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Reaot. g ine t . Calxzl. Let t . , Vol. 33, No. 1, 229-232 (1987)
APPLICATION OF THE SINGH-JHA EQUATION IN THE EVALU/~DN OF
b* OF THE LAIDLER'LANDSKROENER EQUATION
Rabindra Kumar
Department of Chemistry, Patna University, Patna-800 005, India
Received Au4uer 16, 198S Accepted Feb~r~j 14, 1986
The least distance of the closest approach, b*, of the
Laidler-Landskroener equation has been evaluated by
application ofthe Singh-Jha equation in case of acid
catalyzed hydrolysis of benzyl formate in water-DMSO
solvent system. The values obtained are quite reason-
able.
BeHHqHHa HaHMeHbNePO paCCTOHHHR HaH6HHxaRmePo HpH6HHZe-
HHR b M ypaBHeHHH ~a~Hepa-~aH~CKp~Hepa oHpe~eneHa c HO-
MO~b~ ypaBHeHHH CHHPa H H B CHyqae PH~pOnHSa 6eHBH~Op-
MaTa, KaTa~MSHpOBaHHOFO KHCHOTaMM B CHCTeMe Bo~a-~MC0.
HoHyqOHH~O BOHH~HHM BHOHHe HpHOM/IOMId.
INTRODUCTION
The evaluation of b* of Laidler-Landskroener equation [i]
is still a problem for the kineticists of solvent effect. The i
authors [1] proposed a method for its evaluation which has been
appl~d by others [2,3,4] but with limited success. The method !
suffers from a serious drawback as some assumptions regarding
the model of the activated complex has to be made and still
the method can be applied to only those cases in which the
transition states are highly polarized.
Singh and Jha approached [5,6] the problem afresh and fina~
succeeded in proposinq a DMrof equations [6]; this isZ a more
Akad~miai EiadA, Budapest
KUMAR: SINGH JHA EQUATION
general method for evalua~:ing b* irrespective of the polarity
of the transition state. It is significent that no assumption
regarding the model of the activated complex is required. The
authors [ 6] claim the applicability of their equation in reac-
tions such as hydrolysis of esters in differ~It solvent systems.
The present author has studied the acid catalyzed hydro-
lysis of benzyl formate at various compositions of DMSO-water
solvent mixtures at different temperatures with a view to test
the applicability of the equation proposed by Singh and Jha.
EXPERIMENTAL
All the chemicals used were of Merck L.R. grade. They were
adequately purified by known procedures. The preparation of the
solutions and other experimental procedures were similar to
those described by Singh et al. [7,8]. 0.1 M HCl was made in
different solvent mixtures of DMSO varying from 40 to 80 vol.%
in water. After thermostating at the desired temper-
-ature, 1 ml of benzyl formate was added. The kinetics of the
reactions were followed by removing 5 ml of the liquid at dif-
ferent intervals of time and titrated against standard alkali.
Reproducible results (reliable up to 0.05x10-~m/n-1)wereob~ined--
which are shown in Table 1.
Table 1
Specific rate constant (kxl03, min -1) "for acidlhvdrolvsis
of benzyl formate in water-DMSO media
Temperature DMSO(vol.%) (vC) 40 50 60 70 80
20 ,0 .65 0 .61 0 , 5 2 0 .50 0 . 4 i
25 1 .08 1 . 0 2 0 . 8 9 0 .79 0 . 6 6
30 1 .94 1 . 6 8 1 .48 1 .29 1 .08
35 3 .04 2 . 6 5 2 . 4 0 2 .07 1 .69
40 5 .04 4 . 4 4 3 . 7 5 3 . 2 6 2 .57
aso
KUM4R: SINGH JHAEQUATION
RESULTS AND DISCUSSION
The equations proposed by Singh and Jha [6] are as follows: ,
1 _ 1 _~_ I Ix l+u (X+y)] (i) b b* A
log--kl ~[ X _ _~] + y[ 1 1 ] (ii) k2 ~i D2T2 T1 T2
where X/T is the slope of the plot of 16g k against I/D and Dis
the bulk dielectric constant of the solvent mixture;
b is the size of the reactant ion, i.e. H3 O+ ;
is half of the dieledric constant of the ester used;
Y, a constant for a solvent pair, is the m~an (of the Y
va%/es)for different pairs of temperature data obtained
from eq.(ii), and A is equal to e2/2.303x2 k and k is the
Boltzmann constant and e is the electron charge.
The plot of log k against I/D for benzyl formate in
water-DMSO media consists of two straight lines intersecting at
a point. The slope of the longer section (viz. 40 to 70%EMSO)wasused
for calculating b* values. The values of Y were calculated from
eq. (ii) using the data of each pair of temperatures between
20 to 40~ Using the mean of the Y values and the slope of the
plot (log k against I/D} b* values were calculated. They have
been shown in Table 2. The dielectric constant values used for
the various compositions at different temperatures were ob-
tained from the intexpolation of the plots obtained from the
data reported by Wolford [9].
Table 2
b* values calculated from the Singh - Jha equation for
water-DMSO media
Temperature (~ 20 25 30 35 40
b* in A ~ 7.8 7.0 6,8 6.4 6=i
851
EUMAR: SINGH-JHA EQUATION
The value of b* seems to be acceptable. These values are
quite comparable with those of acid catalyzed hydrolysis of.
acetamide in mixed aqueous organic solvent mixtures by Elsemongy
[I0], The decrease in b* with increase of temperature appears
to be justified as the solvation sheath is likely to decrease
with the increase in randomness in the system.
The equation of Singh and Jha could not be tested for re-
gions near pure solvent as at the lower concentrations of DMSO
(below 40%) the ester was not soluble and at the higher concentra-
tions of DMSO (above 80 %) the deviation in the result was ap-
preciable. However, further work is in progres& to examine the
applicability of the equation at extreme conditions of the
solvent compositions.
REFERENCES
i. K.J. Laidler, P.A. Landskroener: Trans. Faraday Soc.,52,
200 (1956).
2. P.L. Nayak, M.K. Rout: Indian Chem. Soc., 48, 141 (1971).
3. E.S. Amis: Solvent Effects on Reaction Rates and Mechanisms,
p.50 Academic Press, New York.
4. P.S.R. Murti, P.S. Patro: Pr0c. Ind. Acad. Sci., 71A, 181
(1970),
5. R.C. Jha, Lallan Singh, S.N. Das: J. Indian Chem.Soc., 51,
657 (1974).
6. Lallan Singh, R.T. Singh, R.K. Singh, R.C. Jha: J. Indian
Chem. Soc., 55, 372 (1978).
7. Lallan Singh, R.T. Singh, R.C. Jha: J. Indian Chem. Soc.,
57, 1089 (1980).
8, Lallan Singh, A.K. Gupta, R.T. Singh, D.K. Verma, R.C. Jha:
React. Kinet. Catal. Lett., 2_44, 161 (1984}.
9. R.K. Wolford: J.Phys. Chem., 6-8, 3392 (1962}.
10. M.M. Elsemongy: Z. Phys. Chem., 94, 69 (1975).
282
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