4145
SOLVOLYSIS OF BENZYL CHLORIDE IN GLYERCOL-WATER MIXTURES systems act in this fashion because the surface tension of hexane is lower than that of the mutually soluble component. Shain and Prausnitz' have used their relationship to calculate (daj/dNz,,)N,,, = 0, the interfacial tension gradient at infinite dilution. I n Table 11, their experimental and callculated value of this parameter in the aqueous phases of two ternary systems can be compared with those calculated using eq 29 and other experimental data.6g6 It should be noted that the results calculated using eq 29 required a knowledge of interfacial tension as a function of the aqueous-phase concentration only, whereas to use Shain and Prausnitds
Table 11: Interfacial Tension Gradient at Infinite Dilution for Two Ternary Two-Phase Systems -(duj/dNp,j)Ni,j = 0, ergs/cm*Shain and Exptl Prausnitz Eq 28
System
Benzene-methanol-water Carbon tetrachloride-
300 3710
250 3680
225 2941
1-propanol-water
equation, molar areas, partial molar volumes, and solubility parameters were also required.
Solvolysis of Benzyl Chloride in Glycerol-Water Mixtures: Relation between Activation Parameters and Thermal Expansivityl by D. L. Gay2and E. Whalley '
Division of Applied Chemistry, National Research Council, Ottawa, Canada
(Received M a y 5, 1058)
The rate of solvolysis of benzyl chloride has been measured in the range 50-70" in glycerol-water mixtures of composition 0-75 vol % ' glycerol. The solvent system was chosen because its thermal expansivity varies little with composition, in contrast to that of many other water-organic mixtures. Then the difference between the constant-volume and constant-pressure activation parameters, which is TaAV * / K , where T is the temperature, a! and K are the thermal expansivity and compressibility, respectively, and AV* is the activation volume, changes little with composition due to changes of a. There is a minimum in the constant-pressure activation enthalpy about 400 cal mol-1 deep in water-glycerol contrasted to one of about 1700 cal mol+ in ethanol-water. The constant-pressure activation parameters for glycerol-water vary with composition more like the constant-volume parameters for ethanol-water than like the constant-pressure parameters. These results appear to imply that the constant-volumeactivation parameters are more appropriate for a fundamental discussion than the constant-pressure parameters.
1. Introduction The enthalpy and entropy of activation for many organic solvolyses in aqueous organic solvents pass through strong minima or maxima as the solvent composition is varied. There are many examples, and they occur for a c i d , - c a t a l y ~ e dbase-~atalyzed,~ ,~~~ and spontaneous6-l1 solvolyses of neutral molecules and for the spontaneous sjolvolysis of positive ions. l2 Some nonsolvolytic reactions also show similar behavior. l3 Many attempts have been made to account for this behavior in terms of, for example, the dielectric con~ t a n t ,specific ~ , ~ ~ o l v a t i o n , 5 ~ or ~ 0the ~ ~structure ~ ~ ~ 4 of the solvent. l5 However, the usual enthalpies and entropies of activation are not the only valid parameters for characterizing the effect of temperature on chemical re-
action rates. Instead of measuring the rate constant at a series of temperatures when the pressure is kept constant, it is at least as valid to measure it at a series of (1) National Research Council No. 10438. (2) National Research Council Postdoctorate Fellow 1965-1967. (3) E. A. Braude, J . Chem. Soc., 442 (1944). (4) E. Tommila and A. Hella, Ann. Acad. Sci. Fennicae, AII, No. 53 (1954). (5) E.Tommila, A. Koivisto, J. P. Lyrra, K. Antell, and S. Heimti, ibid., AII, No. 47 (1952). (6) E. Tommila, M. Tiilikainen, and A. Voipoi, ibid., AII, No. 65 (1955). (7) A. Fainberg and S. Winstein, J . Amer. Chem. Soc., 7 8 , 2770 (1956); 79, 1597, 1602, 2770, 5937 (1957). (8) E.Tommila, E. Paakala, U. K. Virtanen, E. Erva, and S. Varila, Ann. Acad. Sci. Fennicae, AII, No. 91 (1959). (9) J. B. Hyne and R. E, Robertson, Can. J. Chem., 34, 931 (1956). Volume '7% Number 12 November 1968
D. L. GAYAND E. WHALLEY
4146 temperatures when the density is kept constant. Measurement at constant pressure yields the usual enthalpy, AH,*, and entropy, ASp*, of activation at constant pressure, and measurement at constant volume yields the energy, AU,*, and entropy, AS,*, of activation a t constant total volume. The relation between the two sets of parameters is
AH,* - AU,+
=
TAS,* - TAS,* =
T~Av+/K
where T is the temperature, a and K are the thermal expansivity and compressibility of the reaction mixture, respectively, and AV* is the volume of activation. A brief review of constant-volume parameters is given in ref 16. The constant-volume parameters are now known as a function of solvent composition for four reactions. I n two of them, the acid-catalyzed enolization of acetone and of acetophenone in ethan~l-water,'~AH, and AS, have no minima but vary in a compensatory way. The constant-volume parameters, on the other hand, do not vary significantly with the solvent, and entropyenergy compensation is absent. For the other two reactions, the acid-catalyzed hydrolysis of methyl acetate in acetone-waterls and the spontaneous solvolAH, and ysis of benzyl chloride in ethanol-water, AS, have strong minima, whereas AU,' and AS, have no or only small minima. For all these systems, the complicated behavior of AHp* and AS,* is absent in AU,* and ASv* because changes with solvent composition of both the thermal expansivity and the activaK depend strongly on the tion volume cause T ~ A V * / to solvent. The thermal expansivity of the solvent mixtures used differed by a factor of about 3 between water and a 50 vol % water-organic mixture, and this variation caused a large part of the variation of
*
*
*
* *
TCXAV*/K.
The apparent simplicity of the constant-volume parameters suggests that a theoretical understanding of the effect of solvent on the energetics of activation might be obtained more easily by considering them rather than the constant-pressure parameters. The constant-pressure parameters would then be understood in terms of the constant-volume parameters and the quantity T ~ A V * / K .If this is so and if it were possible to find a water-organic system for which the thermal expansivity was essentially independent of solvent composition, then one would expect that the constantpressure parameters in such a system would vary more like the constant-volume parameters in, say, waterethanol mixtures than like the constant-pressure pararneters.'6 It is assumed of course that the volume of activation and compressibility vary in a similar way in both systems. If, on the other hand, the theoretical understanding is better based in the first place on the constant-pressure parameters, the constant-pressure parameters would be expected to be similar in both systems. A test of this argument is therefore in the T h e Journal of Physical Chemistry
nature of a critical experiment that might help decide between two points of view. There are few water-organic mixtures whose thermal expansivities at ordinary temperatures depend only slightly on composition. Among these are waterglyco120 and water-glycerol2' at suitable temperatures. The system chosen for the work reported here is waterglycerol at 60", and at this temperature the solvolysis of benzyl chloride is a convenient reaction for study and has the advantage that it has been well investigated in other solvents.89'0 2. Experimental Methods and Results Conductance cells about 150 cma in volume were made of Pyrex glass. The electrodes were shiny platinum about 20 mm in diameter and were about 120 mm apart. The cells were cleaned with hot concentrated nitric acid, washed thoroughly with distilled water, and treated with 0.1 N hydrochloric acid at 100" until the conductance of 1 mM hydrochloric acid solution a t 60" was constant within 0.06% for 24 hr. Electrode polarization was unimportant, since the conductance of 1 mM hydrochloric acid at 400 and 1000 cps differed by less than 0.08%. The thermostat was controlled to better than =kO.Ol", and its temperature was measured with a platinum resistance thermometer. Fisher reagent grade benzyl chloride was redistilled at 10 mm and 56"; glycerol was redistilled under vacuum; and water was boiled off distilled water of specific conductance about mho cm-l. Water-glycerol mixtures were made up by volume a t 25". The initial concentration of benzyl chloride was about 0.001 M . Conductance cells were filled with the solutions, preheated to the thermostat temperature, placed in the bath, and left to equilibrate for 30 min. The conductance was followed for about 6 half-lives and was taken at intervals suitable for use with the Guggenheim method. The range of conditions covered was 50-70" and 0-75 vol % glycerol. Conductances were measured automatically at 1 kcps by a General Radio Catalog S o . 1680-A automatic (10) J. B. Hyne, R. Wills, and R. E. Wonkka, J . A m e r . Chem. Soc., 84, 2914 (1962).
(11) J. B. Hyne and R. Wills, ibid., 85, 3650 (1963). (12) J. B. Hyne and R. E. Wonkka, reported in J. B. Hyne, Ibid., 82, 5129 (1960). (13) R. A. Fairclough and C. N. Hinshelwood, J . Chem. SOC.,1573 (1937). (14) J. B. Hyne, J . A m e r . Chem. SOC.,82, 5129 (1960). (15) E. M.Arnett, W. G. Bentrude, and J. J. Burke, ibid., 87, 1541 (1965). (16) E. Whalley, Ber. Bunsenges. P h y s . Chem., 70, 958 (1966). (17) B. T. Baliga and E. Whalley, Can. J . Chem., 42, 1835 (1964). (18) B. T. Baliga, R. J. Withey, D. Poulton, and E. Whalley, T r a n s . Faraday Soc., 61, 517 (1965). (19) B. T. Baliga and E. Whalley, J . P h y s . Chem., 71, 1166 (1967). (20) J. K. Ross, I n d . Eng. Chem., 46, 601 (1954). (21) J. Timmermans, "The Physico-Chemical Constants of Binary Systems in Concentrated Solutions," Val. 4,Interscience Publishers, New York, N. Y., 1960, p 256.
4 147
SOLVOLYSIS OP' BENZYL CHLORIDE IN GLYCEROL-WATER ~IIXTURES Table I : Rate Constants for the Solvolysis of Benzyl Chloride in Water-Glycerol Mixtures VOl
-----------------
% 10% sea-I--
glycerol
at 2 5 O
50.00°
0.0 5.0 12.5 25.0 50.0 75.0
218.9 206.7 190.6 162.7 107.0 58.62
219.1 207.1 190.3 162.7 108-0 68.58
566.0 534.7 489.4 415.4 274.1 148.3
162.0 108.0
capacitance-conductance bridge and digital readout. The range of conductance used was about 160-440 pmhos, and the measurement accuracy was increased by connecting to the bridge a reference conductance of about 300 pmhos so that the digital readout was then the conductance of the sample less the reference conductance. The readout covered the range -140 to $140 pmhos and could be obtained to 10 nmhos, or about 30 ppm of the change of conductance during a run. The bridge was calibrated against Sullivan and Griffiths nonreactive resistors and against resistors calibrated from time to time against an Anthony pattern Wheatstone bridge a i 1 kcps. No corrections to the bridge readout were necessary. There is no doubt that this bridge greatly facilitates kinetic measurements by conductance, particularly if several conductance cells are used simultaneously, as they were in this work. The conductances were converted to conductances at infinite dilution by means of the limiting law (for details see Baliga and WhalleyZ2)and were analyzed by digital computer by the Guggenheim method using least squares. The deviations did not differ significantly from random, and the standard errors from internal consistency were about &0.2%,. The rate constants are summarized in Table I. At least two values were obtained at each temperature and solvent composition. The standard error from consistency between runs appears to be about =k0.201,. The activation parameters in pure water, obtained by least squares from these results together with the values obtained by others, are given in Table 11. The agreement is 5,atisfactory.
Table I1 : Activation Parameters for the Solvolysis of Benzyl Chloride in Water a t 60.00" A&
*,
cal deg-1
AH,+, koa1 mol -1
+
19.90 0.05 1 9 . 8 0 i 0.08 20.12 i 0.10
'
70.00°
59.78O
mol-1
Ref
13.7 0.16 13.5 i.0 . 2 3 13.2 =k 0 . 3
a
b c
a Reference 10. R. E. Robertson and J. M. W. Scott, J. Chem. Soc., 15916 (1961). This work.
565.9 535.8 489.3 415.5 273.4 149.1
1442 1348 1231 1034 687.0 376.4
273.5 148.4
1446 1342 1228 1038 689.1 375.1
690.8
Since the main purpose of the work was to investigate the effect of solvent on the activation parameters rather than the activation parameters themselves, the measurements in aqueous glycerol were analyzed by plotting log (kl/kz) against 1/T, where kl and kz are rate constants in pure water and in a mixed solvent, respectively, and alternatively T log ( k ~ / l c z )against T . The slopes and intercepts then give the change AAH, and AAS,* of the enthalpy and entropy of activation directly according to the relation
*
In (kl/lcz) = AAH,+/RT
- AAS,+/R
The graphs of log ( k l / k 2 ) against l / T are given in Figure 1 to indicate the reproducibility of the work. The values of AAH, and AAS, are listed in Table 111,
*
*
Table I11 : Change with Solvent Composition of the Activation Parameters for the Solvolysis of Benzyl Chloride in Water-Glycerol Vol % glycerol
TAASp*
A A G , ~
AAH,*
(&-4),
(*-loo),
(&-loo),
106,
oal mol-1
cal mol-1
des-'
os1 mol-1
0
5.0
37
- 157
- 194
12.5 25.0 50.0 75.0
96 204 480 886
- 361 - 400
- 231
- 327 - 565 - 880 - 1186
- 300
523 517 522 547 560 540
together with estimates of the standard error, and are plotted in Figure 2 with vertical bars showing the estimated standard error. The corresponding values for the solvolysis of benzyl chloride in ethanol-water mixtures obtained by Hyne, Wills, and Wonkka'o are also plotted in Figure 2 for comparison.
3. Discussion The effect of solvent on the activation enthalpy and entropy for the solvolysis of benzyl chloride in waterglycerol and water-ethanol mixtures at 60" are compared in Figure 2. The difference between the two (22) B. T. Baliga and E. Whalley J. Phys. Chem., in press.
Volume 7 2 , Number I2 November 1968
4148
D. L. GAYAND E. WHALLEY
systems is striking. There is a minimum in the activation enthalpy about 400 cal mol-' deep in water-glycerol contrasted with one about 1700 cal mol-' deep in water-ethanol. There is no minimum but only a steady decrease in TAX, in water-glycerol, compared with a minimum of about 2700 cal mol-' in waterethanol. Furthermore, Figure 3 shows that the high enthalpy-entropy compensation in the region of the minimum in water-ethanol is greatly reduced in waterglycerol.
*
parameters. This strongly suggests, according to the argument in the next to the last paragraph in the Introduction, that the constant-volume parameters are more appropriate than the constant-pressure parameters for a fundamental understanding of this reaction in these solvents. Furthermore, the measurements appear to confirm that 'the minimum in the constant-pressure enthalpy and entropy is a t least partly connected with the large variation of the thermal expansivity of the water-organic solvent mixtures with composition.
I
0
E
2.0
I
,
2.9
I
-
I
3.0
3.1
loa T
Figure 1. Graphs of log (kl/kz), where kl and k z are rate constants in pure water and a mixed solvent, respectively, against 1/T. The numbers attached to the curves are the volume per cent a t 25" of glycerol. For 5y0 glycerol, A = 0.0; 12.570, A = 0.033; 25%, A = 0.100; 5O%, A 0.270; 75%, A = 0.520.
It is not easy to associate this difference with anything but the relative variations in the thermal expansivity with solvent composition. I n the first place, glycerol and ethanol are chemically similar, and solvation dependent on chemical properties should not differ greatly. In the second place, the static dielectric constants are 24 and 42, respectively, a t 25" and so they would tend to solvate by multipole-dielectric energies in a similar way. Furthermore, neither the chemical properties nor the dielectric constants of the pure organic components seems to be a major factor, as the activation parameters vary in acetone-water, dioxane-water, and ethanol-water in similar ways.6*10 The observed variation in the activation parameters is closer to that for the constant-volume parameters for water-ethanol mixtures2' than to the constant-pressure The Journal of Physical Chemistry
% V / V ORGANIC COMPONENT
Figure 2. Comparison of effect of solvent composition on the constant-pressure activation enthalpy and entropy for the solvolysis of benzyl chloride in water-glycerol and water-ethanol:10 0, water-glycerol; 0 , water-ethanol.
Presumably, the greater the thermal expansivity, the greater the reduction of solvating power when the temperature is increased at constant pressure. A monotonic fall in the solvating power with increasing organic content, combined with a constant-volume energy that a t a low organic content is almost independent of composition but that rises ever more steeply as the organic content increases,'g explains the observed minima. It is of course quite possible that
4149
SOLVOLYSIS OF BENZYL CHLORIDE IN GLYCEROL-WATER MIXTURES
I
184
I
I
I
I
I
I
I
I
5
I 6
- T A S*/ kcal
I
I
I
I
I
I
I
7
mole-'
Figure 3. Enthalpy-entropy compensation for the solvolysis of benzyl chloride in water-glycerol and water-ethanol:'O 0 , water-ethanol.
e, water-glycerol;
water exerts its specific influence in other ways, in addition to the effect via the thermal expansivity, but
the effect of the thermal expansivity must surely be eliminated if the remaining effects are to be elucidated.
Volume 72, Number 12 November 1968
