Investigations on substituent and solvent eÜects on solvolysis reactions Part IX.§ The in—uence of polar substituents on the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl acetates in water J. Bittner and G. Schmeer* Institut Physikalische und T heoretische Chemie, Regensburg, D-93040 fué r Universitaé t Regensburg, Germany. E-mail : Georg.Schmeer=chemie.uni-regensburg.de Received 5th February 1999, Accepted 29th March 1999 The imidazole catalyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates in water has been investigated at diÜerent temperatures.The observed rates correspond to the bimolecular nucleophilic addition of the imidazole at the carboxylic carbon atom followed by a very fast hydrolysis of the N-acetylimidazole in water. The in—uence of polar substituents in the acid moiety of the ester molecule on the hydrolysis reaction can be described by an electrostatic dipole»dipole interaction in the same way as the neutral hydrolysis of polar substituted ethyl acetates. 1 Introduction The imidazole catalyzed hydrolysis of esters in water»see Fig. 1»proceeds via the addition of imidazole at the carboxylic carbon atom in the sense of nucleophilic catalysis (BAcN)2 forming a tetrahedral intermediate. This intermediate decomposes by the elimination of the alcohol or phenol group, yielding a very reactive N-acetylimidazole which is immediately hydrolysed in aqueous solution. The –nal formation of acids or their corresponding bases is controlled by the dissociation constants of the respective acids (alcohols, phenols and acetic acids).The general base catalysis by a second imidazole (BAc3)2 molecule is of less importance3 due to the relatively high acidity of the leaving 2,4-dinitrophenol and is not (pKS\4.1), observed in water. Therefore, the reaction is purely of –rst order in the ester and in imidazole (cf. eqn. (1)). [ dcEster dt \kcEster cIm (1) Fig. 1 Mechanism of the imidazole catalyzed hydrolysis of esters in water.§ Part VIII, ref. 1. According to the neutral hydrolysis of polar substituted ethyl acetates,4 the rate determining step of the imidazole catalyzed hydrolysis in water is the formation of an intermediate like a mixed ester-amide of ortho-acetic acid via a tetrahedral transition state. According to the neutral hydrolysis of esters, one important contribution to the Gibbs energy of activation, should *Gº, be the electrostatic interaction energy of the dipolar nucleophile molecule (water, imidazole) with the ester molecule. Within the scope of this electrostatic model of the activation step, the change of the Gibbs energy of activation, in a **Gº, series of polar substituted esters with respect to the unsubstituted 2,4-dinitrophenyl acetate (Index 0) is correlated to the change of the electric –eld ([grad of the polar tEster) ester molecule, see eqn.(2). RgT ln(k0/k)\**Gº\*Gº[*G0º \[NA lNucl(grad tEster[grad tEster, 0) (2) is the gas constant, T the temperature, is the dipole Rg lNucl moment of the nucleophile, is the electrostatic potential tEster of the polar ester molecule, and is Avogadroœs number; NA and k and are the rate constants of the respective com- k0 pounds.The other contributions to remain nearly constant in *Gº the series of polar substituted esters and therefore vanish in eqn. (2). Since this simple treatment was very successful for the description of the substituent eÜect of polar substituents on the neutral and alkaline hydrolysis of esters, it should be tested to see if it can also be used for the imidazole catalyzed hydrolysis of esters in aqueous solutions. 2 Experimental The rate constants of the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl acetate, 2,4-dinitrophenyl methoxyacetate, and 2,4-dinitrophenyl chloroacetate have been measured in water between 5 and 45 °C. Phys. Chem. Chem. Phys., 1999, 1, 2593»2596 2593Table 1 Physical data of the prepared esters R-CO2C6H3(NO2)2 Yield (%) Melting point (q/°C) R Exptl.Lit. Exptl. Lit. CH3 55 606 69.5 706 CH3OCH2 53 » 85.5 » ClCH2 50 » 92.5 97»987 2.1 Materials The three esters (2,4-dinitrophenyl acetate, 2,4-dinitrophenyl methoxyacetate, and 2,4-dinitrophenyl chloroacetate) were prepared according to Schmidt and Westheimer.5 15 mmol 2,4-dinitrophenol and 15 mmol pyridine were dissolved in 100 ml dry diethyl ether. Subsequently, 15 mmol of the commercially available acetyl chloride, dissolved in 25 ml dry diethyl ether, was added at room temperature within 30 min.After stirring of the solution for 12 h to complete the reaction, the precipitated pyridinium hydrochloride was –ltrated oÜ and the solvent removed under reduced pressure. The remaining esters were recrystallized from chloroform/n-hexane mixtures (1 :4) until constant melting points were achieved. All procedures were done under dry nitrogen to prevent hydrolysis of the reagents and products.The physical data of the substances are given in Table 1. 2,4-Dinitrophenyl methoxyacetate has not yet been described in the literature (searches in Chemical Abstracts and Beilstein yielded negative results). Its 1H NMR data are given in Table 2. The observed lines in the NMR spectrum are in full accordance with the molecular structure. 1,4-Dioxane»the solvent of the ester stock solutions for the kinetic measurements»was treated with a molecular sieve (Merck, 0.4 nm) for 20 days to decrease the water content, as determined by the Karl Fischer method, from 50 to 15 ppm.The water was deionized via a Millipore column. Imidazole (puriss., Fluka) was used without further puri–- cation. The sodium hydroxide solutions were prepared from 0.1 m stock solutions (Merck) by dilution with water to the appropriate concentration. All solutions were held under nitrogen that was free of carbon dioxide. 2.2 Kinetic measurements The kinetic experiments were performed in a previously described optical apparatus with a multichannel diode array spectrometer1 for the detection of chemical reactions with time constants greater than 0.5 s in the wavelength range from 200 to 620 nm.After –lling the reaction cell with 20 ml of the aqueous solution of imidazole and attaining the appropriate temperature, the reaction was started by the injection of 30 ll of the ester solution. The volume ratio of the solutions of the esters in 1,4-dioxane to the aqueous solutions is less than 0.005 and therefore the in—uence of the organic solvent on the reaction is negligible.The solutions contain imidazole with at least twentyfold excess and therefore the time dependence of Table 2 1H NMR data for 2,4-dinitrophenyl methoxyacetatea d (ppm) Signal J(H»H)/Hz Irel Group 3.57 s » 3 »O»CH3 4.44 s » 2 »CO»CH2»O 9.00 d 2.7 1 Ar»H(3) 8.56 dd 8.9, 2.7 1 Ar»H(5) 7.53 d 8.9 1 Ar»H(6) a Solvent : reference : TMS. s : singlet, d: doublet, dd: double CDCl3 , doublet.The numbers at the aryl hydrogen atoms refer to the numbering of the 2,4-dinitrophenyl group. NMR spectrometer : Bruker AC-250. Table 3 Pseudo-–rst-order rate constants of the imidazole cata- kobs lyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates (units, 10~4 mol l~1, 10~2 s~1). cIm: kobs: cIm kobs cIm kobs 2,4-Dinitrophenyl acetate 5 °C 15 °C 125.0^0.1 2.99^0.03 124.9^0.1 4.97^0.02 200.2^0.1 4.72^0.03 200.0^0.1 7.75^0.03 275.5^0.2 6.49^0.02 275.3^0.2 10.69^0.02 351.1^0.2 8.14^0.03 350.8^0.2 13.47^0.03 25 °C 35 °C 124.7^0.1 7.83^0.01 124.3^0.1 12.06^0.03 199.6^0.1 12.45^0.06 199.0^0.1 19.08^0.10 274.7^0.2 17.01^0.03 274.2^0.2 26.29^0.08 350.0^0.2 21.52^0.06 349.0^0.2 33.03^0.07 45 °C 123.8^0.1 18.69^0.07 198.2^0.1 29.36^0.07 273.2^0.2 40.27^0.15 347.6^0.2 51.28^0.17 2,4-Dinitrophenyl methoxyacetate 5 °C 15 °C 8.07^0.03 4.37^0.03 8.06^0.03 6.68^0.04 15.34^0.04 8.22^0.07 15.33^0.04 12.57^0.09 22.73^0.04 12.04^0.07 22.71^0.04 18.57^0.07 29.99^0.05 16.02^0.11 29.96^0.05 24.43^0.05 25 °C 35 °C 8.04^0.03 9.93^0.07 8.02^0.03 14.62^0.10 15.29^0.04 18.89^0.09 15.25^0.04 27.4^0.3 22.66^0.04 27.7^0.2 22.60^0.04 40.5^0.6 29.90^0.05 36.4^0.2 29.81^0.05 53.1^0.3 45 °C 7.99^0.03 21.0^0.4 15.19^0.04 39.5^0.3 22.51^0.04 58.2^0.2 29.70^0.05 76.4^0.6 2,4-Dinitrophenyl chloroacetate 5 °C 15 °C 1.26^0.02 5.54^0.10 1.26^0.02 8.34^0.11 2.15^0.02 9.29^0.04 2.17^0.02 14.03^0.14 3.09^0.02 13.17^0.09 3.08^0.02 19.92^0.11 3.99^0.02 17.12^0.06 3.99^0.02 25.64^0.13 25 °C 35 °C 1.27^0.02 12.81^0.06 1.26^0.02 18.7^0.2 2.16^0.02 21.5^0.2 2.16^0.02 31.7^0.2 3.08^0.02 30.56^0.12 3.08^0.02 44.9^0.2 3.98^0.02 39.0^0.2 3.97^0.02 57.2^0.6 45 °C 1.26^0.02 26.7^0.2 2.15^0.02 45.2^0.5 3.06^0.02 62.9^0.7 3.94^0.02 81.5^1.3 the absorbance of the solution, A(t), taken at the wavelength of maximum absorption of the 2,4-dinitrophenolate ion (360 nm), is given by the pseudo-–rst-order kinetic equation, eqn.(3) A(t)\A=](A0[A=)e~kobs t (3) where A0 and A= are the absorbances at the beginning and at the end of the reaction. The computer program used, mcskin1 2594 Phys. Chem. Chem. Phys., 1999, 1, 2593»2596Table 4 Rate constants k and activation parameters of the imidazole catalyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates k/l mol~1 s~1 *Gº/ *Hº/ *Sº/ 5 °C 15 °C 25 °C 35 °C 45 °C kJ mol~1 kJ mol~1 J mol~1 k~1 2,4-Dinitrophenyl acetate 2.28^0.02 3.78^0.03 6.07^0.03 9.36^0.08 14.56^0.07 68.6^0.4 31.5^0.2 [124.2^0.8 2,4-Dinitrophenyl methoxyacetate 53.0^0.4 81.0^0.1 121.1^0.6 176.6^0.4 254.8^0.6 61.1^0.2 26.4^0.1 [116.5^0.5 2,4-Dinitrophenyl chloroacetate 423^4 635^3 968^8 1423^9 2037^20 56.0^0.6 26.6^0.3 [98.5^0.9 (developed in our laboratory for the non-linear optimization of rate equations) yields the –tted parameters A0, A= and kobs , their standard deviations, the number of half-life periods, and the turnover of the reaction. 3 Results The experimental rate constants of the imidazole catalyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates in water are collected in Table 3. They are mean values of 6»11 measurements over at least six half-life periods. The second-order rate constants k, given in Table 3, are obtained by linear least-squares –tting of eqn. (4) kobs\kH2O]kcIm (4) with respect to the concentration of imidazole (the correlation coefficients lie between 0.9997 and 0.9999). The neutral hydrolysis of the 2,4-dinitrophenyl acetates in aqueous solution is more than –ve orders of magnitude slower and, there- (kH2O) fore, need not be taken into account.The linear temperature dependence of the rate constants (ln(k/T ) vs. 1/T ) yields the activation parameters with correlation coefficients better than 0.9999. The activation quantities and are given in *Gº, *Hº, *Sº the last three columns of Table 4. The negative activation entropies are in the typical range for such reactions and show clearly the decrease of the degrees of freedom in the tetrahedral transition state.For the rate constant k of the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl acetate the following data can be found in the literature (6.49 l mol~1 s~1 at 26.2 °C in water,8 5.83 l mol~1 s~1 at 25 °C in water»0.4% acetonitrile,3,9 and 4 l mol~1 s~1 at 25 °C in water»3% acetonitrile10). Our result (6.07 l mol~1 s~1) is in good agreement with the –rst two data, whereas the last value shows the in—uence of the less solvating solvent acetonitrile.For the other two esters no experimental values can be found in the literature. 4 Discussion At the molecular level the Gibbs energy of activation, is *Gº, given by the amount of work, which is necessary to bring the imidazole molecule from in–nite distance to its place in the transition state, required to modify the electronic charge distribution in the tetrahedral activated complex, and to rearrange the solvent shell around the reaction centre.In the dielectric model of the transition state, shown in Fig. 2, the interesting contribution to this energy is the electrostatic energy, necessary to transfer the imidazole dipole *Gel , in the electrostatic potential h, r) of the ester molecule k2 t1(r, from a very large distance to the –nal position in the transition state, as is given by eqn. (5) : *Gel\[NA l2(E1(R, h, r)[E1(O, h, r))\NAWel (5a) E1(r, h, r)\[grad t1(r, h, r) (5b) E1(O, h, r)\0 (5c) The transition state is imbedded in a dielectric sphere with radius a and with internal permittivity and surrounded by ei , the homogenous solvent with permittivity e.The acid moiety is characterised by the dipole moment of the polar bond k1, C»Cl. The term R is the distance between the two dipoles, h1 and are the angles between the dipole vectors and this dis- h2 tance, and r is the dihedral angle between the two dipoles around the axis R. The electrostatic potential h, r) W1(r, results from the superposition of all charges within the molecule.The solution of the Poisson equations for the potential inside and outside of the dielectric sphere yields the potential h, r) and its gradient with the help of appropriate t1(r, boundary conditions. The resulting electrostatic energy W el , eqn. (6), Wel\ k1 k2 R3 GC1[ e[2 e]1 AR aB3Dsin h1 sin h2 cos r [C2] e[2 e]1 AR aB3Dcos h1 cos h2H]W @ (6) can be subdivided into the contribution of the substituent dipole (e.g.and the constant contribution W @ of the k1 kChCl) residual molecule, which will vanish in the energy diÜerence with respect to the unsubstituted reference molecule. R, and r are the relative coordinates of the two h1, h2 , dipoles in the transition state. Due to free rotation around the C»C-axis in the ester, the mean value of r is D90°, and therefore the –rst term in eqn. (6) is zero. The change in the rate constants is then given by eqn.(7) ln(k/k0)\ NA k2 RT C2] e[2 e]1 AR aB3D*Ak1 cos h1 cos h2 R3 B (7) Fig. 2 Model of the transition state of the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl chloroacetate (R\C6H3(NO2)2 . Phys. Chem. Chem. Phys., 1999, 1, 2593»2596 2595Table 5 Structural data and electrostatic substituent parameters cos cos of the esters The eÜective dipole *(k1 h1 h2/R3) RCO2C6H3(NO2)2 . moment of the methoxy group is calculated via the superposition of the two C»O dipoles in the direction of the C»O bond. (Substituent parameter: D nm~3; rate constants k and taken from Table 3 at 25 °C) k0 nCCX Rest R Bonding d/nm (°) R/nm cos h1 cos h2 kChX/D */(k1 cos1 cos h2/R3) log k/k0 C»C 0.154 C»N 0.147 CH3 C»H 0.107 109.5 0.376 0.362 0.892 [0.4 0.0 0.0 CH2OCH3 O»C 0.143 109.5 0.383 0.402 0.882 0.74 7.1 1.3 (O»CH3) (105) (1.1) CH2Cl Cl»C 0.176 110.0 0.390 0.437 0.871 1.46 11.8 2.2 with the substituent parameter according to eqn.(8) *Ak1 cos h1 cos h2 R3 B\Ak1 cos h1 cos h2 R3 B [Ak1 cos h1 cos h2 R3 B0 (8) In this model of the substituent parameter it is assumed, that the ratio (R/a) in eqn. (6) remains constant in the diÜerent molecules. The atomic distances, bond angles, and dipole moments are taken from standard tables.11,12 In the scope of this model, the geometrical parameters of stable compounds are taken also for the unstable transition states. Because only energy diÜerences are discussed, this procedure is justi–ed.The length R is determined as the distance between the centre of the dipole of the imidazole and the centre of the substituent dipole C»X Cl for the polar substi- (X\OCH3 , tuted esters, and H for the reference molecule with Index 0). The former point is calculated from the bond lengths and angles of the planar imidazole molecule13 and from its charge distribution14 as the midpoint between the negative and the positive charge. The latter point is calculated as the midpoint of the C»X bond from standard bond lengths and angles with the assumption r\90°. The relevant data for the calculations are given in Table 5.Fig. 3 shows the function cos cos log(k/k0)\f M*[(k1 h1 according to this electrostatic model. The linearity of h2)/R3]N the function (line 1 in the –gure) is ful–lled in the whole range. Line (2) in Fig. 3 is the straight line obtained from the neutral hydrolysis of ethyl acetates,4 which is ful–lled over seven decades for the rate constants.The diÜerence in slope is mainly due to the diÜerent dipole moments of water and imidazole. The ratio of the two (k2) slopes is f\2.47, whereas the ratio of the two dipole Fig. 3 Linear dependence of the rate shift at 25°C on the log(k/k0) electrostatic substituent parameter. Line (1) shows the linear dependence of the imidazole catalyzed hydrolysis, line (2) that of the neutral hydrolysis of the polar substituted ethyl acetates.4 moments D14 and D15; 1 (kImidazole\3.87 kH2O\1.85 DB3.335 64]10~30 C m) is 2.09.The consistency of the two values is remarkably good, taking into account that, on the one hand, the dipole moments are determined in the gas phase and, on the other hand, the slopes in Fig. 3 contain the in—uence of the solvent water on the reacting molecules and the transition state. This result shows that the solvation eÜects in the two series of esters remain nearly constant and play only a minor role in the discussion of the in—uence of polar substituents on the reaction rate.The in—uence of the two different leaving groups on the reaction rate is eliminated in the respective shifts of the rate constants, log(k/k0). Recent quantum-mechanical calculations of the neutral hydrolysis of polar substituted ethyl acetates16 at the ab initio level in the gas phase con–rm the assumption that electronegative substituents in the acyl moiety decrease the energy barrier of the tetrahedral transition state.Acknowledgements are grateful to the ììFonds der Chemischen Industrie We (Frankfurt/Main)œœ for –nancial support. References 1 G. Schmeer, C. Six and J. Steinkirchner, J. Solution Chem., 1999, 28, 211. 2 E. K. Euranto, Ann. Acad. Sci. Fenn., A 2, 1970, 152, 1. 3 J. F. Kirsch and W. P. Jencks, J. Am. Chem. Soc., 1964, 86, 837. 4 G. Schmeer and J. Barthel, Z. Phys. Chem. N.F., 1984, 140, 17. 5 D. E. Schmidt and F. H. Westheimer, Biochemistry, 1971, 10, 1249. 6 D. B. Olsen, T. W. Hepburn, S. Lee, B. M. Martin, P. S. Mariano and D. Dunaway-Mariano, Arch. Biochem. Biophys., 1992, 296, 144. 7 V. V. Katyshkina and M. Y. Kraft, J. Gen. Chem. USSR, 1959, 29, 65. 8 M. L. Bender and B. W. Turnquest, J. Am. Chem. Soc., 1957, 79, 1656. 9 W. P. Jencks and M. Gilchrist, J. Am. Chem. Soc., 1968, 90, 2622. 10 K. Koé hler, R. Skora and E. H. Cordes, J. Am. Chem. Soc., 1966, 88, 3577. 11 A. D. Mitchell, L. C. Cross and L. E. Sutton, in T able of Interatomic Distances and Con–guration in Molecules and Ions, Chemical Society, London, Specialist Publ. No. 11, 1958, pp. 1. 12 O. Exner, in Dipole Moments in Organic Chemistry, Georg Thieme Verlag, Stuttgart, 1975. 13 B. M. Craven, R. K. McMullan, J. D. Bell and H. C. Freeman, Acta Crystallogr. Sect. B, 33, 2585. 14 R. D. Brown and B. A. W. Coller, T heor. Chim. Acta, 1967, 7, 259. 15 P. W. Atkins, in Physical Chemistry, Oxford University Press, Oxford, 1990. 16 G. Schmeer and P. Sturm, Phys.Chem. Chem. Phys., 1999, 1, 1025. Paper 9/01004A 2596 Phys. Chem. Chem. Phys., 1999, 1, 2593»2596 Investigations on substituent and solvent eÜects on solvolysis reactions Part IX.§ The in—uence of polar substituents on the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl acetates in water J. Bittner and G. Schmeer* Institut Physikalische und T heoretische Chemie, Regensburg, D-93040 fué r Universitaé t Regensburg, Germany. E-mail : Georg.Schmeer=chemie.uni-regensburg.de Received 5th February 1999, Accepted 29th March 1999 The imidazole catalyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates in water has been investigated at diÜerent temperatures.The observed rates correspond to the bimolecular nucleophilic addition of the imidazole at the carboxylic carbon atom followed by a very fast hydrolysis of the N-acetylimidazole in water. The in—uence of polar substituents in the acid moiety of the ester molecule on the hydrolysis reaction can be described by an electrostatic dipole»dipole interaction in the same way as the neutral hydrolysis of polar substituted ethyl acetates. 1 Introduction The imidazole catalyzed hydrolysis of esters in water»see Fig. 1»proceeds via the addition of imidazole at the carboxylic carbon atom in the sense of nucleophilic catalysis (BAcN)2 forming a tetrahedral intermediate. This intermediate decomposes by the elimination of the alcohol or phenol group, yielding a very reactive N-acetylimidazole which is immediately hydrolysed in aqueous solution.The –nal formation of acids or their corresponding bases is controlled by the dissociation constants of the respective acids (alcohols, phenols and acetic acids). The general base catalysis by a second imidazole (BAc3)2 molecule is of less importance3 due to the relatively high acidity of the leaving 2,4-dinitrophenol and is not (pKS\4.1), observed in water. Therefore, the reaction is purely of –rst order in the ester and in imidazole (cf.eqn. (1)). [ dcEster dt \kcEster cIm (1) Fig. 1 Mechanism of the imidazole catalyzed hydrolysis of esters in water. § Part VIII, ref. 1. According to the neutral hydrolysis of polar substituted ethyl acetates,4 the rate determining step of the imidazole catalyzed hydrolysis in water is the formation of an intermediate like a mixed ester-amide of ortho-acetic acid via a tetrahedral transition state. According to the neutral hydrolysis of esters, one important contribution to the Gibbs energy of activation, should *Gº, be the electrostatic interaction energy of the dipolar nucleophile molecule (water, imidazole) with the ester molecule.Within the scope of this electrostatic model of the activation step, the change of the Gibbs energy of activation, in a **Gº, series of polar substituted esters with respect to the unsubstituted 2,4-dinitrophenyl acetate (Index 0) is correlated to the change of the electric –eld ([grad of the polar tEster) ester molecule, see eqn.(2). RgT ln(k0/k)\**Gº\*Gº[*G0º \[NA lNucl(grad tEster[grad tEster, 0) (2) is the gas constant, T the temperature, is the dipole Rg lNucl moment of the nucleophile, is the electrostatic potential tEster of the polar ester molecule, and is Avogadroœs number; NA and k and are the rate constants of the respective com- k0 pounds. The other contributions to remain nearly constant in *Gº the series of polar substituted esters and therefore vanish in eqn.(2). Since this simple treatment was very successful for the description of the substituent eÜect of polar substituents on the neutral and alkaline hydrolysis of esters, it should be tested to see if it can also be used for the imidazole catalyzed hydrolysis of esters in aqueous solutions. 2 Experimental The rate constants of the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl acetate, 2,4-dinitrophenyl methoxyacetate, and 2,4-dinitrophenyl chloroacetate have been measured in water between 5 and 45 °C.Phys. Chem. Chem. Phys., 1999, 1, 2593»2596 2593Table 1 Physical data of the prepared esters R-CO2C6H3(NO2)2 Yield (%) Melting point (q/°C) R Exptl. Lit. Exptl. Lit. CH3 55 606 69.5 706 CH3OCH2 53 » 85.5 » ClCH2 50 » 92.5 97»987 2.1 Materials The three esters (2,4-dinitrophenyl acetate, 2,4-dinitrophenyl methoxyacetate, and 2,4-dinitrophenyl chloroacetate) were prepared according to Schmidt and Westheimer.5 15 mmol 2,4-dinitrophenol and 15 mmol pyridine were dissolved in 100 ml dry diethyl ether.Subsequently, 15 mmol of the commercially available acetyl chloride, dissolved in 25 ml dry diethyl ether, was added at room temperature within 30 min. After stirring of the solution for 12 h to complete the reaction, the precipitated pyridinium hydrochloride was –ltrated oÜ and the solvent removed under reduced pressure. The remaining esters were recrystallized from chloroform/n-hexane mixtures (1 :4) until constant melting points were achieved.All procedures were done under dry nitrogen to prevent hydrolysis of the reagents and products. The physical data of the substances are given in Table 1. 2,4-Dinitrophenyl methoxyacetate has not yet been described in the literature (searches in Chemical Abstracts and Beilstein yielded negative results). Its 1H NMR data are given in Table 2. The observed lines in the NMR spectrum are in full accordance with the molecular structure. 1,4-Dioxane»the solvent of the ester stock solutions for the kinetic measurements»was treated with a molecular sieve (Merck, 0.4 nm) for 20 days to decrease the water content, as determined by the Karl Fischer method, from 50 to 15 ppm. The water was deionized via a Millipore column.Imidazole (puriss., Fluka) was used without further puri–- cation. The sodium hydroxide solutions were prepared from 0.1 m stock solutions (Merck) by dilution with water to the appropriate concentration.All solutions were held under nitrogen that was free of carbon dioxide. 2.2 Kinetic measurements The kinetic experiments were performed in a previously described optical apparatus with a multichannel diode array spectrometer1 for the detection of chemical reactions with time constants greater than 0.5 s in the wavelength range from 200 to 620 nm. After –lling the reaction cell with 20 ml of the aqueous solution of imidazole and attaining the appropriate temperature, the reaction was started by the injection of 30 ll of the ester solution.The volume ratio of the solutions of the esters in 1,4-dioxane to the aqueous solutions is less than 0.005 and therefore the in—uence of the organic solvent on the reaction is negligible. The solutions contain imidazole with at least twentyfold excess and therefore the time dependence of Table 2 1H NMR data for 2,4-dinitrophenyl methoxyacetatea d (ppm) Signal J(H»H)/Hz Irel Group 3.57 s » 3 »O»CH3 4.44 s » 2 »CO»CH2»O 9.00 d 2.7 1 Ar»H(3) 8.56 dd 8.9, 2.7 1 Ar»H(5) 7.53 d 8.9 1 Ar»H(6) a Solvent : reference : TMS.s : singlet, d: doublet, dd: double CDCl3 , doublet. The numbers at the aryl hydrogen atoms refer to the numbering of the 2,4-dinitrophenyl group. NMR spectrometer : Bruker AC-250. Table 3 Pseudo-–rst-order rate constants of the imidazole cata- kobs lyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates (units, 10~4 mol l~1, 10~2 s~1). cIm: kobs: cIm kobs cIm kobs 2,4-Dinitrophenyl acetate 5 °C 15 °C 125.0^0.1 2.99^0.03 124.9^0.1 4.97^0.02 200.2^0.1 4.72^0.03 200.0^0.1 7.75^0.03 275.5^0.2 6.49^0.02 275.3^0.2 10.69^0.02 351.1^0.2 8.14^0.03 350.8^0.2 13.47^0.03 25 °C 35 °C 124.7^0.1 7.83^0.01 124.3^0.1 12.06^0.03 199.6^0.1 12.45^0.06 199.0^0.1 19.08^0.10 274.7^0.2 17.01^0.03 274.2^0.2 26.29^0.08 350.0^0.2 21.52^0.06 349.0^0.2 33.03^0.07 45 °C 123.8^0.1 18.69^0.07 198.2^0.1 29.36^0.07 273.2^0.2 40.27^0.15 347.6^0.2 51.28^0.17 2,4-Dinitrophenyl methoxyacetate 5 °C 15 °C 8.07^0.03 4.37^0.03 8.06^0.03 6.68^0.04 15.34^0.04 8.22^0.07 15.33^0.04 12.57^0.09 22.73^0.04 12.04^0.07 22.71^0.04 18.57^0.07 29.99^0.05 16.02^0.11 29.96^0.05 24.43^0.05 25 °C 35 °C 8.04^0.03 9.93^0.07 8.02^0.03 14.62^0.10 15.29^0.04 18.89^0.09 15.25^0.04 27.4^0.3 22.66^0.04 27.7^0.2 22.60^0.04 40.5^0.6 29.90^0.05 36.4^0.2 29.81^0.05 53.1^0.3 45 °C 7.99^0.03 21.0^0.4 15.19^0.04 39.5^0.3 22.51^0.04 58.2^0.2 29.70^0.05 76.4^0.6 2,4-Dinitrophenyl chloroacetate 5 °C 15 °C 1.26^0.02 5.54^0.10 1.26^0.02 8.34^0.11 2.15^0.02 9.29^0.04 2.17^0.02 14.03^0.14 3.09^0.02 13.17^0.09 3.08^0.02 19.92^0.11 3.99^0.02 17.12^0.06 3.99^0.02 25.64^0.13 25 °C 35 °C 1.27^0.02 12.81^0.06 1.26^0.02 18.7^0.2 2.16^0.02 21.5^0.2 2.16^0.02 31.7^0.2 3.08^0.02 30.56^0.12 3.08^0.02 44.9^0.2 3.98^0.02 39.0^0.2 3.97^0.02 57.2^0.6 45 °C 1.26^0.02 26.7^0.2 2.15^0.02 45.2^0.5 3.06^0.02 62.9^0.7 3.94^0.02 81.5^1.3 the absorbance of the solution, A(t), taken at the wavelength of maximum absorption of the 2,4-dinitrophenolate ion (360 nm), is given by the pseudo-–rst-order kinetic equation, eqn.(3) A(t)\A=](A0[A=)e~kobs t (3) where A0 and A= are the absorbances at the beginning and at the end of the reaction. The computer program used, mcskin1 2594 Phys. Chem. Chem. Phys., 1999, 1, 2593»2596Table 4 Rate constants k and activation parameters of the imidazole catalyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates k/l mol~1 s~1 *Gº/ *Hº/ *Sº/ 5 °C 15 °C 25 °C 35 °C 45 °C kJ mol~1 kJ mol~1 J mol~1 k~1 2,4-Dinitrophenyl acetate 2.28^0.02 3.78^0.03 6.07^0.03 9.36^0.08 14.56^0.07 68.6^0.4 31.5^0.2 [124.2^0.8 2,4-Dinitrophenyl methoxyacetate 53.0^0.4 81.0^0.1 121.1^0.6 176.6^0.4 254.8^0.6 61.1^0.2 26.4^0.1 [116.5^0.5 2,4-Dinitrophenyl chloroacetate 423^4 635^3 968^8 1423^9 2037^20 56.0^0.6 26.6^0.3 [98.5^0.9 (developed in our laboratory for the non-linear optimization of rate equations) yields the –tted parameters A0, A= and kobs , their standard deviations, the number of half-life periods, and the turnover of the reaction. 3 Results The experimental rate constants of the imidazole catalyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates in water are collected in Table 3. They are mean values of 6»11 measurements over at least six half-life periods. The second-order rate constants k, given in Table 3, are obtained by linear least-squares –tting of eqn.(4) kobs\kH2O]kcIm (4) with respect to the concentration of imidazole (the correlation coefficients lie between 0.9997 and 0.9999). The neutral hydrolysis of the 2,4-dinitrophenyl acetates in aqueous solution is more than –ve orders of magnitude slower and, there- (kH2O) fore, need not be taken into account. The linear temperature dependence of the rate constants (ln(k/T ) vs. 1/T ) yields the activation parameters with correlation coefficients better than 0.9999.The activation quantities and are given in *Gº, *Hº, *Sº the last three columns of Table 4. The negative activation entropies are in the typical range for such reactions and show clearly the decrease of the degrees of freedom in the tetrahedral transition state. For the rate constant k of the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl acetate the following data can be found in the literature (6.49 l mol~1 s~1 at 26.2 °C in water,8 5.83 l mol~1 s~1 at 25 °C in water»0.4% acetonitrile,3,9 and 4 l mol~1 s~1 at 25 °C in water»3% acetonitrile10).Our result (6.07 l mol~1 s~1) is in good agreement with the –rst two data, whereas the last value shows the in—uence of the less solvating solvent acetonitrile. For the other two esters no experimental values can be found in the literature. 4 Discussion At the molecular level the Gibbs energy of activation, is *Gº, given by the amount of work, which is necessary to bring the imidazole molecule from in–nite distance to its place in the transition state, required to modify the electronic charge distribution in the tetrahedral activated complex, and to rearrange the solvent shell around the reaction centre.In the dielectric model of the transition state, shown in Fig. 2, the interesting contribution to this energy is the electrostatic energy, necessary to transfer the imidazole dipole *Gel , in the electrostatic potential h, r) of the ester molecule k2 t1(r, from a very large distance to the –nal position in the transition state, as is given by eqn.(5) : *Gel\[NA l2(E1(R, h, r)[E1(O, h, r))\NAWel (5a) E1(r, h, r)\[grad t1(r, h, r) (5b) E1(O, h, r)\0 (5c) The transition state is imbedded in a dielectric sphere with radius a and with internal permittivity and surrounded by ei , the homogenous solvent with permittivity e. The acid moiety is characterised by the dipole moment of the polar bond k1, C»Cl. The term R is the distance between the two dipoles, h1 and are the angles between the dipole vectors and this dis- h2 tance, and r is the dihedral angle between the two dipoles around the axis R.The electrostatic potential h, r) W1(r, results from the superposition of all charges within the molecule. The solution of the Poisson equations for the potential inside and outside of the dielectric sphere yields the potential h, r) and its gradient with the help of appropriate t1(r, boundary conditions. The resulting electrostatic energy W el , eqn.(6), Wel\ k1 k2 R3 GC1[ e[2 e]1 AR aB3Dsin h1 sin h2 cos r [C2] e[2 e]1 AR aB3Dcos h1 cos h2H]W @ (6) can be subdivided into the contribution of the substituent dipole (e.g. and the constant contribution W @ of the k1 kChCl) residual molecule, which will vanish in the energy diÜerence with respect to the unsubstituted reference molecule. R, and r are the relative coordinates of the two h1, h2 , dipoles in the transition state. Due to free rotation around the C»C-axis in the ester, the mean value of r is D90°, and therefore the –rst term in eqn. (6) is zero.The change in the rate constants is then given by eqn. (7) ln(k/k0)\ NA k2 RT C2] e[2 e]1 AR aB3D*Ak1 cos h1 cos h2 R3 B (7) Fig. 2 Model of the transition state of the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl chloroacetate (R\C6H3(NO2)2 . Phys. Chem. Chem. Phys., 1999, 1, 2593»2596 2595Table 5 Structural data and electrostatic substituent parameters cos cos of the esters The eÜective dipole *(k1 h1 h2/R3) RCO2C6H3(NO2)2 .moment of the methoxy group is calculated via the superposition of the two C»O dipoles in the direction of the C»O bond. (Substituent parameter: D nm~3; rate constants k and taken from Table 3 at 25 °C) k0 nCCX Rest R Bonding d/nm (°) R/nm cos h1 cos h2 kChX/D */(k1 cos1 cos h2/R3) log k/k0 C»C 0.154 C»N 0.147 CH3 C»H 0.107 109.5 0.376 0.362 0.892 [0.4 0.0 0.0 CH2OCH3 O»C 0.143 109.5 0.383 0.402 0.882 0.74 7.1 1.3 (O»CH3) (105) (1.1) CH2Cl Cl»C 0.176 110.0 0.390 0.437 0.871 1.46 11.8 2.2 with the substituent parameter according to eqn.(8) *Ak1 cos h1 cos h2 R3 B\Ak1 cos h1 cos h2 R3 B [Ak1 cos h1 cos h2 R3 B0 (8) In this model of the substituent parameter it is assumed, that the ratio (R/a) in eqn. (6) remains constant in the diÜerent molecules. The atomic distances, bond angles, and dipole moments are taken from standard tables.11,12 In the scope of this model, the geometrical parameters of stable compounds are taken also for the unstable transition states.Because only energy diÜerences are discussed, this procedure is justi–ed. The length R is determined as the distance between the centre of the dipole of the imidazole and the centre of the substituent dipole C»X Cl for the polar substi- (X\OCH3 , tuted esters, and H for the reference molecule with Index 0). The former point is calculated from the bond lengths and angles of the planar imidazole molecule13 and from its charge distribution14 as the midpoint between the negative and the positive charge.The latter point is calculated as the midpoint of the C»X bond from standard bond lengths and angles with the assumption r\90°. The relevant data for the calculations are given in Table 5. Fig. 3 shows the function cos cos log(k/k0)\f M*[(k1 h1 according to this electrostatic model. The linearity of h2)/R3]N the function (line 1 in the –gure) is ful–lled in the whole range.Line (2) in Fig. 3 is the straight line obtained from the neutral hydrolysis of ethyl acetates,4 which is ful–lled over seven decades for the rate constants. The diÜerence in slope is mainly due to the diÜerent dipole moments of water and imidazole. The ratio of the two (k2) slopes is f\2.47, whereas the ratio of the two dipole Fig. 3 Linear dependence of the rate shift at 25°C on the log(k/k0) electrostatic substituent parameter. Line (1) shows the linear dependence of the imidazole catalyzed hydrolysis, line (2) that of the neutral hydrolysis of the polar substituted ethyl acetates.4 moments D14 and D15; 1 (kImidazole\3.87 kH2O\1.85 DB3.335 64]10~30 C m) is 2.09.The consistency of the two values is remarkably good, taking into account that, on the one hand, the dipole moments are determined in the gas phase and, on the other hand, the slopes in Fig. 3 contain the in—uence of the solvent water on the reacting molecules and the transition state. This result shows that the solvation eÜects in the two series of esters remain nearly constant and play only a minor role in the discussion of the in—uence of polar substituents on the reaction rate.The in—uence of the two different leaving groups on the reaction rate is eliminated in the respective shifts of the rate constants, log(k/k0). Recent quantum-mechanical calculations of the neutral hydrolysis of polar substituted ethyl acetates16 at the ab initio level in the gas phase con–rm the assumption that electronegative substituents in the acyl moiety decrease the energy barrier of the tetrahedral transition state. Acknowledgements are grateful to the ììFonds der Chemischen Industrie We (Frankfurt/Main)œœ for –nancial support.References 1 G. Schmeer, C. Six and J. Steinkirchner, J. Solution Chem., 1999, 28, 211. 2 E. K. Euranto, Ann. Acad. Sci. Fenn., A 2, 1970, 152, 1. 3 J. F. Kirsch and W. P. Jencks, J. Am. Chem. Soc., 1964, 86, 837. 4 G. Schmeer and J. Barthel, Z. Phys. Chem. N.F., 1984, 140, 17. 5 D. E. Schmidt and F. H. Westheimer, Biochemistry, 1971, 10, 1249. 6 D. B. Olsen, T. W. Hepburn, S. Lee, B. M. Martin, P. S. Mariano and D. Dunaway-Mariano, Arch. Biochem. Biophys., 1992, 296, 144. 7 V. V. Katyshkina and M. Y. Kraft, J. Gen. Chem. USSR, 1959, 29, 65. 8 M. L. Bender and B. W. Turnquest, J. Am. Chem. Soc., 1957, 79, 1656. 9 W. P. Jencks and M. Gilchrist, J. Am. Chem. Soc., 1968, 90, 2622. 10 K. Koé hler, R.Skora and E. H. Cordes, J. Am. Chem. Soc., 1966, 88, 3577. 11 A. D. Mitchell, L. C. Cross and L. E. Sutton, in T able of Interatomic Distances and Con–guration in Molecules and Ions, Chemical Society, London, Specialist Publ. No. 11, 1958, pp. 1. 12 O. Exner, in Dipole Moments in Organic Chemistry, Georg Thieme Verlag, Stuttgart, 1975. 13 B. M. Craven, R. K. McMullan, J. D. Bell and H. C. Freeman, Acta Crystallogr. Sect. B, 33, 2585. 14 R. D. Brown and B. A. W. Coller, T heor.Chim. Acta, 1967, 7, 259. 15 P. W. Atkins, in Physical Chemistry, Oxford University Press, Oxford, 1990. 16 G. Schmeer and P. Sturm, Phys. Chem. Chem. Phys., 1999, 1, 1025. Paper 9/01004A 2596 Phys. Chem. Chem. Phys., 1999, 1, 2593»2596 Investigations on substituent and solvent eÜects on solvolysis reactions Part IX.§ The in—uence of polar substituents on the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl acetates in water J. Bittner and G. Schmeer* Institut Physikalische und T heoretische Chemie, Regensburg, D-93040 fué r Universitaé t Regensburg, Germany.E-mail : Georg.Schmeer=chemie.uni-regensburg.de Received 5th February 1999, Accepted 29th March 1999 The imidazole catalyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates in water has been investigated at diÜerent temperatures. The observed rates correspond to the bimolecular nucleophilic addition of the imidazole at the carboxylic carbon atom followed by a very fast hydrolysis of the N-acetylimidazole in water.The in—uence of polar substituents in the acid moiety of the ester molecule on the hydrolysis reaction can be described by an electrostatic dipole»dipole interaction in the same way as the neutral hydrolysis of polar substituted ethyl acetates. 1 Introduction The imidazole catalyzed hydrolysis of esters in water»see Fig. 1»proceeds via the addition of imidazole at the carboxylic carbon atom in the sense of nucleophilic catalysis (BAcN)2 forming a tetrahedral intermediate.This intermediate decomposes by the elimination of the alcohol or phenol group, yielding a very reactive N-acetylimidazole which is immediately hydrolysed in aqueous solution. The –nal formation of acids or their corresponding bases is controlled by the dissociation constants of the respective acids (alcohols, phenols and acetic acids). The general base catalysis by a second imidazole (BAc3)2 molecule is of less importance3 due to the relatively high acidity of the leaving 2,4-dinitrophenol and is not (pKS\4.1), observed in water.Therefore, the reaction is purely of –rst order in the ester and in imidazole (cf. eqn. (1)). [ dcEster dt \kcEster cIm (1) Fig. 1 Mechanism of the imidazole catalyzed hydrolysis of esters in water. § Part VIII, ref. 1. According to the neutral hydrolysis of polar substituted ethyl acetates,4 the rate determining step of the imidazole catalyzed hydrolysis in water is the formation of an intermediate like a mixed ester-amide of ortho-acetic acid via a tetrahedral transition state.According to the neutral hydrolysis of esters, one important contribution to the Gibbs energy of activation, should *Gº, be the electrostatic interaction energy of the dipolar nucleophile molecule (water, imidazole) with the ester molecule. Within the scope of this electrostatic model of the activation step, the change of the Gibbs energy of activation, in a **Gº, series of polar substituted esters with respect to the unsubstituted 2,4-dinitrophenyl acetate (Index 0) is correlated to the change of the electric –eld ([grad of the polar tEster) ester molecule, see eqn.(2). RgT ln(k0/k)\**Gº\*Gº[*G0º \[NA lNucl(grad tEster[grad tEster, 0) (2) is the gas constant, T the temperature, is the dipole Rg lNucl moment of the nucleophile, is the electrostatic potential tEster of the polar ester molecule, and is Avogadroœs number; NA and k and are the rate constants of the respective com- k0 pounds.The other contributions to remain nearly constant in *Gº the series of polar substituted esters and therefore vanish in eqn. (2). Since this simple treatment was very successful for the description of the substituent eÜect of polar substituents on the neutral and alkaline hydrolysis of esters, it should be tested to see if it can also be used for the imidazole catalyzed hydrolysis of esters in aqueous solutions. 2 Experimental The rate constants of the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl acetate, 2,4-dinitrophenyl methoxyacetate, and 2,4-dinitrophenyl chloroacetate have been measured in water between 5 and 45 °C.Phys. Chem. Chem. Phys., 1999, 1, 2593»2596 2593Table 1 Physical data of the prepared esters R-CO2C6H3(NO2)2 Yield (%) Melting point (q/°C) R Exptl. Lit. Exptl. Lit. CH3 55 606 69.5 706 CH3OCH2 53 » 85.5 » ClCH2 50 » 92.5 97»987 2.1 Materials The three esters (2,4-dinitrophenyl acetate, 2,4-dinitrophenyl methoxyacetate, and 2,4-dinitrophenyl chloroacetate) were prepared according to Schmidt and Westheimer.5 15 mmol 2,4-dinitrophenol and 15 mmol pyridine were dissolved in 100 ml dry diethyl ether. Subsequently, 15 mmol of the commercially available acetyl chloride, dissolved in 25 ml dry diethyl ether, was added at room temperature within 30 min. After stirring of the solution for 12 h to complete the reaction, the precipitated pyridinium hydrochloride was –ltrated oÜ and the solvent removed under reduced pressure.The remaining esters were recrystallized from chloroform/n-hexane mixtures (1 :4) until constant melting points were achieved. All procedures were done under dry nitrogen to prevent hydrolysis of the reagents and products. The physical data of the substances are given in Table 1. 2,4-Dinitrophenyl methoxyacetate has not yet been described in the literature (searches in Chemical Abstracts and Beilstein yielded negative results).Its 1H NMR data are given in Table 2. The observed lines in the NMR spectrum are in full accordance with the molecular structure. 1,4-Dioxane»the solvent of the ester stock solutions for the kinetic measurements»was treated with a molecular sieve (Merck, 0.4 nm) for 20 days to decrease the water content, as determined by the Karl Fischer method, from 50 to 15 ppm. The water was deionized via a Millipore column. Imidazole (puriss., Fluka) was used without further puri–- cation.The sodium hydroxide solutions were prepared from 0.1 m stock solutions (Merck) by dilution with water to the appropriate concentration. All solutions were held under nitrogen that was free of carbon dioxide. 2.2 Kinetic measurements The kinetic experiments were performed in a previously described optical apparatus with a multichannel diode array spectrometer1 for the detection of chemical reactions with time constants greater than 0.5 s in the wavelength range from 200 to 620 nm.After –lling the reaction cell with 20 ml of the aqueous solution of imidazole and attaining the appropriate temperature, the reaction was started by the injection of 30 ll of the ester solution. The volume ratio of the solutions of the esters in 1,4-dioxane to the aqueous solutions is less than 0.005 and therefore the in—uence of the organic solvent on the reaction is negligible. The solutions contain imidazole with at least twentyfold excess and therefore the time dependence of Table 2 1H NMR data for 2,4-dinitrophenyl methoxyacetatea d (ppm) Signal J(H»H)/Hz Irel Group 3.57 s » 3 »O»CH3 4.44 s » 2 »CO»CH2»O 9.00 d 2.7 1 Ar»H(3) 8.56 dd 8.9, 2.7 1 Ar»H(5) 7.53 d 8.9 1 Ar»H(6) a Solvent : reference : TMS.s : singlet, d: doublet, dd: double CDCl3 , doublet. The numbers at the aryl hydrogen atoms refer to the numbering of the 2,4-dinitrophenyl group. NMR spectrometer : Bruker AC-250. Table 3 Pseudo-–rst-order rate constants of the imidazole cata- kobs lyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates (units, 10~4 mol l~1, 10~2 s~1).cIm: kobs: cIm kobs cIm kobs 2,4-Dinitrophenyl acetate 5 °C 15 °C 125.0^0.1 2.99^0.03 124.9^0.1 4.97^0.02 200.2^0.1 4.72^0.03 200.0^0.1 7.75^0.03 275.5^0.2 6.49^0.02 275.3^0.2 10.69^0.02 351.1^0.2 8.14^0.03 350.8^0.2 13.47^0.03 25 °C 35 °C 124.7^0.1 7.83^0.01 124.3^0.1 12.06^0.03 199.6^0.1 12.45^0.06 199.0^0.1 19.08^0.10 274.7^0.2 17.01^0.03 274.2^0.2 26.29^0.08 350.0^0.2 21.52^0.06 349.0^0.2 33.03^0.07 45 °C 123.8^0.1 18.69^0.07 198.2^0.1 29.36^0.07 273.2^0.2 40.27^0.15 347.6^0.2 51.28^0.17 2,4-Dinitrophenyl methoxyacetate 5 °C 15 °C 8.07^0.03 4.37^0.03 8.06^0.03 6.68^0.04 15.34^0.04 8.22^0.07 15.33^0.04 12.57^0.09 22.73^0.04 12.04^0.07 22.71^0.04 18.57^0.07 29.99^0.05 16.02^0.11 29.96^0.05 24.43^0.05 25 °C 35 °C 8.04^0.03 9.93^0.07 8.02^0.03 14.62^0.10 15.29^0.04 18.89^0.09 15.25^0.04 27.4^0.3 22.66^0.04 27.7^0.2 22.60^0.04 40.5^0.6 29.90^0.05 36.4^0.2 29.81^0.05 53.1^0.3 45 °C 7.99^0.03 21.0^0.4 15.19^0.04 39.5^0.3 22.51^0.04 58.2^0.2 29.70^0.05 76.4^0.6 2,4-Dinitrophenyl chloroacetate 5 °C 15 °C 1.26^0.02 5.54^0.10 1.26^0.02 8.34^0.11 2.15^0.02 9.29^0.04 2.17^0.02 14.03^0.14 3.09^0.02 13.17^0.09 3.08^0.02 19.92^0.11 3.99^0.02 17.12^0.06 3.99^0.02 25.64^0.13 25 °C 35 °C 1.27^0.02 12.81^0.06 1.26^0.02 18.7^0.2 2.16^0.02 21.5^0.2 2.16^0.02 31.7^0.2 3.08^0.02 30.56^0.12 3.08^0.02 44.9^0.2 3.98^0.02 39.0^0.2 3.97^0.02 57.2^0.6 45 °C 1.26^0.02 26.7^0.2 2.15^0.02 45.2^0.5 3.06^0.02 62.9^0.7 3.94^0.02 81.5^1.3 the absorbance of the solution, A(t), taken at the wavelength of maximum absorption of the 2,4-dinitrophenolate ion (360 nm), is given by the pseudo-–rst-order kinetic equation, eqn.(3) A(t)\A=](A0[A=)e~kobs t (3) where A0 and A= are the absorbances at the beginning and at the end of the reaction. The computer program used, mcskin1 2594 Phys. Chem. Chem.Phys., 1999, 1, 2593»2596Table 4 Rate constants k and activation parameters of the imidazole catalyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates k/l mol~1 s~1 *Gº/ *Hº/ *Sº/ 5 °C 15 °C 25 °C 35 °C 45 °C kJ mol~1 kJ mol~1 J mol~1 k~1 2,4-Dinitrophenyl acetate 2.28^0.02 3.78^0.03 6.07^0.03 9.36^0.08 14.56^0.07 68.6^0.4 31.5^0.2 [124.2^0.8 2,4-Dinitrophenyl methoxyacetate 53.0^0.4 81.0^0.1 121.1^0.6 176.6^0.4 254.8^0.6 61.1^0.2 26.4^0.1 [116.5^0.5 2,4-Dinitrophenyl chloroacetate 423^4 635^3 968^8 1423^9 2037^20 56.0^0.6 26.6^0.3 [98.5^0.9 (developed in our laboratory for the non-linear optimization of rate equations) yields the –tted parameters A0, A= and kobs , their standard deviations, the number of half-life periods, and the turnover of the reaction. 3 Results The experimental rate constants of the imidazole catalyzed hydrolysis of polar substituted 2,4-dinitrophenyl acetates in water are collected in Table 3. They are mean values of 6»11 measurements over at least six half-life periods.The second-order rate constants k, given in Table 3, are obtained by linear least-squares –tting of eqn. (4) kobs\kH2O]kcIm (4) with respect to the concentration of imidazole (the correlation coefficients lie between 0.9997 and 0.9999). The neutral hydrolysis of the 2,4-dinitrophenyl acetates in aqueous solution is more than –ve orders of magnitude slower and, there- (kH2O) fore, need not be taken into account. The linear temperature dependence of the rate constants (ln(k/T ) vs. 1/T ) yields the activation parameters with correlation coefficients better than 0.9999. The activation quantities and are given in *Gº, *Hº, *Sº the last three columns of Table 4. The negative activation entropies are in the typical range for such reactions and show clearly the decrease of the degrees of freedom in the tetrahedral transition state. For the rate constant k of the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl acetate the following data can be found in the literature (6.49 l mol~1 s~1 at 26.2 °C in water,8 5.83 l mol~1 s~1 at 25 °C in water»0.4% acetonitrile,3,9 and 4 l mol~1 s~1 at 25 °C in water»3% acetonitrile10).Our result (6.07 l mol~1 s~1) is in good agreement with the –rst two data, whereas the last value shows the in—uence of the less solvating solvent acetonitrile. For the other two esters no experimental values can be found in the literature. 4 Discussion At the molecular level the Gibbs energy of activation, is *Gº, given by the amount of work, which is necessary to bring the imidazole molecule from in–nite distance to its place in the transition state, required to modify the electronic charge distribution in the tetrahedral activated complex, and to rearrange the solvent shell around the reaction centre.In the dielectric model of the transition state, shown in Fig. 2, the interesting contribution to this energy is the electrostatic energy, necessary to transfer the imidazole dipole *Gel , in the electrostatic potential h, r) of the ester molecule k2 t1(r, from a very large distance to the –nal position in the transition state, as is given by eqn.(5) : *Gel\[NA l2(E1(R, h, r)[E1(O, h, r))\NAWel (5a) E1(r, h, r)\[grad t1(r, h, r) (5b) E1(O, h, r)\0 (5c) The transition state is imbedded in a dielectric sphere with radius a and with internal permittivity and surrounded by ei , the homogenous solvent with permittivity e.The acid moiety is characterised by the dipole moment of the polar bond k1, C»Cl. The term R is the distance between the two dipoles, h1 and are the angles between the dipole vectors and this dis- h2 tance, and r is the dihedral angle between the two dipoles around the axis R. The electrostatic potential h, r) W1(r, results from the superposition of all charges within the molecule. The solution of the Poisson equations for the potential inside and outside of the dielectric sphere yields the potential h, r) and its gradient with the help of appropriate t1(r, boundary conditions.The resulting electrostatic energy W el , eqn. (6), Wel\ k1 k2 R3 GC1[ e[2 e]1 AR aB3Dsin h1 sin h2 cos r [C2] e[2 e]1 AR aB3Dcos h1 cos h2H]W @ (6) can be subdivided into the contribution of the substituent dipole (e.g. and the constant contribution W @ of the k1 kChCl) residual molecule, which will vanish in the energy diÜerence with respect to the unsubstituted reference molecule.R, and r are the relative coordinates of the two h1, h2 , dipoles in the transition state. Due to free rotation around the C»C-axis in the ester, the mean value of r is D90°, and therefore the –rst term in eqn. (6) is zero. The change in the rate constants is then given by eqn. (7) ln(k/k0)\ NA k2 RT C2] e[2 e]1 AR aB3D*Ak1 cos h1 cos h2 R3 B (7) Fig. 2 Model of the transition state of the imidazole catalyzed hydrolysis of 2,4-dinitrophenyl chloroacetate (R\C6H3(NO2)2 .Phys. Chem. Chem. Phys., 1999, 1, 2593»2596 2595Table 5 Structural data and electrostatic substituent parameters cos cos of the esters The eÜective dipole *(k1 h1 h2/R3) RCO2C6H3(NO2)2 . moment of the methoxy group is calculated via the superposition of the two C»O dipoles in the direction of the C»O bond. (Substituent parameter: D nm~3; rate constants k and taken from Table 3 at 25 °C) k0 nCCX Rest R Bonding d/nm (°) R/nm cos h1 cos h2 kChX/D */(k1 cos1 cos h2/R3) log k/k0 C»C 0.154 C»N 0.147 CH3 C»H 0.107 109.5 0.376 0.362 0.892 [0.4 0.0 0.0 CH2OCH3 O»C 0.143 109.5 0.383 0.402 0.882 0.74 7.1 1.3 (O»CH3) (105) (1.1) CH2Cl Cl»C 0.176 110.0 0.390 0.437 0.871 1.46 11.8 2.2 with the substituent parameter according to eqn.(8) *Ak1 cos h1 cos h2 R3 B\Ak1 cos h1 cos h2 R3 B [Ak1 cos h1 cos h2 R3 B0 (8) In this model of the substituent parameter it is assumed, that the ratio (R/a) in eqn. (6) remains constant in the diÜerent molecules. The atomic distances, bond angles, and dipole moments are taken from standard tables.11,12 In the scope of this model, the geometrical parameters of stable compounds are taken also for the unstable transition states.Because only energy diÜerences are discussed, this procedure is justi–ed. The length R is determined as the distance between the centre of the dipole of the imidazole and the centre of the substituent dipole C»X Cl for the polar substi- (X\OCH3 , tuted esters, and H for the reference molecule with Index 0).The former point is calculated from the bond lengths and angles of the planar imidazole molecule13 and from its charge distribution14 as the midpoint between the negative and the positive charge. The latter point is calculated as the midpoint of the C»X bond from standard bond lengths and angles with the assumption r\90°. The relevant data for the calculations are given in Table 5. Fig. 3 shows the function cos cos log(k/k0)\f M*[(k1 h1 according to this electrostatic model.The linearity of h2)/R3]N the function (line 1 in the –gure) is ful–lled in the whole range. Line (2) in Fig. 3 is the straight line obtained from the neutral hydrolysis of ethyl acetates,4 which is ful–lled over seven decades for the rate constants. The diÜerence in slope is mainly due to the diÜerent dipole moments of water and imidazole. The ratio of the two (k2) slopes is f\2.47, whereas the ratio of the two dipole Fig. 3 Linear dependence of the rate shift at 25°C on the log(k/k0) electrostatic substituent parameter. Line (1) shows the linear dependence of the imidazole catalyzed hydrolysis, line (2) that of the neutral hydrolysis of the polar substituted ethyl acetates.4 moments D14 and D15; 1 (kImidazole\3.87 kH2O\1.85 DB3.335 64]10~30 C m) is 2.09. The consistency of the two values is remarkably good, taking into account that, on the one hand, the dipole moments are determined in the gas phase and, on the other hand, the slopes in Fig. 3 contain the in—uence of the solvent water on the reacting molecules and the transition state. This result shows that the solvation eÜects in the two series of esters remain nearly constant and play only a minor role in the discussion of the in—uence of polar substituents on the reaction rate. The in—uence of the two different leaving groups on the reaction rate is eliminated in the respective shifts of the rate constants, log(k/k0). Recent quantum-mechanical calculations of the neutral hydrolysis of polar substituted ethyl acetates16 at the ab initio level in the gas phase con–rm the assumption that electronegative substituents in the acyl moiety decrease the energy barrier of the tetrahedral transition state. Acknowledgements are grateful to the ììFonds der Chemischen Industrie We (Frankfurt/Main)œœ for –nancial support. References 1 G. Schmeer, C. Six and J. Steinkirchner, J. Solution Chem., 1999, 28, 211. 2 E. K. Euranto, Ann. Acad. Sci. Fenn., A 2, 1970, 152, 1. 3 J. F. Kirsch and W. P. Jencks, J. Am. Chem. Soc., 1964, 86, 837. 4 G. Schmeer and J. Barthel, Z. Phys. Chem. N.F., 1984, 140, 17. 5 D. E. Schmidt and F. H. Westheimer, Biochemistry, 1971, 10, 1249. 6 D. B. Olsen, T. W. Hepburn, S. Lee, B. M. Martin, P. S. Mariano and D. Dunaway-Mariano, Arch. Biochem. Biophys., 1992, 296, 144. 7 V. V. Katyshkina and M. Y. Kraft, J. Gen. Chem. USSR, 1959, 29, 65. 8 M. L. Bender and B. W. Turnquest, J. Am. Chem. Soc., 1957, 79, 1656. 9 W. P. Jencks and M. Gilchrist, J. Am. Chem. Soc., 1968, 90, 2622. 10 K. Koé hler, R. Skora and E. H. Cordes, J. Am. Chem. Soc., 1966, 88, 3577. 11 A. D. Mitchell, L. C. Cross and L. E. Sutton, in T able of Interatomic Distances and Con–guration in Molecules and Ions, Chemical Society, London, Specialist Publ. No. 11, 1958, pp. 1. 12 O. Exner, in Dipole Moments in Organic Chemistry, Georg Thieme Verlag, Stuttgart, 1975. 13 B. M. Craven, R. K. McMullan, J. D. Bell and H. C. Freeman, Acta Crystallogr. Sect. B, 33, 2585. 14 R. D. Brown and B. A. W. Coller, T heor. Chim. Acta, 1967, 7, 259. 15 P. W. Atkins, in Physical Chemistry, Oxford University Press, Oxford, 1990. 16 G. Schmeer and P. Sturm, Phys. Chem. Chem. Phys., 1999, 1, 1025. Paper 9/01004A 2596 Phys. Chem. Chem. Phys., 1999, 1, 2593»2596