1721
Anal. Chem. 1985, 57. 1721-1725
with excellent agreement with data gathered on individual components as-shown in Figure 2a and in Table I. Fitting the V matrix one column a t a time takes a proportionally much longer computation than that for the twocomponent case since the npK's must be optimized ( n + 1) times. For each column of V, the success of the fitting procedure was found to be significantly influenced by the starting values of the n pK's and the ( n 1)values hgk,in eq 8; for the results in Table I, the search had to be initiated near the optimum determined previously by least squares value decomposition, as above. The spectral and pK errors are reasonable for components which are titrated at the lowest and highest pH, methyl orange and phenol red. The two components titrated at intermediate pH values, bromcresol green and chlorophenol red, have been confused by the single column analysis as indicated by the large range of pK values found and the ten times larger spectral error, as illustrated in Figure 2b. While the entire 9 matrix contains sufficient information to extract a single accurate set of n pK's, the individual columns of the matrix may lack adequate information to allow convergence when the number of components is large. The incorporation of matrix least squares into the singular value decomposition analysis appears to combine the advantages of both eigenvector projection, which reduces the size of the
+
matrix to be fit, and reiterative least squares, which utilizes all of the information in the data simultaneously. The combined least squares singular value decomposition technique is considerably faster for the particular minimization routine used and is at least as accurate as both of the two methods on which it is based.
LITERATURE CITED Shrager, R. I.; Hendler, R. W. Anal. Chem. 1982, 5 4 , 1147-1152. Frans, S . D.; Harris, J. M. Anal. Chem. 1984, 5 6 , 466-470. Gordon, W. E. Anal. Chem. 1982, 5 4 , 1595-1601. Goiub, G. H.; Kahan, W. SIAM Numer. Anal. 1985, 2 , 202-204. Fletcher, R. "Fortran Subroutines for Minimizing by Quasi-Newton Methods"; Report R7125 AERE; Harweil: London, 1972. Lorber, A. Anal. Chem. 1984, 5 6 , 1004-1010. Lawton, W. H.; Sylvester, E. A. Technometrlcs 1971, 13, 617-833. Knorr, F. J.; Futrell, J. H. Anal. Chem. 1979, 5 1 , 1236-1241. Sharaf, M. A.; Kowaiski, B. R. Anal. Chem. 1981, 5 3 , 518-522. Osten, D. W.; Kowalski, B. R. Anal. Chem. 1984, 5 6 , 991-995. Stang, G. "Applied Linear Algebra"; Academic Press: New York, 1976.
RECEIVED for review June 28,1985. Resubmitted April 8,1985. Accepted April 8,1985. This research was supported in part with funds provided by the National Institutes of Health through Biomedical Research Support Grant No. RR7092. Additional funding by the donors of the Petroleum Research Fund, administered by the American Chemical Society, is acknowledged.
Nonlinear Regression Model for the Representation of Dielectric Constants for Binary Aprotic Solvents Orland W.Kolling Chemistry Department, Southwestern College, Winfield, Kansas 67156
For many cosoivent systems which are important in analytical chemistry, lncludlng nonp0lar:polar aprotlc palrs, the static dleiectric constant ( E ) Is a continuous but nonlinear function of the solvent composltlon. Rational functlong were applied to such systems In place of the more conventlonai polynomial regressions for E = t ( X ) . Advantages which the ratlonai functions have for the economical storage of dielectrlc constant data include a reduction In the number of empirical coefficients required because of only a flrst power dependence on mole fraction ( X ) and a computatlonal dmpilcity In reproducing reliable E values over the total mole fraction range. The equatlons were tested on eight nonllnear data sets for n0npolar:polar solvent palrs. Also, current values for dielectric constants and Indexes of refraction were used In a crltlcal revlew of the Bekarek equatlons for the estimation of ?r* dlpolarlty numbers of aromatic hydrocarbons as nonseiect solvents.
Among the many intensive physical properties of liquids, the static dielectric constant (€1,viscosity, and index of refraction ( n )remain the common solvent parameters used to interpret medium effects upon solute solubilities, acid-base equilibria, electrolytic and redox behavior, and mechanisms of reaction for polar and ionic species. For example, the dielectric constant is the key variable characterizing the solvent in the Fuoss-Onsager model for electrolytic conductance and the influence of the solvent environment upon solute
ion pair and ion cluster formation (1,2). In the Amis-Jaff6 treatment of Coulombic energy contributions to activation energies, 6 is also the sole variable representing the role of a polar solvent on ion-ion and ion-dipolar molecule reactions (3). The physical model for the justification of the KamletTaft general scale of solvent dipolarities utilizes the BlockWalker reaction field parameter in dielectric constant, as derived by Abboud and Taft (4) and reinterpreted by Brady and Carr (5). Dielectric constant information for liquids is more directly relevant to those problems in analytical chemistry where solvent effects upon ionic equilibria and electrochemical data are observed (6). In addition the t value of a medium is one of the primary properties to be considered in selecting a solvent for potentiometric titrations in a nonaqueous medium (7). Similarly, by monitoring the changes in dielectric constant it is possible to determine the end point in titrations involving reactants and products with differing dipole moments, and this technique has been thoroughly explored by Megargle et al. (8). Although extensive tabulations of reliable t values for pure solvents have been available for some time, literature data for potentially useful binary solvent systems are often incomplete and may be reported only as empirical graphs. Because plots of dielectric constant vs. solvent composition are usually nonlinear, estimated E values for unknown solvent mixtures are subject to substantial interpolation errors and especially so where the original data base for a given solvent pair is too limited. In the present investigation nonlinear regression
0003-2700/85/0357-1721$01.50/00 1985 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 57, NO. 8, JULY 1985
1722
_ I
Table I. Dielectric Constants (at 25 "C) for Cosolvents Containing Benzene -.
benzene: acetone
benzene: acetonitrile
benzene: n-hexane
X1
ern
X1
em
Xl
ern
0.0oO
20.70a 18.78 16.96 15.84 13.71 11.88 10.04 8.30 6.88 5.06 3.77
0.000
36.01' 32.41 28.77 25.21 21.08 17.70 14.65 11.48 8.54 5.38 3.93
0.045 0.070 0.103 0.242 0.335 0.431 0.494 0.613 0.752 0.859
2.25 2.23 2.20 2.15
0.063 0.128 0.172 0.262 0.356 0.453 0.554 0.659 0.768 0.882
0.062 0.129 0.202 0.283 0.371 0.470 0.579 0.703 0.842 0.918
1.000
2.11
2.08 2.05 2.00 1.96 1.92 1.89"
benzene: nitrobenzene
benzene: tetrahydrofuran
benzene: nitromethane
X1
ern
X1
ern
X1
ern
0.000
34.82 28.04 22.56 18.10 14.39 11.38 8.26 7.05 4.96 3.83 2.275O
0.000
7.596 6.65 5.84 5.09 4.65 4.17 3.57 3.10 2.83 2.51
0.000
35.72b 31.39 28.45 25.18 21.66 19.42 14.31 11.74 8.56 6.13 4.90 4.01 3.46 2.52
0.149 0.283 0.403 0.512 0.612 0.703 0.786 0.863 0.934 1.000
0.130 0.261 0.377 0.467 0.569 0.694 0.801 0.863 0.946
0.067 0.110
0.183 0.242 0.315 0.434 0.522 0.641 0.755 0.827 0.883 0.924 0.979
'Literature values (10) used as calibration standards. Redetermined values for Dure solvents. functions were examined for = f ( X ) where X is the mole fraction, and for nonhydrogen bonding cosolvent systems composed of nonpolar and polar aprotic components, the data adequately fit rational correlation functions within the uncertainties in the data base itself. Of the ten model binary solvent systems selected for this study, most include an aromatic hydrocarbon as one component, and the approximate dielectric constant range represented by these cosolvents is from 2 to 36 (at 25 'C). In addition to such applications of correlation functions to cosolvents, the Bekarek equation (asf (e,n))for the estimation of ?r* dipolarity numbers for pure aromatic solvents (9) was reexamined more critically using "best available" dielectric constant values.
EXPERIMENTAL SECTION Reagents. All solvents were spectroscopic (ACS) grade and were dried initially for 1 week over anhydrous calcium sulfate. This was followed by redistillation through a 52-cm Raschig column with retention of the center 60% cut of distillate. Just prior to the preparation of solvent mixtures (v/v), the final drying of each of the pure solvents was made by a single pass through a column of activated alumina. Criteria for solvent purity were reliable literature values of boiling points, indexes of' refraction ( n ~ and ) , densities at 25 "C ( I O ) . Instrumentation. Dielectric constants were meavured by changes in dielectric cell capacitance with a Sargent Model 5 ( 5 MHz) cathode coupled oscillator. The instrument was calibrated using literature values for the pure solvents (IO): n-hexane, benzeue, nitroboiizene, carbon tetrachloride, acetone, and acetonitrile. Procedures for the determination of the dielectric constants at 25 "C for the cosolventa have been reported in detail elsewhere (11). The overall experimental uncertainty in t values for the
Table 11. Dielectric Constants (at 25 "C) for Other Aprotic Cosolvents carbon tetrachloride: toluene
carbon tetrachloride: nitrobenzene b
X1
ern
X1
ern
0.000
2.367' 2.360 2.354 2.347 2.333 2.314 2.298 2.280 2.259 2.241 2.235 2.228'
0.000
34.69" 30.11 26.17 24.82 20.71 18.90 16.20 12.09 9.07 7.57 4.96 4.07
0.061 0.107 0.153 0.277 0.405 0.528 0.644 0.769 0.877 0.942 1.000
0.106 0.210 0.247 0.361 0.413 0.494 0.625 0.727 0.781 0.879 0.920
p-dioxane: acetonitrileb
n-hexane: acetoneb
XI
em
X1
ern
0.054 0.097 0.209 0.291 0.381 0.480 0.590 0.712 0.847 0.922
32.87 30.52 24.85 21.39 18.01 14.55 11.27 8.03 4.98 3.55 2.21'
0.000
20.42 17.82 15.22 12.87 10.83 8.64 6.77 5.51 4.18 2.92 1.89'
1.000
0.070 0.144 0.224 0.310 0.402 0.503 0.611 0.729 0.858 1.000
'Reliable literature values used as standards (10). *New experimental results combined with literature data of Hirsch and Fuoss (211, Johari (221, and D'Aprano and Triolo (23). binary solvent mixtures within the 2-36 dielectric constant range is f0.15 (standard deviation); and for the pairs in the narrow 1.9-2.4 range, the precision is h0.008 e unit. Mean values from five replicates for each cosolvent containing benzene are listed in Table I and the dielectric constants for all other aprotic pairs are given in Table 11.
RESULTS AND DISCUSSION The "nonpolar" components selected for the po1ar:nonpolar solvent mixtures were benzene, toluene, n-hexane, and carbon tetrachloride. Although the ?r* (dipolarity) numbers for the aromatic hydrocarbons are appreciable (0.54-0.58), their dielectric constants are quite low and are similar to the e values of the alkanes whose ?r* numbers are near zero (12). Likewise, all of these less polar components have hydrogen bond basicities in the 0-0.1 range (12). Thus, even though the polar aprotic components listed in Tables I and I1 include three extremely weak HBD solvents (acetone, acetonitrile, and nitromethane), the dominant molecular interactions between the component pairs which influence dielectric behavior would be expected to be dipolar in character. Dielectric Constants for Mixed Solvents. The empirical curves in Figure 1 depicting the trend in dielectric constant as a function of cosolvent composition illustrate the general patterns observed for nonpo1ar:polar systems. For the specific cases involving benzene as one component, the plots gradually shift from linear (n-hexane) toward increasingly concave curvature as the dielectric constant of the more polar component is increased. Since conclusions about departures from linearity for the lower curves in Figure 1 can be misleading when based on visual inspection alone, algebraic or derivative expressions derived from the empirical e vs. X plots become necessary. A simple though effective measure of nonlinearity is the excess
ANALYTICAL CHEMISTRY, VOL. 57,NO. 8, JULY 1985
1723
A 30.
4
I
0
x2
Flgure 1. Trend in dielectric constant (e,)
as a function of mole fractlon
( X , ) for cosolvents containing benzene paired with: (1) acetonitrile; (2) nitromethane; (3) acetone; (4) tetrahydrofuran; (5) n-hexane.
function in dielectric constant (Ae) which has been defined by Payne and Theodorou (13) using
AE, = e,
- (Xiel + X2e2)
(1)
Here, m refers to the mixture and el and €2 are the dielectric constants for the pure components having mole fractions X1 and X p Clearly, Ae, = 0 for an ideal (linear) case, and the pairs, n-hexane:benzene and to1uene:carbon tetrachloride, conform to this condition. The excess function plots for all of the other binary solvents included in this study are shown in Figure 2. It is obvious that the deviations in Figure 2 are generally negative (or in the limit zero) for these po1ar:nonpolar cosolvents; and therefore one would expect that there should be a single algebraic form for E = f ( X ) in common to the whole group. At the molecular level, it has been argued (13) that the small negative Ae, values (less than -5) are a consequence of either weak dipolar associations between components 1and 2 or some increase in dipolar association by component 2 itself to form species of lower dipole moment. The first rationalization appears to be applicable to benzene paired with tetrahydrofuran, acetone, acetonitrile, and nitromethane, since the magnitudes of the At values a t their minima (in Figure 2B) increase with increasing ?r* number for component 2. Model Correlation Equations. In an attempt to establish useful correlation functions for nonlinear relationships like those in Figure 1,various options are available: (a) the direct application of curve-fitting techniques to identify suitable functions representing the pattern in the unaltered data points; (b) the transformation of the nonlinear data plot into a linear relationship between the variables by using a formal transformation function (14); or (c) transformation by forcing linear convergence through a polynomial with higher power terms and having the general form of ,e
= f ( X J = a0
+ a,X, + a2Xt + ... + anX1”
(2)
Although linearized polynomials are commonly used in fitting chemical data, it has been demonstrated by King and Queen (15) that rational functions hold several advantages over functions like eq 2. The most general form of the rational function for e, I= f ( X J is the quotient of the two polynomials
+ a,X, + a,X,2 + ... + a,X,P = bo + blX1 + b2XI2 + ... + bqX1* a,
e,
(3)
A
Flgure 2. Shift of the excess function (Ae,) with changing mole fraction ( X , )for binary solvents: (cosolvents In part A) (1) CCI,-toluene; (2) CCI,-nitrobenzene; (3) n -hexane-acetone; (4) p dioxane-acetonitrile; (part B) benzene paired with (5) n-hexane; (6) tetrahydrofuran; (7)acetone; (8) nitrobenzene; (9) acetonitrile; (IO) nitromethane; (11)
ethylene carbonate (data of Payne and Theodorou ( 13)). Here, the added restrictions on the function are that X Ihas limits of 0 and 1, that the likely optimum condition corresponds t o p = q (15), and that the polynomial in the denominator cannot become zero. A more restricted form of the rational function in eq 3 for which bo = 1 (by assignment) is known as the Pad6 approximant (15). However, based on the arguments of King and Queen (15),the standard Pad6 approximant was not adopted herein but instead the KingQueen algorithm was used to evaluate the constants in the generalized rational function (eq 3). For the eight nonideal cosolvent pairs included in this investigation, the rational correlation function has the specific form of eq 4,where X I refers to the component with the lower e value and only the first power terms in X,were necessary. E,
=
a0 + alx, bo + blX1
(4)
Final values for the parameters for each binary solvent system are listed in Table 111,along with the uncertainties in em(calcd). An overall correlation coefficient of 0.988 was obtained for the complete set. It should be noted that eq 4 must reproduce the values of el and e2 at the respective limits of X I = 1 and x i = 0. Trial correlations using the polynomial in eq 2 were made on the benzene:nitrobenzene system. Because it became apparent that higher power terms up to n = 4 were required to yield the same level of uncertainties in em(calcd),this approach was abandoned. On the other hand, the two ideal pairs (nhexane:benzene and CCL:toluene) follow the simple first power linear function, and the values of uo and ul for these systems are included in Table 111. Estimation of ?r* Numbers from f(e,n2). In the course of this work dielectric constants for a number of pure solvents were redetermined. Since the aromatics are classified among the “nonselect solvents” in the Kamlet-Taft system of linear solvation energy relationships (16), the various functions proposed by others were reexamined using revised or best values for dielectric constants. The indexes of refraction and revised dielectric constants for pure liquid aromatic hydrocarbons and their representative derivatives are summarized in Table IV. Because it has already been shown that theoretical models relating a* dipolarities to parameters in dielectric constant alone are less reliable in the calculation of a* values for select solvents (17-19), only the better functions
1724
ANALYTICAL CHEMISTRY, VOL. 57, NO. 8, JULY 1985
Table 111. Constants for Regression Functions: c = f ( X , ) solvent pair
emcdcd
a1
(SD)
Rational Functions 1.000 0.994 0.994 0.997 0.994 0.999
C,&:acetone C6Hs:acetonitrile C6H6:nitrobenzene CsH6:nitromethane C6Hs:tetrahydrofuran CC4:nitrobenzene di0xane:acetonitrile n-hexane:acetone overall uncertainities (SD)
0.0483 0.0276 0.0286 0.0279 0.131 0.0288 0.0278 0.0490 h0.0003
-0.815 -0.876 -0.892 -0.852 -0.578 -0.911 -0.885 -0.765 10.001
1.000
1.001 10.001
0.0332 0.0241 0.0163 0.0371 0.0520 0.0106 0.0244 0.0760 h0.0002
10.07 10.24 10.16 10.20 10.02 10.14 10.13 10.24
Linear Functions C6Hs:n-hexane CC14:toluene overall uncertainities (SD)
2.275 2.367 10.003
-0.385 -0.139 10.001
10.02 h0.003
Table IV. Application of f(t,n) Equations to the Calculation of Dipolaritites for Pure Aromatic Solvents a* values €a
benzene cumene mesitylene toleuene m-xylene o-xylene p-xylene
2.275 2.383 2.279 2.379 2.374 2.468 2.270
nDa
exptlb
eq 6
eq 5
eq 7
eq 8
1.4979 1.4889 1.4968 1.4941 1.4946 1.5029 1.4932
0.59 0.41 0.41 0.54 0.47 O.5Oc 0.43
0.19 0.21 0.19 0.22 0.22 0.25 0.18
0.36 0.38 0.36 0.38 0.38 0.40 0.36
0.21 0.22 0.21 0.23 0.23 0.25 0.21
0.47 0.46 0.44 0.48 0.47 0.51 0.43
1.01 0.60 1.05 0.76 0.72 0.71 0.94 0.60 0.62
0.82 0.59 0.84 0.68 0.66 0.65 0.78 0.59 0.60 0.88 0.76
1.03 0.51 0.94 0.62 0.60 0.58 0.79 0.49 0.53 1.05 0.88
Aromatic Derivatives acetophenone anisole benzonitrile bromobenzene chlorobenzene m-dichlorobenzene o-dichlorobenzene diphenyl ether fluorobenzene nitrobenzene pyridine
17.39 4.33 25.20 5.40 5.62 5.04 9.93 3.69 5.42 34.82 12.31
1.5342 1.5143 1.5257 1.5571 1.5248 1.5434 1.5491 1.5762 1.4684 1.5499 1.5076
0.90 0.73 0.90 0.79 0.71 0.67 0.80 0.66 0.62 1.01
1.12
0.87
0.91
a Dielectric constants and indexes of refraction from literature and experimental values (10). Most recent dipolarity values summarized by Kamlet et al. (12). CNewexperimental value.
in both 6 and nD were reconsidered herein. The three key predictive functions asf(c,n2)used to compare estimated ir* values are given in eq 5-7 with their identified sources. Bekarek (9) (aromatics): ir*
= 8.09
(E
(2E
+ 1)(2n2 + 1)
1
- l ) ( n 2 - 1)
1 - 0.573 _ _
- l)(n2- 1)
Bekarek (9) (aliphatics): ir*
r ""1
= 14.cK
(E
(2E + 1)(2n2 + 1)
Abboud et al. (18) (select gas phase):
+ 5.54[
-
1 1
-1
(5)
(6)
- 1.05
(7) Although the Abboud et al. (18) function is not intended to apply to nonselect solvents like the aromatics, it was included in order to compare the results obtained with this multiple regression containing n2terms with those from the Bekarek equations. (The two other variations on eq 7 given as eq 17
and 19 by Abboud et al. (18) were applied here as well; however, the results closely parallel the outcomes with eq 7.) The T* values which were calculated by the three functions are summarized in Table IV where they may be compared to the experimental dipolarity numbers. It is clear from separating the two classes of solvents that the most systematic and substantial errors occur for only the aromatic hydrocarbons as a group and not their derivatives, and each of the equations including eq 5 predicts nearly a constant ir* value for the hydrocarbons. This arises from the fact that nD values for the aromatics are all in the narrow 1.49-1.50 range and that even in eq 7 the second term in n2 alone dominates the outcome with only about 3% contributed by the first term in both c and n. On the other hand, for the representative set of 11 aromatic derivatives in Table IV the results from both eq 6 and 7 exhibit similar random errors of f0.09 and f0.13 (standard deviation), respectively. Thus, the evidence fails to support the use of eq 5 and there appears to be no overall statistical justification for excluding the aromatic derivatives from Bekarek's eq 6 developed for aliphatic and select solvents. For the estimation of ir* values for the special cases of the aromatic hydrocarbons, there is the one realistic option, namely, to incorporate a d8 term like that proposed by Taft, Abboud, and Kamlet in their original linear solvation energy relationships (16). When added as a perturbation term to eq
Anal. Chem. 1985, 57, 1725-1728
6, the corrected function becomes
The uncertainty in the revised d coefficient is f0.03 when 6 = 1.0 ( I 6 ) ,and the observed precision in r*(calcd) of f0.07 (standard deviation) for the seven aromatics is similar to the results for the large set of select solvents (18). By contrast to the usual situation for LSE functions, it will be noted that the d6 polarizability correction in eq 8 is positive. Such a d6 term was required for the computation of r* values for one other cosolvent system (20). The final composite uncertainty for r*(calcd) of all 18 solvents listed in Table IV using eq 6 and eq 8 is f0.08 (standard deviation) and r = 0.982.
LITERATURE CITED (1) Bishop, W. J . fhys. Chem. 1979, 8 3 , 2338. (2) Nicolas, M.; Reich, R. J . fhys. Chem. 1981, 8 5 , 2843. (3) Amis, E. S. “Solvent Effects on Reaction Rates and Mechanisms”; Academic Press: New York, 1966; Chapters 1 and 2. (4) Abboud, J.; Taft, R. J . Phys. Chem. 1979, 83, 412.
1725
(5) Brady, J.; Carr, P. J . fhys. Chem. 1984, 88, 5796. (6) Lagowski, J. J., Ed. “The Chemlstry of Nonaqueous Solvents”; Academic Press: New York, 1978; Voi. VA, pp 121-178. (7) Kratochvil, E. Anal. Chem. 1982, 5 4 , 105R-121R. (8) Megargle, R.; Jones, G.; Rosenthal, D. Anal. Chem. 1969, 4 7 , 1214; 1970, 42, 1293. (9) Bekarek, V. J . Phys. Chem. 1981, 8 5 , 722. (10) Riddick, J.; Bunger, W. “Organic Solvents”, 3rd ed.; Wlley-Interscience: New York, 1970; Chapter 5, pp 121-177. (11) Koiiing, 0. W. Trans. Kans. Acad. Sci. 1979, 8 2 , 218. (12) Kamlet, M.; Abboud, J.; Abraham, M.; Taft, R. J . Org. Chem. 1983, 48, 2877. (13) Payne, R.; Theodorou, I . J . Phys. Chem. 1972, 76, 2892. (14) Chatterjee, S.; Price, E. ”Regresslon Analysis by Example”; Wiley: New York, 1977; pp 27-50. (15) King, M.; Queen, N. J . Chem. Eng. Data 1979, 2 4 , 178. (16) Taft, R.; Abboud, J.; Kamlet. M. J . Am. Chem. SOC.1981, 703, 1080. (17) Brady, J.; Carr, P. J . fhys. Chem. 1982, 86, 3053. (18) Abboud, J.; et ai. J . Phys. Chem. 1984. 8 8 , 4414. (19) Kolling, 0. W. Trans. Kans. Acad. S d . 1981, 84, 32. (20) Kolling, 0. W. Anal. Chem. 1984, 56, 2988. (21) Hirsch, E.; Fuoss, R. J . Am. Chem. SOC. 1980, 8 2 , 1018. (22) Johari, G. J . Chem. Eng. Data 1968, 13, 541. (23) D’Aprano, A.; Trioio. R. J . fhys. Chem. 1987, 7 7 , 3474.
RECEIVED for review February 5,1985. Accepted April 5,1985.
Use of Catalytic Thermometric Titrimetry To Investigate the Interaction of Dipolar Aprotic Solvents with Water Oswaldo E. S. Godhino’ and Edward J. Greenhow*2
Department of Chemistry, Chelsea College, University of London, Manresa Road, London SW3 6LX, England
The lnteractlon between water and the dlpolar aprotlc solvents dimethyl sutfoxkle (Me,SO), dlmethytformamlde (DMF), and hexamethylphosphoramlde(HMPA) Is Investigated by a klnetlc procedure In whlch catalytic thermometric tltrlmetry, with acrylonitrile as the thermornetrlc Indlcator, is used to determlne reaction rates. The lnteractlon Is measured by determining the Influence of the solvents on the lnhlbitlng effect of water on the base-catalyzed polymerlratlon and cyanoethylation reactions occurrlng at the end point of the tltratlon. The reactlvlty of the water Is reduced by hydrogen bonding with the solvents, and dlscontlnultles In the reiatlonship between solvent-water molar ratio and end-point reaction rate conflrm that assoclatlon complexes are formed corresponding to molar ratlos of 1:l and 21, 1:l and 2:1, and 1:1, for Me,SO, DMF, and HMPA, respectlvely.
A variety of methods have been used to evaluate the interaction between dimethyl sulfoxide and water. These range from determining heats of mixing (2),viscosities of mixtures (2),and the velocity of sound in paper treated with mixtures of water and dimethyl sulfoxide (3) to measuring effects on the infrared (4)and nuclear magnetic resonance (I, 4-6) spectra of the water and rates of reactions, involving water as a reagent (7-1I), when increasing amounts of dimethyl Present address: Instito de Quimica, University Estadual de Campinas, Campinas, Sao Paulo, Brazil. Present address: Analytical Chemistry Group, Birkbeck College, University of London, Christopher Ingold Laboratories, 20 Gordon St., London WClE, UK.
sulfoxide are added. Some of these investigations have shown that discontinuities occur in the measured parameters when dimethyl sulfoxide and water become present in molar ratios of 1:l (11),1:2 (2,5-8),3:6 (I), 2:l (4,5,II), 2:6 (I), and 2:3 (11). The 3:6 and 2:6 ratios ( I ) are proposed to account for the occurrence of oligomeric units. The kinetic methods (7-11) gave a direct indication of the effect of dimethyl sulfoxide on the reactivity of water in specific circumstances. Tommila and Murto (7)find that the rate of hydrolysis of ethyl acetate under acidic conditions reaches a maximum when dimethyl sulfoxide, used as a solvent, is present in a 1:2 molar ratio with water. Rammler and Zafforoni (8), studying the enzymic activity of trypsin in protein degradation, found similarly that the activity changes abruptly when the molar ratio of dimethyl sulfoxide to water reaches 1:2 and also that the loss of activity becomes irreversible at a lower ratio of 1:2.9. Jezorek and Mark (11)have measured the decay of anthracene and naphthalene anion radicals, prepared by polarographic reduction of the parent hydrocarbons, when water functions as a proton donor in the presence of various solvents, including dimethyl sulfoxide and dimethylformamide. They find that protonation rates reach a maximum only when the water content exceeds values dependent on the nature of both the dipolar aprotic solvent and the radical anion and correspond to molar ratios of dipolar aprotic solvent to water approximating to 2:1, 1:1, and 2:3. In the present study, the technique of catalytic thermometric titrimetry is used to investigate the interaction between water and the three dipolar aprotic solvents, dimethyl sulfoxide, dimethylformamide, and hexamethylphosphoramide. The technique offers a way of measuring the influence of these
0003-2700/85/0357-1725$01.50/00 1985 American Chemlcal Society
