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).

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