Indian Journal of ChemistryVO\. 21A. December 1982, pp. 1079-1082

Effect of Dielectric Constant & Temperature onHammett Reaction Constants in Substitution Reactions of

cis-[Coenz(Hz(»)zJ3 + Ion withBenzoic Acids

Chhaya Chaudhury & S K Siddhanta*

Department of Chemistry, University of Burdwan, Burdwan 713104

Receired 3 June 1982; revised and accepted 17 September 1982

The reactions of cls-[Coen2(H20h]3+ with benzoic and substituted benzoic acids have been studied: (a) in solvents ofdifferent dielectric constants, at constant temperature (30'C); and (b) in the same solvent [15 nn (v/v) ethanol-water mixture] atdifferent temperatures. It has been conclusively established that the reactions proceed only by S,,2 mechanisms. Hammettreaction constants (p) have been determined in all the cases. The linear plot of p versus I/O provides support to the. S,,2mechanism. The linear plot of p versus l.T establishes the dependence of the activation parameters on Hammett substituentconstant (<1).

In our previous paper", we have shown that theHammett relationship is applicable to the reactions ofcis-[Coen2(1-[20hJ3 + with benzoic and substitutedbenzoic acids. Presently we have studied the effect ofvarying dielectr ic constant and temperature onHammett reaction constants (p) of the reactions of cis-[Coen2(H20}z]3 + ion with benzoic acids.

Materials and Methodscis-[Coen2(I-I20}z](N03h was prepared and

characterised as described earlier!. The ligands usedwere the ammonium salts of benzoic and substitutedbenzoic acids. The reaction products cis-[Coen2(H20)Lf + (where L = benzoate or substitutedbenzoate) were isolated and characterised as given inour earlier paper '.

Ethanol-water mixtures containing 15,22,30,35 and40 "i" (vIv) ethanol were prepared using doubly distilledwater and ethanol obtained by distilling absolutealcohol over quick lime. The dielectric constants ofethanol-water mixtures containing 15, 22, 30, 35 and40'>" (v/v) ethanol were collected from the data givenby Gosta Akerlof". The pKo values of benzoic andsubstituted benzoic acids at 30C in 30°;) ethanol-water mixture have been taken from our earlierpublication", but the pKa values at 30°C in otherethanol-water mixtures used were determined afreshanalogously.

In the present study, kobs values were determinedunder pseudo conditions ([NH4L] in 10-fold excess,[L -] low and constant due to buffer action of NH4L)at constant pH (4.4) and ionic strength (0.08 mol dm - 3)in every case: (a) in solvents of different dielectricconstants at constant temperature (30'C); and (b) atdifferent temperatures 30, 35', 40 and 45"C in the

same solvent, i.e. 15°" (v/v) ethanol-water mixture. Inthe case of p-methoxybenzoate, however the reactionwas studied at pH 5.9 for reasons stated in our earlierpaper '. This ligand was not used for studies at highertemperatures since base hydrolysis of the complexinterfered with the reaction of the complex with theligand.

Results and DiscussionIn our previous paper", we showed that equilibria (1)

and (2) contributed to the reaction of cis-[Coen2(H20}z]3 + with NH4L

HL~H+ +L - ... (1)

cis-[Coen2(H20h]3 + + L -~[A]

cis-[Coen2(H20)L]2 + + H20[B]

... (2)

To decide whether the reaction between A and L -proceeds by an SN2 or an ion-pair OP) path, weconsidered the general case, where the complex (A)reacted with the benzoate ion [L -] in two parallelpaths: SN2 path with a second order rate constant k2;

and IP path with a first order rate constant k, toproduce complex (B) as the end product of each path.

Since ion pairing equilibrium (association constant=K;) is veryfast, we have

Rate = k2[A] [L -] + k;[I]

or (k2 + kiK;) [A] [L -] ... (3)

since[I] =K;[A] [L-]

Now if [A]o is the initial concentration of complex

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INDIAN J. CHEM., VOL. 21A, DECEMBER 1982

(A) and [A]un is the concentration of the unreactedcomplex (A) not converted into complex (B),

[AJun = [AJo - [BJ = [A] + [I]

=[A] {I +K;[l -]} ... (4)

From Eqs (3) and (4), we have

(k2 + kjKj)[A]un[l -]Rate=·· I+K;[l-] ... (5)

But, Rate = kobs[A]un

k2+kjKj - (6)Therefore,kobs=T+K,[L~][l ] ...

Eq. (6) indicates that a plot of kobs versus [L -] will benon-linear starting from the origin ([l -] = 0, kobS = 0)and becoming parallel to the abcissa (kobs = constant) atlarge [l -] where K j[L "J > \. However, such aplot is linear passing through the origin (values of k"h,at varying concentrations of L - are given in Table I).

This anomalous behaviour can be regarded asconsistent with Eq. (6) only if Kj[L -] in thedenominator is ~ I, i.e. if K i is of the order of I or less,since [L -J is of the order of 0.05 (Table I). To decide asto what might be the actual magnitude of the ion-association constant (K j), the following procedure wasadopted. Eq. (6) can easily be transformed into Eq. (7).

I I K;--- -- .+ ... (7)kobs (k2+Kjkj)[L-] (k2+Kjkj)

Eq. (7) indicates that a plot I/k,,/>, versus I/[L· Jshould be linear with slope = II(k 1 + K jkj) andintercept = K;/(kl + KjkJ Though such a plot is linearit passes practically through the origin (Fig. I)indicating that the intercept K;/(k2 + Kh) ~Q, i.e. thenumerator K, ~O. This means that stable ion-pairs arenot formed in the present systems and there is no I Pmechanism operative here.

If we put Kj=O in Eq. (7) we getkobs=kz[l -]Rate = k"[A] [L -J where k" = k2 ... (8)

in which k" is a pure second order rate constant. TheHammett relation is straight forward applicable to 5,\"2reactions.

Table l 0" Effect of Varying [L -] on ko",

Temp = 30 C: [Complex] =0.005 mol drn" J; L- = Benzoate

[NH.L] pH [L.0

] k"h,xIOs I[L"] Ik"h.'x 10- 5

moldm-.l mol dm " Is ') mnl-'dm' Is)

0.05 4.4 O.1I16 1.15 6~.5 0.R70.05 4.7 0'()24 1.90 41.0 OS)005 5.0 OJ)).' 2.62 30.3 O.3Xv.IO 4.7 O.1I49 :1.X4 20.) 0.26

1080

1.0

08

0.6

",,!8~ 04~

0.2

00 20 40 60 801/[8z],,.,-1

Fig. I Plot of I k"h' against I [Bz

In the title system L - is the only reacting species: theentity HL, though present does not take any significantpart in the reaction. This is proved by two facts: (a) ko/>,versus [L -] plot is linear passing through the originshowing that /.:"I>s is directly proportional to [L -]. Thiswould not have been the case if HL was also parti-cipating in the reaction: (b) When the experimentwas conducted with the reaction mixture having therecipe [A] = 0.005 mol drn -.1; [l'-l H~Bz)0.05 mol drn - J; pH 3.0; and temp.-30 C (under whichconditions. [Bz-]=O.O()09moldl1l J. and [HBz]=O.(W)ll1loldm-J

) it was found that there was nochange III absorbance even after 10 hr. Thisconclusively proved that I-IBz did not react to anymeasurable extent. Thus,

k=k"[L -]=k".K [HLJ![H '"]on.1i ""

(9)where Ku = dissociation constant of the acid H L.

The Hammett equation for the reaction of benzoateand substituted benzoate ions with complex (A) for anyone solvent mixture can be written as

log k'' = log k~ + (J P ... (10)

where k" is the second order rate constant for anysubstituted benzoate with the substituent constant (J:

k;; that for the parent benzoate ion and p the reactionconstant for a particular solvent mixture. From theslopes of the linear plots of log k" versus (J for eachreaction mixture, the p-values at 30 C in the reactionmedium of varying dielectric constants were calculatedusing the least squares method (Table 2:1. The plot of pagainst I D was also found to be linear.

Similarly. the different, p-values for the samereactions at different temperatures using the samesolvent (15°" ethanol-water) were determined. Thesereaction constants (Table 3) are linearly related to thereciprocal of the corresponding temperatures (Fig. 2).

The activation parameters tlH! and ~S! have beencalculated for the reaction (2) and the values are givenin Table 4.

CHAUDHURY & SIDDHANTA:SUBSTITUTION REACTIONS OF cis-[Coen2(H20),]J+

Table 2-ElTect of Varying Dielectric Constant on pKa. kobS and k"

(Temp = 30°C; pH =4.4; [Complex] =0.005 moldm-l; [NH4L] =0.05 moldm-l; It:::::0.08moldm-')

Solvent pKa. Benzoic acid p ValuekOb,(s-l)

% of Dielectric and k" Unsubstituted p-Hydroxy m-Hydroxy m-Nitro m-Methyl p-Methoxyethanol constant (mol-'dmls-')

pKa 4.34 4.83 4.12 3.64 4.40 4.62IS 71 105kobs 1.60 3.20 1.10 0.22 2.74 3.10 -1.58

10'k" 0.60 2.36 0.34 0.05 1.09 1.65

pK. 4.60 5.03 4.35 3.89 4.68 4.9022 68 105kob, 1.23 3.00 1.68 0.38 2.01 2.88 -1.39

10lk" 0.65 3.16 0.64 0.10 1.17 2.40

pKo 4.72 5.23 4.57 4.01 4.80 5.0930 63 105kob, 1.15 2.11 1.92 0.69 1.82 2.27 -1.15

10'k" 0.71 3.27 0.95 0.18 1.27 2.68

pK. 4.94 5.43 4.78 4.23 5.01 5.2135 60 105 «: 2.04 1.72 1.81 1.19 2.18 1.98 -0.92

10lk" 1.82 4.03 1.23 0.40 2.22 2.95

pK. 5.12 5.66 5.02 4.39 5.18 5.4040 57 105kob, 2.33 1.90 2.29 2.11 2.66 1.66 -0.79

10'k" 2.91 7.31 2.37 0.83 3.74 3.66- __ 0 _______ •• ____________ - ..

Table 3-Variation of kobs and k" with Temperature

(Solvent = 15 ~-:;(v/v) ethanol; pH =4.4; [Complex] =0.005 mol dm -'; [NH4L] =0.05 mol dm -3; II~ O.OS mol dm J)

Temp kob,(s -') Benzoic acid p(OC) and k"

(mol-'dm's-') unsubstituted p-hydroxy m-hydroxy m-nitro m-methyl30 105

kOb' 1.60 3.20 1.10 0.22 2.74 -1.5810'k" 0.60 2.36 0.34 0.05 1.09

35 105kob, 5.00 5.91 3.67 0.86 6.25 -1.2810lk" 1.87 4.36 1.12 0.20 2.50

40 105kob, 8.02 8.55 5.12 1.74 9.92 -1.14lO'k" 3.00 6.31 1.56 0.41 3.97

45 105kobs 14.34 13.48 10.90 3.72 18.05 -1.0210lk" 5.37 9.95 3.32 0.87 7.22

Table 4-Relationship between Activation Parameters and Substituent Constants

t1H~- t1Htt

Benzoic Substituent t1Ht t1S!t1So - t1st----

(J (Jacid constant, (J kJ mol-' J deg -'mol- J mol-' J deg - 'mol- ,

m-Nitro +0.71 168.28 225.58 - 8.24 x 104 -f39.5m-Hydroxy +0.12 120.35 84.05 -8.79 x 104 -237.5Unsubstituted 0'.00 109.80 55.55m-Methyl -0.08 102.81 35.66 -8.74x 104 -248.6p-Hydroxy -0.37 79.07 -36.71 -8.31 x 104 - 249.4

t1H~-t1H! t1H~-t1Ht----= -0.44 x 104 whence -8.5 x 104 J mol-'

2.303(JR (J

t1S~- t1st t1S~- t1S! _ _,- .. -.-.- = - 12.92 whence - = - 249.1 J deg ••mol2.303(JR (J

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INDIAN J. CHEM .. VOl. 21A. DECEMBER 1982

-1.2o

f'-14

-1.6

-/.B 3.0 1I 3.2 13 3.4

+ ,/0'

Fig. 2-·Plot of p against (liT)

In an SN2 reaction between two oppositely chargedions, the transition state is more easily attained inmedia of lower dielectric constants resulting in arelatively low values of the activation energy; inotherwords the reaction rate increases as the dielectricconstant of the reaction medium decreases in an S.,,2reaction between oppositely charged ions. The slope ofp versus liD plot is positive showing that p increases asI/D increases i.e. as D decreases. this providing strongevidence for the reaction to proceed by an SI\·2 path.

A comparison of the reaction constant values (p) atdifferent temperatures (Table 3) shows that thenegative value of p decreases with rise in temperatureand p varies linearly with IIT(Fig. 2). This is also to beanticipated since at high temperature, the selectivity ofthe reagent becomes less due to thermal randomisationand therefore the sensitivity of the reaction towards theelectron density changes at the reaction site decreases.

A comparison of !1H:j: and !1S:j: values (Table 4) fordifferent Iigands shows that the values of !1H:j: and !1S:j:follow the order: p-hydroxybenzoic acid < m-methylbenzoic acid < benzoic acid < m-hydroxybenzoic acid < m-nitro benzoic acid. An explanationfor this trend has been provided in an earlierpublication:'.

It has been presumed that the stronger theassociation, the more ordered is the activated complexand the less will be the magnitude of the positive !1st.As has been argued earlier. the strength of theassociation in the seven coordinated activated complex[Coenz(HzO)zL -]z+ decreases as the ligand L - isvaried in the order of their decreasing basicitiesnamely. p-hydroxy-bcnzoate > m-methyl benzoate>benzoate > m-hydroxy benzoate > »r-nitrobenzoate,and hence the positive values of !1S:j: increase in thesame order. In the case of p-hydroxybenzoate,however. !1st has a low negative value perhaps

1082

showing that the decrease in activation entropyresulting from the strong association in the activatedcomplex has more than compensated for the increasein the same due to desolvation effects. It may beremarked that in the case of the activated complex[Coenz(HzO)CI- L - J + formed in the reaction betweencis-(Coenz(HzO)CI]l + and L - studied by Ghoshaland Siddhanta ', the entropy of activation value was+ Ig.8 e.u. when L - p-hydroxybenzoate:presumably, the strength of association in the sevenmembered activated complex [Coen2(H10)Z( p-(Bz -)r + is greater than that in [Coen2(HzO)Clp-Bz' )] + in which some instability is caused by theproximity of two negatively charged ions in thecomplex.

A plausible explanation for the p versus' liT linearrelationship has been provided III an earlierpublication:'. It was pointed out that if (!1Hb - !1Ht)/aand (!1Stl - !1st )/a are constants then p versus 1/ T plotbecomes linear with slope (!1H;l - !1Hn;2.J03aR andintercept (!1Sb - !1st), 2.303aR respectively. !1Hb. !1Ht.!1Sb. !1st are respectively the enthalpies and entropiesof activation corresponding to the rate constantsk;; and k", In Table 4 we have tabulated the valuesof (!1H(i - !1H:j:) a and (!1Sd - !1S:j:)iO for the pairsbcnzoic-p-hyd roxybenzoic: benzoic-m-hyd roxy-benzoic. benzoic-m-methylbenzoic and benzoic-m-nitrobenzoic acids. The values are found to beapproximately constant. The experimental values ofslope and intercept of the plot of p versus I /T have beenfound to be approximately equal to -0.44 x 104 and- 12.92 respectively.

The near constancy in (!1Hi) - Mf:n, a and (!1Sb-!1S:j:)!a values (Table 4) indicates that the differencebetween enthalpiesentropies of activation in the tworeactions. viz. the reaction of A with unsubstituted L -and the reaction of A with any substituted L - isproportional to the substituent constant a. which isagain a measure of electron density difference bet-ween the - COO reaction sites of the unsubstitutedand substituted L .

Acknowledgement

One or the authors (C C) is indebted to the UGCNew Delhi for the award of a senior researchfellowshi p.

References1 Chaudhury C & Siddhanta S K.lntiielllJ eht'lI!. 20A (1981) 896.2 Akerloff Gosta. J All! "/11'111 So«, 54 (1932) 4125.3 Ghoshal A & Siddharua S K.lndieJIIJ Chell!. 20A (1981) 661.