J. Phys. Chem. 1987, 91, 6022-6027
6022
Description of Solvent Dependence of Rate Constants in Terms of Pairwise Group Gibbs Function Interaction Parameters. Medium Effects for Hydrolysis of p -Methoxyphenyl Dlchloroacetate in Aqueous Solutions Containing Urea and Alkyl-Substituted Ureas Wilfried Blokzijl, Jan B. F. N. Engberts,* Jan Jager, Department of Organic Chemistry, University of Groningen, 9747 AG Groningen, The Netherlands
and Michael J. Blandamer* Department of Chemistry, University of Leicester, Leicester LE1 7RH, England (Received: March 2, 1987; In Final Form: June 3, 1987)
Rate constants for neutral hydrolysis of p-methoxyphenyl dichloroacetate in aqueous solutions are sensitive to the molality of added urea and alkyl-substitutedureas. These dependences are considered in the light of pairwise Gibbs function parameters describing interaction between solutes in aqueous solutions. In the next stage these interactions are examined by using the Savage-Wood additivity principle for pairwise group interaction parameters involving organic solutes and both initial and transition states for the hydrolysis reaction. The basis of the approach is described showing how kinetic and thermodynamic data are drawn together and used to comment on mechanisms of reaction in aqueous solutions. For the hydrolysis of the dichloroacetate ester, we account for the observed dependence of rate constant on solvent in terms of a reaction that is second order with respect to water, where the transition state exposes three OH groups to the aqueous solution, and in terms of derived group interaction parameters involving these OH groups and both CH2 and CONH groups in added solutes.
Introduction Rate constants and derived activation parameters for chemical reactions involving solutes in aqueous solutions are often dramatically changed when organic cosolvents are added.' In this paper we report the effects of urea (U), 1,3-dimethylurea (DMU), 1,3-diethylurea (DEU), and tetramethylurea (TMU) on the rate constant for the neutral hydrolysis of p-methoxyphenyl dichloroacetate in aqueous The reaction mechanism3 is shown in Scheme I. The hydrolysis proceeds via a dipolar transition state containing two water molecules with three protons in flight.6 The reaction is summarized in eq 1, where S is the s(aq)
+ NH20
-
[S-NH2OITS(aq)
-
Y(aq)
I
60
Ii
(1)
substrate ester, Y represents the products of reaction, and N is the order with respect to water. We examine the dependences of rate constants on the nature of the added solute and the composition of the aqueous solution in terms of the corresponding dependences of the activity coefficients of both initial and transition states. An interesting procedure has been suggested by Wood and c o - ~ o r k e r s ' - (see ~ ~ also ref 12) and by Lilley and coworker^^^,^^
for describing quantitatively solutesolute interactions in aqueous solution. The set of kinetic data describing the neutral hydrolysis of p-methoxyphenyl dichloroacetate (Scheme I) in aqueous solutions of urea and alkyl-substituted ureas affords a challenging test of the merits of the Savage-Wood additivity principle (orI4 Savage-Wood additivity of group interactions, SWAG) with respect to the analysis of medium effects on kinetic parameters for reactions in solution. Wood and co-workers*-" build on a treatment of partial molar enthalpies for solutes in aqueous solutions15discussed by Savage and Wood,7 extending the methods to include consideration of Gibbs functions G and related chemical potentials. In summary, solutesolute interactions in dilute aqueous solutions are described with pairwise group interaction parameters which offer a powerful predictive tool.9b In the application reported here to kinetic data, we use transition-state theory16 to link phenomenological rate constants and parameters calculated from equilibrium properties of aqueous solutions. In general terms the rate constants for ester hydrolysis are sensitive to the molality of urea, U, as a result of U transition-state and U initial-state interactions and of the effect of urea on the stru~ture'~.l* (and reactivity) of water (cf. Scheme
(1) Blandamer, M. J.; Burgess, J.; Engberts, J. B. F. N. Chem. SOC.Reu. 1985, 14, 237.
(2) Engberts, J. B. F. N. Water. A Comprehensiue Treatise; Franks, F., Ed.; Plenum: New York, 1979; Vol. 6, Chapter 4. ( 3 ) Engbersen, J. F. J.; Engberts, J. B. F. N. J . Am. Chem. SOC.1974, 96, 1231. (4) Holterman, H. A. J.; Engberts, J. B. F. N. J . Am. Chem. SOC.1980, 102, 4256. (5) Holterman, H. A. J.; Engberts, J. B. F. N. J . Org. Chem. 1983, 48, 4025. (6) Karzyn, W.; Engberts, J. B. F. N., unpublished work. (7) Savage, J. J.; Wood, R. H. J . Solution Chem. 1976, 5, 733. (8) Harris, A. L.; Thompson, P. T.; Wood, R. H. J. Solution Chem. 1980, 9, 305. (9) (a) Spitzer, J. J.; Suri, S. K.; Wood, R. H. J. Solution Chem. 1985, 14, 561. (b) Spitzer, J. J.; Suri, S. K.; Wood, R. H. J . Solution Chem. 1985, 14, 571. (10) Suri, S. K.; Spitzer, J. J.; Wood, R. H.; Abel, E. G.; Thompson, P. T. J. Solution Chem. 1985, 14, 781. (11) Suri, S . K.; Wood, R. H. J. Solution Chem. 1986, 15, 705. (12) Cassel, R. B.; Wood, R. H. J . Phys. Chem. 1974, 78, 2460. (13) Blackburn, G. M.; Kent, H. E.; Lilley, T. H. J. Chem. SOC.,Faraday Trans. 1 1985, 81, 2191 (and references cited therein). (14) Kent, H. E.; Lilley, T. H.; Milburn, P. J.; Bloemendal, M.; Somsen, G. J. Solution Chem. 1985, 14, 101.
0022-3654187 , ,12091-6022$01.50/0 I
-
-
(1 5) See also Tasker, I. R.; Wood, R. H. J. Solution Chem. 1982, 11,729. (16) Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941. (17) Franks, F.; Reid, D. reference 2, Vol. 2, Chapter 5. (18) Tanaka, H.; Nakanishi, K.; Touhara, H. J . Chem. Phys. 1985, 82, 5 184.
0 1987 American Chemical Societv -
The Journal of Physical Chemistry, Vol. 91, No. 23, 1987 6023
Hydrolysis of p-Methoxyphenyl Dichloroacetate
TABLE I: Dependences of Rate Constants for Neutral Hydrolysis of p-Methoxyphenyl Dichloroacetate at 25 "C on Molality of Added Cosolvent in Aaueous Solution m/mol kg-'
urea
DMU
DEU
TMU
0 0.279 0.561 0.846 1.13 1.43 1.72 2.02
3.00 3.04 3.08 3.12 3.15 3.18 3.22 3.24
3.00 2.70 2.45 2.25 2.09 1.93 1.80 1.68
3.00
3.00 2.35 1.90 1.54 1.22 1.02
2.50 2.16 1.83 1.60 1.40 1.23 1.09
0.84 0.71
I). We examine the procedures described by Wood and coworkers"" in formulating these solutesolute interactions in terms of pairwise Gibbs function interaction parameters and hence their success in accounting for trends in kinetic data. RecentlyI9 we showed that this type of analysis has reasonable success in accounting for kinetic data describing the hydrolysis of l-acyl1,2,4-triazoles in aqueous solution containing monohydric alcohols.20*21 Experimental Section
Materials. p-Methoxyphenyl dichloroacetate was prepared according to a standard procedure.22 Urea (Baker) was used as supplied. 1,3-Dimethylurea and 1,3-diethylurea were purified by recrystallization from ethanol and petroleum ether, respectively. Tetramethylurea (TMU) was distilled in vacuo. Demineralized water was distilled twice in an all-quartz unit. All solutions were prepared by weight and contained lo-' mol dm-' HCl to suppress catalysis of the hydrolysis reaction by hydroxide ions. Kinetic Measurements. Reaction rates were determined by following the change in absorbance at 288 nm (formation of cm3 of stock solution of the p-methoxyphenol). About 8 X mol dm-3 in acetonitrile) was added to the substrate (5.2 X reaction medium in quartz cells and placed in a thermostated (*0.05 "C)cell compartment of a Perkin-Elmer Lambda 5 spectrophotometer. The reaction was followed for about 10 half-lives, with excellent first-order kinetics being observed. Rate constants were calculated by using a data station PEA5 connected to the spectrophotometer and were reproducible to within 2%. Results
At 298 K and ambient pressure, the pseudo-first-order rate constant for ester hydrolysis (Scheme I) is 3.00 X lo-' s-l in aqueous solution, pH 3.5; see Table I. Pseudo-first-order rate constants for ester hydrolysis at 298 K are recorded as a function of molality of added solute in aqueous solutions containing urea (U), 1,3-dimethylurea (DMU), 1,3-diethylurea (DEU), and tetramethylurea (TMU); see Table I.
Analysis In this section we draw together the SavageWood description of solute-solute interactions6J0 and transition-state theory for chemical reactions in s ~ l u t i o n . ' ~ Chemical Potentials. A given aqueous solution contains two solutes, S and U, having molalities m, and mu, respectively. Here S represents the substrate undergoing chemical reaction and U represents an added solute (or cosolvent), e.g., urea. For substrate S at temperature T and pressure p in an aqueous solution where the molality of cosolvent is mu, the chemical potential of substrate S, p,, is related2' to m,: M, = clso + R T In (m,r,/m") (2) Here p> is the standard chemical potential of solute S in an ideal (19) Blokzijl, W.; Jager, J.; Engberts, J. B. F. N.; Blandamer, M. J. J. Am. Chem. SOC.1986, 108, 6411. (20) Haak, J. R.; Ennberts, J. B. F. N.; Blandamer, M. J. J . Am. Chem. Sac. 1985, 107, 6031. (21) Jager, J.; Engberts, J. B. F. N. J . Org. Chem. 1985, 50, 1474. (22) Engbersen, J. F. J.; Engberts, J. B. F. N. J. Am. Chem. SOC.1975, 97, 1563.
aqueous solution where m, = 1.O mol kg-' at the same temperature and standard pressure, po (=lo5 N m-l) and mo = 1 mol kg-'. (We assume that ambient pressure p is close to the standard pressure.) By definition,%lim (m,--O, mu+) y,= 1.O at all temperatures and pressures. Thus pso is determined by S -water interactions. In a real aqueous solution y, # 1.0 as a result of S U, S S,and, indirectly (cf. communication described by the GibbsU solute-solute interactions. If, as Duhem equation2'), U suggested above, S is a substrate, the rate of reaction is expected to depend on the naturb and molality of cosolvent U. Exactly analogous arguments apply to the transition state, TS, as a solute in aqueous solution. According to Scheme I, water is both solvent and reactant. The chemical potentia1 of water in the aqueous reaction mixture (where the sum of the molalities of all solutes in solution, m = m, mTs mu my) is related to the molality m and p*(H20,1,T,p), the chemical potential of pure liquid water, molar mass MI, at the same temperature and pressure; where water = substance 1, then
- -
-
+
+ +
p ( H 2 0 ) = p*(H20) - 4RTMlm (3) Here 4 is the practical osmotic coefficient where by definition2' lim ( m - 4 ) 4 = 1.0 at all temperatures and pressures. In an ideal solution (where y, = 1 for all solutesj and 4 # l.O), the chemical potential of substrate S is a logarithmic function of molality, m (cf. Henry's law) but the chemical potential of the solvent, water, is a linear function of m (cf. Raoult's law). Transition-State Theory. The chemical reaction described by Scheme I is summarized in eq 1 where N is the order of reaction with respect to water.25 The rate constant k(aq;m) is given by eq 4, where kb and h are Boltzmann's and Planck's constants, k(aq;m) = (kbT/h)*K"(%/rTS) exp(-"dMd
(4)
respectively. * K O is independent of the nature and molality of solute U (cf. eq 3). According to the dilute solution approximation, activity coefficients y,and yTs are determined by S U and TS U solutesolute interactions. In other words, y,and yTsdepend on the molality of solute U. Solvent Dependence of Rate Constant k(aq;m). Various interesting conditions are identified by using eq 4. If the molality of solute U, mu, is 0, then within the limits of the dilute solution approximation, y, = yTs = 1.0 and exp(-N4Mlm) = 1.0. Hence
-
-
k(m,=O;id) = (kbT/h)*Ko
(5)
Here k(m,=O;id) is, to a good approximation, given by k(obsd) for hydrolysis of the ester (Scheme I) in aqueous solution where m,, = 0. If the molality of added solute mu is not 0 but the solution is dilute in substrate and also ideal, y, = yTS= 4 = 1.0. Hence k(m,;id) = (kbT/h)*Ko exp(-NMlmu)
(6)
Although rate constant k(m,;id) cannot be measured, eq 6 provides a marker against which to examine trends in k(obsd). Comparison of eq 5 and 6 yields In [k(m,;id)/k(m,=O;id)] = -NMIm, (7) If therefore the chemical reaction is zero order in solvent, the rate constant for reaction in ideal solution is independent of the nature and molality of added solute U. If, however, N # 0, this rate constant decreases with increases in m,,, the pattern being the same for all solutes and independent of the nature of added solute. In other words addition of solute U lowers the rate constant by virtue of a fall in chemical potential (reactivity) of water. Although we a r e only concerned h e r e with o n e class of compounds, this s a m e pattern would emerge for all reactions that involve nucleophilic attack by water at a substrate, e.g., SN2solvolysis of alkyl halides in aqueous solution.24 In the unlikely event that y,and yTs are (23) McGlashan, M. L. Chemical Thermodynamics; Academic: London, 1979. (24) Garrod, J. E.; Herrington, T. M. J . Chem. Educ. 1969, 46, 165. (25) Blandamer, M. J.; Burgess, J.; Robertson, R. E.; Koshy, K. M.; KO, E. C. F.; Golinkin, H. S.;Scott, J. M. W. J. Chem. SOC.,Faraday Trans. 1 1984, 80, 2287.
6024
The Journal of Physical Chemistry, Vol. 91, No. 23, 1987
Blokzijl et al.
unity but 4 # 1.O, the rate constant for hydrolysis in real solutions where mu # 0 would be given by In [ k ( m , ; y , = y T ~ = l ) / k ( m , = O= ) ] -N4M,mu (8)
In terms of Gibbs functions, the pairwise solutesolute interaction parameter for solutes P and Q, namely, g(P-Q), is expressed in the form
In another exercise linked to eq 8, we compare the rate constant for reactions in solution where the molality of urea is mu for the cases where the solution is real and ideal; Le., 4 # 1.0 and 1.0, respectively. Then, In [k(m,;ys=yTs= 1;4# l)/k(m,;y,=yTs= 1;4=1)] is examined as a function of (1 - 4)NM,m,. In the case of urea solutions the dependence of 4 on mu is calculated from the parameters reported by Stokes27;see below. Finally, for a solution where both ysand yTs are not unity (i.e., real systems), the key relationship is given by eq 9 (eq 5 describes the reference):
g(P-Q) = [ x ( i = l ; i = k ) x ( j = l d = l ) nP(i) nQ(j) C(i-j)]
In [k(m,)/k(m,=O)]
= In ys- In
- N4MIm,
~ T s
(9)
Pairwise Solute-Solute Interaction Parameters. A given aqueous solution comprises 1 kg of water, m, moles of solute S, and mu moles of solute U. The excess function GE expresses the difference between the Gibbs function for this and the corresponding ideal solution.28 For dilute solutions GE is determined by pairwise interaction between solute^;^^^^^ g(S-S), g(U-S), and g(U-U) are the corresponding pairwise solutesolute Gibbs function interaction p a r a m e t e r ~ : ~ l - ~ ~
GE = g(S-S)
(m,/m0)2
+ 2 g(U-S)
msm,/mo2 + g(U-U) (m,/m0)2 (10)
Granted, this equation describes the dependence of GE(aq;T;p) on composition; the corresponding equations for (1 - 4) and activity coefficients for substrate S and cosolvent U are readily The activity coefficient for substrate S is obtained as the differential of eq 10 at constant T, p , and mu;In ys = ( l / R T ) (dGE/dms). Hence
RT In y, = 2 g(S-S)
ms/mo2 + 2 g(U-S)m,/mo2
For a solution dilute in substrate S (Le., m,
R T In ys = 2 g(U*S)
(1 1)
