(4.91), I: 45.92 (45.54)
Calcd for C10H12O3 (Found):
C: 66.66 (66.51); H: 6.66
(6.80)
Calcd for C11H16O2 (Found):
C: 73.30 (72.92); H: 8.80
(8.93)
–
85/0.15(263-5) [44]
64–65
–
102/0.25
92/0.25
Calcd for C11H16O (Found):
C: 80.50 (80.12); H: 9.76
(9.82)
R3
C(Me)=CH2
CMe2Cl
CMe2OH
(i) CH3MgBra
(ii) H3O+
90% aq. acetone
HCl
(2)
+
R2
R2
R2
R2
R1
R1
(3)
R1
(1)
R1
(2)
a
R3 = CO Me (
) = MgBr (1f). Me CO for
1a–1e
1f
2
2
R1 = R2 = H (
) ; R1 = CH , R2 = F (
) ; R1 = CH , R2 = Br (
)
1c, 2c, 3c
1a, 2a, 3a
1b, 2b, 3b
3
3
R1 = CH , R2 = I (
) ; R1 = CH , R2 = OCH (
) ; R1 = CH , R2 = CH (
)
2f, 3f
1d, 2d, 3d
1e, 2e, 3e
3
3
3
3
3
Scheme 1 Synthesis and solvolysis of cumyl chlorides, R1R2·C6H4CMe2Cl (3).
International Journal of Chemical Kinetics DOI 10.1002/kin.20617

518
TAHA
Table II Observed and Calculated Rates of Solvolysis of 3,4-Disubstitued and 3,4,5-Trisubstituted
2-Chloro-2-phenylpropanes in 90% Aqueous Acetone at 298 K Together with Their ꢀσ+ Values
kXY (105 s−1
(Observed)
)
Correlation
Coefficient
kXY (105 s−1
)
(Calculated)
Substituent
Compound
ꢁσ+
da
kobsd/kcalcd
3-F, 4-Me
3b
+0.041
+0.088
+0.094
+0.048
0.143
−0.132
−0.264
−0.377
−0.437
−0.490
−0.255
7.00 0.20b
3.83c
0.999
–
0.993
0.999
–
0.05
0.09
0.12
0.16
0.33
0.04
0.08
0.05
0.04
0.05
0.03
8.04
4.88
4.62
7.47
2.75
49.3
195
635
1272.5g
–
0.87
0.79
0.72
0.68
0.44
0.96
1.43
1.028
0.990
–
3-Cl, 4-Me
3-Br, 4-Me
3-I, 4-Me
3-Cl, 4-t-Bu
3-Me, 5-Me
3-MeO, 4-Me
3-Me, 4-Me
3,4,5-Me3
3c
3d
3.36 0.03
5.09 0.05
1.22c
47.3d
–
3e
3f
278
2
0.995
–
652e
1260f
2200f
184f
3-Cl, 4-MeO
3-CN, 4-MeO
–
–
aDeviation from regression line in log kXY/kHH units.
bStandard error for two rate runs.
cFrom [25].
d From [34].
eExtrapolated from values at 268 K, kXY = 20.32 × 105 s−1; at 273 K, kXY = 35.39 × 105 s−1; and at 278 K, kXY = 67.42 × 105 s−1
.
f From [9].
gCalculated from data in [9].
Table III Rate Constants (kXY) and Derived Activation Parameters for the Solvolysis of Disubstituted
2-Chloro-2-phenylpropanes (3) in 90% Aqueous Acetone at Three Different Temperatures
Compound
T (◦K)
kobsd (105 s−1) (SD)
ꢀEa (kJ mol−1
)
ꢀH‡ (kJ mol−1
)
ꢀS‡ (J K−1 mol−1
)
3b
288
298
308
288
298
308
288
298
308
273
288
298
268
273
278
2.25 0.01 (0.14)
7.00 0.20 (0.24)
19.9 0.70 (0.12)
1.03 0.02 (0.1)
3.36 0.03 (0.04)
10.7 0.02 (0.07)
1.64 0.01 (0.02)
5.09 0.05 (0.06)
14.9 0.02 (0.08)
17.2 0.40 (0.55)
96.1 1.50 (0.25)
278 2.0 (1.6)
79.7 (r2 = 0.999)
86.3 (r2 = 1)
77.9 (r2 = 1)
−62.7
3c
3d
3e
3f
83.7 (r2 = 0.999)
79.0 (r2 = 1)
−49.2
−61.5
−49.1
−44.7
81.6 (r2 = 0.999)
75.3 (r2 = 1)
72.7 (r2 = 1)
20.3 0.4 (1.1)
35.4 0.4 (0.40)
67.4 0.2 (1.6)
74.4 (r2 = 0.997)
72.0 (r2 = 0.997)
Rates are average of duplicate runs. SD indicates standard deviation for n ≥ 8. r2 indicates correlation for the Arrhenius plot.
disubstitutedchlorides R1R2-C6H4·CMe2Clweremea-
RESULTS AND DISCUSSION
sured in 90% aqueous acetone at 288, 298, and 308 K,
Hammett–Brown Equation and Additive
Substituent Effects
and the values are given in Tables II and III. These mea-
sured rate constants gave excellent first-order behavior,
as shown by the constancy of the rate coeffi-
cient throughout the course of a single run. Cor-
relation coefficients were determined using an Ex-
cel least-square best-fitted line package and were
in the range 0.993–0.999 for the whole series of
substituents.
Brown [2] chose to define the new substituent con-
stant σ+ using solvolysis of cumyl chlorides in 90%
aqueous acetone at 298 K as a model of electron-
deficient systems. The values of Hammett–Brown σ+
constants [32] and Taft’s Es constants [33] for various
substituents are given in Table IV.
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SOLVOLYSIS OF 2-CHLORO-2(3,4-DISUBSTITUTED)PHENYLPROPANES
519
Table IV Values of Hammett–Brown σ+ Constants [32] and Taft’s Es Constants [33] for Various Substituents
Substituent
4-Me
3-Me
3-F
3-Cl
3-Br
3-I
3-OMe
σ+
−0.311
−1.24
−0.066
+0.352
−0.46
+0.399
−0.97
+0.405
−1.16
+0.359
−1.40
+0.047
E
s
–
–
Figure 1 Plot of log kXY/kHH rate constants for the solvolysis in 90% aqueous acetone at 298 K of 2-chloro-2(3-
halo-4-methyl)phenylpropanes (3b–3d), 2-chloro-2(3-methoxy-4-methyl) phenylpropane (3e), and 2-chloro-2(3-methyl-4-
methyl)phenyl propane (3f) against ꢁσ+ constants [32]. In the figure, letters in superscripts indicate references: a[34], b[25],
c[30], d[31], and e[9]. ∗For monosubstituents, X = H, Y = 3-F,3-Me or 3-MeO, and ꢁσ+ = 0+σ+ for Ysubstituent.
Using Hammett–Brown σ+ constants and taking
2.5
the value of the reaction constant ρ+ = – 4.54, the
3-Cl,4-t-Bua
2
1.5
1
calculated rate constant kXY for disubstituted 2-chloro-
2-phenylpropane was obtained utilizing the following
Hammett–Brown equation:
G‡
–
G‡
ΔΔ
(kJ)
calcd
ΔΔ
obsd
3-I,4-Me
3-Br,4-Me
3-Cl,4-Mea
3-F,4-Me
log(kXY/kHH) = ρ+ꢁσ+
(7)
0.5
0
log kobsd/kcalcd
–3.5 –3
The observed and calculated rate values are given
in Table II together with ꢁσ+ values. A plot of log
(kXY/kHH) rate constants against ꢁσ+ for the solvoly-
sis of substituted 2-chloro-2-phenylpropanes (3b–3d;
Fig. 1 and Table II), together with mainly di-, but also
tri- and mono-substituents from the literature, is linear
with a correlation coefficient of 0.990, showing the ex-
tent of validity of Hammett-Brown ꢁσ+ for assessing
the additive effect of these substituents. Small devia-
tions from additivity in the observed rate constants for
these compounds under investigation have been shown
to be in accordance with steric requirements of the
three-halogen atom (Fig. 2) and its inhibition of res-
onance of the adjacent 4-methyl group. The fluorine
atom, being the one with the least steric demand due to
its smaller size, adheres most closely to the additivity
principle. A good correlation coefficient of 0.994 was
obtained when log kobs/kcalc was plotted against Taft’s
–0.5
–4
–2.5
ΣEs
–2
–1.5
Figure 2 Plot of log kobsd/kcalcd rate constants (lower plot)
and the values of free energy of activation divergences,
(ꢀꢀG‡)obsd – (ꢀꢀG‡)calcd(upper plot) for 2-chloro-2-
(3-halo-4-methyl)phenylpropanes (3b–3d) together with 2-
chloro-2-(3-chloro-4-methyl)- and 2-chloro-2-(3-chloro-4-t-
butyl)phenylpropanesa [25] against Taft’s steric parameter,
ꢁE .
s
steric parameter [33], ꢁEs, (Fig. 2) computed from
individual values of methyl and halogen substituents
(Table IV).
Close adherence to additivity is expected to take
place in cases where interaction between two adjacent
International Journal of Chemical Kinetics DOI 10.1002/kin.20617

520
TAHA
substituents is minimal. Brown and Cleveland [34]
reported the solvolysis of 2-chloro-2-(3,5-dimeth-
ylphenyl)propane to show excellent additivity; the ob-
served value of k was 96% of the calculated value.
However, it is striking to note that the observed rate
constant of 2-chloro-2-(3,4-dimethylphenyl)propane
currently examined in this work does not differ re-
markably from the anticipated rate. The observed rate,
within experimental error, adheres remarkably well
to the calculated value. This shows that steric hin-
drance to free rotation of the benzene ring–Me bond
and hence to resonance is negligible. Brown [26]
demonstrated that the rate of solvolysis of 2-chloro-
2-(3,4-dimethylphenyl)propane at 273 K is precisely
predicted from the rate of 3- and 4-methyl deriva-
tives; the predicted(calculated) and observed relative
rates are 58.4 and 60.0, respectively, with a ratio of
kobsd/kcalcd = 1.03. This is similar to the ratio of
kobsd/kcalcd = 1.03 obtained in the present work for
the same compound from the extrapolated observed
value in Table II. Similar results were found by Has-
san and coworkers [35] (ratio kobsd/kcalcd = 1.02)
for the chlorination of ortho-xylene at 298 K using
chlorine acetate in the presence of perchloric acid
catalyst.
The effect of the m-methoxy group on the
rate of solvolysis of 2-chloro-2-(3-methoxy-4-
methylphenyl)propane investigated in this work was
found to be far less deactivating than that would be
expected from the slightly positive σm+ value for the
methoxy group. This value of σm+ = +0.047 obtained
by Brown [26] establishes the methoxy group in the
meta position as being rate retarding. The value we ob-
tained (ratio kobsd/kcalcd = 1.43) in Table II shows that
the m-methoxy group to be unexpectedly far less rate
retarding. Similar values were found by de la Mare
and Vernon [36] and by Stock and Brown [24] for
the noncatalytic bromination of anisole, which leads
the former to suggest the presence of a nonclassi-
cal structure resonance contribution operating from
the meta position. Built-in dipole interactions could
also, perhaps, contribute to this enhanced reactivity.
However, none of the results obtained by direct mea-
surement of the reactivity of the position meta to the
methoxy group indicated larger activation than ex-
pected [37–39]. As it seems, the additivity principle
perhaps fails to accommodate adequately the variation
in π-complex character of the transition state result-
ing from substituent–substituent interactions, leading
to larger rate values than predicted. Further work is
needed to investigate this diminished retarding effect
of m-methoxy substituent in various disubstituted ben-
zenes observed [24,36]. Another obvious weakness of
the additivity is found in the fact that, whereas Eq. (7)
proposes the strength of 2,3- and 2,5-disubstituted ben-
zoic acids should be identical, it is found that in prac-
tice they are often distinctly different. Supplementary
resonance interactions in some cases can well lead to
serious departures from additivity, e.g., in 2-hydroxy-
3-nitrobenzoic acid [40].
There is a general tendency in processes in solution
for heats and entropies to compensate one another [41].
And since the free energy of activation ꢀG‡ is equal
to ꢀH‡ − T ꢀS‡, no variation in ꢀG‡ is expected to
occur in such processes. Therefore, for homologous se-
ries reactions like the one in our hand, the plots of ꢀH‡
against ꢀS‡ should give straight lines. These values of
activation were obtained following Cagle and Eyring
[42], and they give a straight line of approximately unit
slope (0.993) (Fig. 3).
The rate constants at three different tempera-
tures and the derived activation parameters for the
88
86
3-Cl,4- -Bu
t
84
3-F,4-Me
82
80
78
3-Cl,4-Me
3-Br,4-Me
3-I,4-Me
–65
–60
–55
–50
–45
–40
Δ S ‡
Figure 3 Plot of ꢀH‡ (kJ mol−1) against ꢀS‡(J K−1 mol−1) values for 2-chloro-2-(3-halo-4-methyl)phenylpropanes
(3b–3d) together with values by Hassan for 2-chloro-2-(3-chloromethyl)phenylpropane and 2-chloro-2-(3-chloro-4-t-
butyl)phenylpropanes [25].
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SOLVOLYSIS OF 2-CHLORO-2(3,4-DISUBSTITUTED)PHENYLPROPANES
521
Table V Divergences between Observed and Calculated Differences in Free Energy of Activation for the Disubstituted
2-Chloro-2-phenylpropanes (3b–3f)
Substituent
(ꢀꢀG‡)aobsd (kJ)
(ꢀꢀG‡)bcalcd (kJ)
[(ꢀꢀG‡)obsd – (ꢀꢀG‡)calcd] (kJ)
3-F, 4-Me
+1.41
+2.88c
+3.23
+2.20
+5.73c
−3.32d
−9.82
−7.72
+1.06
+2.26
+2.48
+1.28
+3.77
−3.43
−9.78
−6.84
+0.35
+0.62
+0.75
+0.92
+1.96
+0.11
−0.040
−0.88
3-Cl, 4-Me
3-Br, 4-Me
3-I, 4-Me
3-Cl, 4-t-Bu
3-Me, 5-Me
3-Me, 4-Me
3-MeO, 4-Me
a(ꢀꢀG‡)obsd is (ꢀG‡ – ꢀGo‡)obsd
.
b(ꢀꢀG‡)calcd is (ꢀG‡ – ꢀGo‡)calcd; calculated by using Eq. (8).
cCalculated from rate constants by Hassan et al. [25].
d Calculated from rate constants by Brown and Cleveland [34].
solvolysis of substituted 2-chloro-2-phenylpropanes in
90% aqueous acetone are given in Table V.
be maintained in reactions of the type where the electri-
cal effects of the substituent can be described with pre-
cision. However, the additivity principle perhaps tends
to oversimplify the role of factors arising when two
constituents are in the vicinity of each other. In such
cases, deviations are bound to occur. Thus in the case
of 2-chloro-2-(3-halo-4-methyl)phenylpropanes (3b–
3d), divergences, albeit small, from additivity calcula-
tions for the free energy differences increase in mag-
nitude according to the increase in the steric require-
ments of the halogen atom. For the m-methoxy deriva-
tive, the additivity calculations overestimate the deac-
tivating effect of the m-methoxy group to the extent
of 0.88 kJ per mol. Only the 2-chloro-2-(3-methyl-4-
methyl)phenylpropane rate values show a close fit to
additivity calculations.
A good correlation coefficient of 0.983 was ob-
tained when divergences from additivity in the free
energy of activation of (ꢀꢀG‡)obsd – (ꢀꢀꢀG‡)calcd
for 2-chloro-2-(3-halo-4-methyl)phenylpropanes (3b–
3d) together with values by Hassan [25] for 3-chloro-
4-methyl and 3-chloro-4-t-butyl were plotted against
Taft’s steric parameter, ꢁEs, values of methyl and halo-
gen substituents, as shown in Fig. 2.
Additive Effects of Substituents on Free
Energy of Activation
Assuming the constancy of the entropy factor, the
change in the free energy of activation produced by
a single substituent may be calculated by means of the
relation (ꢀꢀ‡ – ꢀꢀ0‡) = –2.303RT log k/k0, and if,
moreover, substituent effects are additive, the observed
difference in the free energy of activation due to two
substituents will be the sum of the differences due to
each substituent alone, i.e. [42],
ꢀ
‡ꢁ
ꢀG‡ − ꢀG0
= ꢀG‡ − ꢀG0 + ꢀG‡ − ꢀG0
XY
ꢀ
‡ꢁ
ꢀ
‡ꢁ
(8)
X
Y
Within the limits of experimental error, the entropies
of ionization (ꢀS‡) of 2-chloro-2-phenylpropanes and
their mono- and disubstituted derivatives appear to be
constant. Consequently, th‡e difference in free energies
of activation (ꢀG‡ − ꢀGo; Table V) may be taken as
a measure of the relative stabilities of transition states
and the ability of each substituent to stabilize such
transition states [43].
CONCLUSION
The differences in the free energy of activation for
disubstituted 2-chloro-2-phenylpropanes are given in
Table V. Figure 2, showing the divergences in additiv-
ity between observed and calculated energies of acti-
vation, summarizes the trend.
Analysis of the data given above in Table V will
show the validity of assessing the role of substituent
on reactivity in terms of a free energy relationship. The
concept of additivity based on these assessments will
3-Halogeno, -methyl, and -methoxy derivatives of 4-
methylcumyl chlorides (3) when dissolved in 90%
aqueous acetone undergo both solvolysis and elimi-
nation to give the corresponding alcohols (by SN 1)
and olefins (by E1). Since both SN 1 and E1 have a
common rate-determining (carbocation-forming) step,
measurement of the solvolysis rate gives the overall
rate of reaction. These specific rates for the various
disubstituents (3b–3f) given in Table IV have been
International Journal of Chemical Kinetics DOI 10.1002/kin.20617

522
TAHA
analyzed using, and with the purpose of testing the
validity of, the extended Hammett–Brown equation,
log (kX/kH) = ρ+ ꢁσ+, where ꢁσ+ is the sum of
meta- and para-substituent constants. Additive effects
of disubstituents 3-F,4-Me, 3-Br,4-Me, 3-I,4-Me, 3-
Me,4-Me, and 3-MeO,4-Me on the rate of solvolysis
of the parent chloride (3) are well correlated using the
extended Hammett–Brown equation. The plot of log
(kX/kH) against ꢁσ+ has a linear correlation coeffi-
cient of 0.990, which gives a measure of the validity of
the equation to depict such systems. Figure 1 includes,
together with the values for present work, values for
mono-, di-, and tri-substituents from the previous work.
From Fig. 1, it is clear that polymethyl substituents
whether in the meta or para positions show no de-
parture from additivity, with 3,4-Me2 (present work),
3,5-Me2 ([34], Fig. 1), and 3,4,5-Me3 ([9], Fig. 1) fit-
ting nicely on the regression line. The introduction of
a third methyl group does not seem to bear on their
resonance demands predicted by the Hammett–Brown
equation. A good fit is also seen in Fig. 1 for the
3-Cl,4-OMe and 3-CN,4-OMe disubstituents plotted
values obtained from Fujio et al. [9]. However, the
3-OMe,4-Me disubstituent gives a departure toward
higher values from the regression line (lower retard-
ing effect than that predicted by the Hammett–Brown
equation). It seems that the meta-methoxy group has
a lesser steric inhibitory effect on the resonance de-
mands of the para-methyl group than that predicted
by the Hammett–Brown equation, or that the meta-
methoxy substituent has an unusual residual resonance
contribution, resulting in a lower rate retardation than
the designated σm+ = +0.047 would suggest. This role
of the meta-methoxy group warrants further investiga-
tion. The relative (kobsd/kcalcd) rate ratios of the dif-
ferent substituents, shown in Table II, give the extent
of conformity with additivity. The small degree of de-
parture from additivity for each substituent is found to
correlate with the steric demand of the halogen sub-
stituents. Thus, plots of log of these rate ratios against
Taft’s steric factor of each halogen (the sum of 3-halo
and 4-methyl substituents) give a linear correlation co-
efficient of 0.994 for the 3-halo substituents. The 3-
explanation for this enhanced reactivity of the methoxy
group lies in its ability to indulge from its meta posi-
tion in a resonance electron-enrichment process at the
position ortho to the reaction center (the ipso position),
from which it can be relayed by induction to the reac-
tion center. This explanation was suggested earlier by
Brown et al. [30] to account for the enhanced reactiv-
ity of the monosubstituted m-methoxycumyl chloride.
Similar trends were found for the free energy of acti-
vation (ꢀꢀG‡)obsd – (ꢀꢀG‡)calcd differences, which
correlate linearly to a coefficient of 0.983 with Taft’s
steric factor of halogen atoms, as shown in Fig. 2. The
values obtained earlier by Hassan et al. [25] for 3-
chloro-4-methyl and 3-chloro-4-t-butyl derivatives fit
nicely in this plot of Fig. 2 for the relationship between
Taft’s steric factor and the substituent bulk. As for the
m-methoxy derivative, the free energy calculations es-
timate the deactivating effect of the m-methoxy group
to the extent of 0.88 kJ per mol. This is can be recog-
nized in terms of a second-order relay of the mesomeric
effect of the methoxy from the ortho position to the
reaction center mentioned above [30]. The 2-chloro-2-
(3-methyl-4-methyl)phenylpropane rate values show a
close fit to additivity calculations, with a deviation of
0.04 kJ per mol. As a final conclusion, it is necessary
to allow for steric interactions between adjacent sub-
stituents for the additivity principle to hold true; this
can be done, perhaps, by incorporating a steric factor
in the extended Hammett–Brown equation (4) of the
type shown in Eq. (9):
log(kXY/kHH) = ρ+ꢁσ+ + δꢁEs
(9)
where δ is measure of the susceptibility of a particular
reaction toward steric effects. However, the role of meta
substituents in polysubstituted cumyl systems, such as
the case of m-methoxy group, needs to be resolved by
further work.
I thank Professor Dennis N. Kevill, Northern Illinois Uni-
versity, and Professor Mizue Fujio, Kyushu University, for
valuable information and Sami Habeeb and Makki Dafalla,
University of Bahrain, for technical assistance.
methyl substituent, which has a relative (kobsd/kcalcd
)
rate ratio of 1.03, shows excellent additivity, preclud-
ing any type of steric rate retardation as a result of the
proximity of the two methyl substituents. It is hypoth-
esized that, unlike the 3-halo derivatives, the methyl
group can freely rotate about the benzene–Me bond,
and by doing so, militates against the steric interaction
and hence rate retardation. The 3-methoxy group is
found to have a relative rate ratio of 1.43. This shows
the group unexpectedly to be far less deactivating than
that predicted by the Hammett–Brown equation. One
BIBLIOGRAPHY
1. Anslyn, E. V.; Dougherty, D. A. Modern Physical Or-
ganic Chemistry; University Science Books: Mill Valley,
CA, 2006.
2. Brown, H. C.; Okamoto, Y. J Am Chem Soc 1958, 80,
4979–4987.
3. Brown, H. C.; Okamoto, Y. J Am Chem Soc 1957, 79,
1913–1917.
International Journal of Chemical Kinetics DOI 10.1002/kin.20617

SOLVOLYSIS OF 2-CHLORO-2(3,4-DISUBSTITUTED)PHENYLPROPANES
523
4. Takeuchi, K.; Takasuka, M.; Ohga, Y.; Okazaki, Y. J Org
Chem 1999, 64, 2375–2380.
25. Hassan, M.; Salama, A.; Bombala, M. U. J Chem Soc,
Perkin Trans 2 1972, 410–412.
5. Cho, J. H.; Shin, J.-H. Bull Korean Chem Soc 1996, 17,
347–348.
6. Liu, K.-T.; Duann, Y.-F.; Yu, D.-G. J Chin Chem Soc
1998, 45, 153–158.
7. Yukawa, Y.; Fujio, M. In Advances in Physical Organic
Chemistry; Bethell, D., Ed.; Academic Press: London,
1999; Vol. 32, pp. 276–380.
26. Brown, H. C. In Steric Effect in Conjugated Systems,
Chemical Society Symposium; Grey, G. W., Ed.; But-
terworths Scientific: London, 1958; p. 117.
27. Vogel, A. I. Practical Organic Chemistry, 3rd ed.; Long-
man: London, 1967; p.781.
28. Pearson, D. E.; Stamper, W. E.; Suthers, B. R. J Org
Chem 1963, 28, 3147–3149.
8. Binev, I. G.; Kolev, T. M.; Juchnovski, I. N. Can J Chem
1985, 63, 3149–3154.
29. Kenner, J.; Witham, E. J Chem Soc 1913, 103, 235–237.
30. Brown, H. C.; Brady, J. D.; Grayson, H.; Bonner, W. H.
J Am Chem Soc 1957, 79, 1897–1902.
31. Brown, H. C.; Okamoto, Y.; Ham, G. J Am Chem Soc
1957, 79, 1906–1909.
32. Brown, H. C; Stock, L. M. In Advances in Physical
Organic Chemistry; Gold, V., Ed.; Academic Press:
London, 1963; Vol. 1, pp. 35–154.
33. Jones, R. A. Y. Physical and Mechanistic Organic Chem-
istry, 2nd ed.; Cambridge University Press: Cambridge,
UK, 1984; p. 67.
34. Brown, H. C.; Cleveland, J. D. J Am Chem Soc 1966,
88, 2051–2502.
35. Eldusoqui, M. O.; Hassan, M.; Elnadi, A.; Yousif, G. J
Chem Soc, Perkin Trans 2 1976, 359.
36. de la Mare, P. B. D.; Vernon, C. A. J Chem Soc 1951,
1764–1767.
37. Illuminati, O. J Am Chem Soc 1958, 80, 4945–4948.
38. Kochi, K.; Hammond, G. S. J Am Chem Soc 1953, 75,
3445–3451.
9. Fujio, M.; Adachi, T.; Shibuya, Y.; Murata, A.; Tsuno,
Y. Tetrahedron Lett 1984, 25, 4557–4560.
10. Murata, A.; Sakaguchi, S.; Fujiyama, R.; Mishima, M.;
Fujio, M.; Tsuno,Y. Bull Chem Soc Jpn 1990, 63(4),
1138–1145.
11. Liu, K. T. J Chin Chem Soc 1992, 39, 617–23.
12. Jaffe´, H. H. Chem Rev 1953, 53, 244.
13. (a) Stone, R. M.; Pearson, D. E. J Org Chem 1961, 26,
257–259; (b) Furuyama, S.; Golden, D. M.; Benson, S.
W. Int J Chem Kinet 1971, 3, 237–248.
14. Benson, S.W. Thermochemical Kinetics, 2nd ed.; Wiley-
Interscience: New York, 1976.
15. Huang, H.; Dunford, H. B. Can J Chem 1990, 68, 2159–
2163.
16. Mokrosz, J. L.; Ekiert, I. Chromatographia 1984, 18(7),
401–405.
17. Swami, P.; Yajurvedi, D.; Mishra, P.; Sharma, P. K. Int J
Chem Kinet 2009, 42, 50–55.
18. Rangappa, K. S.; Anitha, N.; Made Gowda, N. M. Synth
React Inorg, Met-Org, Nano-Met Chem 2001, 31, 1499–
1518.
19. Harrison, A. G. J Mass Spectrom 1999, 34, 577–589.
20. Pytela, O.; Kulhanek, J.; Ludwig, M.; Riha, V. Collect
Czech Chem Commun 1994, 59, 627–638.
21. Zhong, W.; Gallimran, J. P.; Zhang, Y.; Li, L.; Lester,
H. A.; Dougherty, D. A. Proc Natl Acad Sci USA 1998,
95, 12088–12093.
22. Sayyed, F. B.; Suresh, C. H. New J Chem 2009, 33,
2465–2471.
23. de la Mare, P. B. D.; Ridd, J. H. Aromatic Substitution;
Butterworths: London, 1959.
39. Okamoto, Y.; Brown, H. C. J Am Chem Soc 1957, 79,
1909–1912.
40. (a) Kuivila, J.; Hendrickson, A. R. J Am Chem Soc
1952, 74, 5068; (b) Wheeler, S. E.; Houk, K. N. J Chem
Theory Comput 2009, 5, 2301–2312.
41. Laidler, J. K. Reaction Kinetics; Pergamon Press:
Oxford, UK, 1963; Vol. 2, p. 47.
42. Chang, R. Physical Chemistry for the Biosciences; Uni-
versity Science Books: Sausalito, CA, 2005; pp. 338–
342.
43. Johnson, C. D. The Hammett Equation; Cambridge Uni-
versity Press: Cambridge, UK, 1980.
44. Brown, F. J.; Yee, Y. K.; Cronk, L. A.; Hebbel, K. C.;
Knell, R. D.; Snyder, D. W. J Med Chem 1990, 33,
1771–1781.
24. Stock, L. M.; Brown, H. C. J Am Chem Soc 1960, 82,
1942–1947.
International Journal of Chemical Kinetics DOI 10.1002/kin.20617