R. BARILE,A I . CEFOLA,P. GENTILE,AND A. CELIANO
1358
computer calculations, and to A h . E. N. Wescott of the Monsanto Research Corp. Boston Laboratory for assistance in problem preparation. Finally, A. K.
XI. S. H. wishes to thank Dr. J. N. Butler of Tyco Laboratories, Inc., Waltham, Rlass., for helpful discussions during the preparation of this paper.
The Effect of Solvent on the Rate of Formation of Monoacetylacetonatocopper(I1) Ion
by Raymond C. Barile, Department of Chemistry, Manhattan College, Bronx, New York
Michael Cefola, Philip S. Gentile, Department of Chemistry, Fordham University, Bronx, N m York 1048
and Alfred V. Celiano Department of Chemistry, Seton Hall University, South Orange, New Jersey (Received June 28, 1965)
+
The kinetics of the reaction of copper(I1) ion acetylacetone e monoacetylacetonatocopper(I1) ion in mixed solvents of methanol-water and ethanol-water was investigated conductometrically in the temperature range -20 to 0". I n all solvents the reaction obeyed second-order kinetics, first order with respect to the concentration of copper ion and first order with respect to the concentration of the enol form of acetylacetone. The initial rate in representative solvents was independent of initial hydrogen ion concentration, indicating that the reaction does not involve prior ionization of acetylacetone but most likely a direct combination of the two reacting species. The log of the forward rate constant, kl,was found to be a linear function of the reciprocal of the macroscopic dielectric constant of the solvent over a range of 80 to 40. The energy of activation, E,, was separated into a contribution due to change of dielectric constant, ( E a ) T , and into a contribution due to a change of temperature, ( E a ) D .
Introduction The reactions between metal ions and P-diketones have been the subject of considerable investigation. I n the sphere of kinetics of complex ions interest has been focused mainly on the mechanism of substitution reactions rather than the rate of complex According to principles enunciated by Bjerrum,' The JOUTnd of Physical Chemistry
complex formation of copper ion with acetylacet,one (HAA) takes place in a series of two reversible steps (1) D. W. Margerum, J. Am. Chem. Sac., 78, 4211 (1956). (2) T. Leo, I. Kolthoff, and D. Leussing, ibid., 70, 3596 (1948). (3) P. Krumholz, J. Phys. Chem., 60, 87 (1956). (4) J. H. Baxendale and P. George, T r a m . Faraday Soc., 46, 736 (1950).
RATEOF FORMATION OF MONOACETYLACETONATOCOPPER(~~) ION
ki
+ HAA Cu(AA)+ + HAA Cu2+
k2
Cu(AA)+ ks
+ H+
(1)
+
(2)
CU(AA)~ H + k4
Assuming a concert,ed mechanism for reaction 1, K1 = kl/kz, and for reaction 2, Kz = k3/k4, then the first complex formation constant is (3) and the second complex formation constant is
The values of the formation constants determined under many experiment’alcondit,ions5indicate the rat’io of Kl/K2 2 10. The conversion between the tautomeric forms of acetylacetone is believed t,o follow the mechanisms
k m
~ E I
where HAAK is the keto form, HAAE is the enol form, AA- is the enolate ion, kK1 = 1.4 X sec-’, and kE2 = 3 X 101O 111-1sec-l. From the data of Eigens and Celiano6 the rate of first complex formation of Cu2+ with acetylacetone is much greater than the rate of conversion of the keto form to the enol form of acetylacetone. In the present study, the forward rate constant for the first complex formation, k ~ was , measured conductometrically in solvents of varying compositions of methanol-water and ethanol-water a t temperatures The enol content of acetylof 0, -10, and -20’. acetone was measured in all the solvents at each experimental temperature. Experimental Section
Materials. ACS grade methanol was refluxed for 1 hr over magnesium methoxide9 and then distilled through a 90-cm column. The first portion of the distillate was discarded, and a second distillation was made over 2,4,6-trinitrobenzoic acid through a 15-plate Oldershaw column; bp 64.70’ (lit.lo 64.75’). ACS grade 95% ethanol was refluxed for 1 hr and then distilled through an Oldershaw column. The first portion of the distillate was discarded, and the constant boiling point fraction was collected; bp 78.15’ (1it.l1 7’8.15’). Fisher Purified 1-propanol was refluxed over AIg ribbon and then distilled through a 15-plate Oldershaw column. The first fraction was discarded, and the second fraction was collected a t a temperature
1359
of 97.1 f 0.1’ (lit.12 97.4’). Laboratory-distilled water was passed through a Fisher demineralizer, and the eluent water had a specific conductance less than mho. CP grade acetylacetone was used without further purification. Analytical reagent grade copper perchlorate hexahydrate (G. Frederick Smith) was used without further purification. Complexometric and ion-exchange analyses13gave assays of Cu(C104)2. 6H20 between 99.20 and 99.60%. Analytical reagent grade anhydrous NaC104 (G. Frederick Smith) was dried in a finely powdered form a t 200°14and was used without further purification. Aqueous perchloric acid (70%), doubly distilled and lead free (G. Frederick Smith), was used without further purification. Solutions. Calibrated glassware and weights were used throughout. Stock solutions of Cu(C104)z in the various alcohol-water solvents were standardized by complexometric titration with 0.1 N EDTA. Sodium perchlorate stock solutions in the different alcoholwater solvents were standardized by an ion-exchange method. Perchloric acid stock solutions in the alcoholwater solvents were standardized by titration with 0.1 N NaOH. The alcohol-water solvents were made up by weight in a 50-1. bottle and stored under nitrogen. The exact composition of the solvent was determined by measurement of the density in vacuo a t 25’. All stock solutions were kept in automatic burets and protected from atmospheric moisture and COz. Solutions employed in the kinetic determinations were made from stock solutions. All kinetic determinations were M sodium made in solutions containing 1.04 X perchlorate. The reasons for employing a neutral salt are twofold: it decreases the percentage change in the ionic strength during the reaction and allows the initial resistance of the acetylacetone and the copper perchlorate solutions to be adjusted to within 500 ohms of (5) R. Taft and E. Cook, J . Am. C h a . Soc., 81, 46 (1959). (6) A. V. Celiano, RI. Cefola, and P. S. Gentile, ibid., 65, 2194 (1961). (7) J. Bjerrum, “Metal Ammine Formation in Aqueous Solution,” P. Haase and Son, Copenhagen, 1941. (8) M. Eigen and L. DeMaeyer in ”Techniques of Organic Chemistry,” Vol. VIII, Part 11, Interscience Publishers, Inc., New York, N. Y., 1963, p 1037. (9) A. Weissberger, “Techniques of Organic Chemistry,” Vol. V I I , Interscience Publishers, Inc., New York, N. Y.. 1955, p 336. (10) G. E. Coates and J. E. Coates, J . Am. Chem. SOC.,55, 2733 (1933). (11) R. W. Merriam, J . Chem. SOC.,103, 628 (1913). (12) F. G. Keyes and W. J. Winninghoff, J . Bm. Chem. SOC.,38, 1178 (1916). (13) F. J. Welcher, “The Analytical Uses of Ethylenediamine Tetraacetic Acid,” D. Van Nostrand Co., Inc., New York, N. Y., 1958, p 242.
(14) C. Duval, “Inorganic Thermogravimetric Analysis,” Elsevier Publishing Co., New York, N. Y., 1953.
Volume 70,Number 6 May 1966
R. BARILE,&I.CEFOLA,P. GENTILE,AND A. CELIANO
1360
each other.6 Acetylacetone was weighed in a pycnometer-type cell having 0.5-mm capillary side arms to prevent vaporization. The enol content of 0.04 M solutions of acetylacetone in the alcohol-water solvents containing 1.04 X M NaC104 was determined by the Kurt Neyer titration method as modified by Cooper and Barnes.I5 Apparatus. The reaction of copper(I1) ion acetylacetone S monoacetylacetonatocopper(I1) ion hydrogen ion is far too rapid to be followed by conventional techniques, and thus a continuous-flow apparatus was adopted. The apparatus employed in this study was modified by Celianoe from the original design by Dalziel.lB Xeasurements. Ideal operation of the apparatus involves mixing of equal amounts of material from both reagent containers. The experimental mixing ratio (AIR) was determined a t all temperatures and fluid drive pressures in all solvents by mixing in the apparatus an approximately 0.1 N HC104 solution from the right reagent container with solvent from the left reagent container. Aliquots of the diluted acid, undiluted acid, and the solvent (blank) were titrated in excess water with NaOH to a phenolphthalein end point. Mixing efficiency was assessed by the physical dilution process in which a solution of HClOl was mixed with the pure solvent. The efficiency of mixing was evaluated by comparing the experimentally measured resistance of the flowing solutions after mixing with the resistance calculated for perfect mixing by 1/R, = MR(l/R,) (1 - MR)(l/R,), where R, = calculated resistance, AIR = mixing ratio, R, = nieasured resistance of acid solution, and R, = experimentally measured resistance of the solvent. The tests for mixing efficiency were performed in the most viscous solvents a t a flow rate less than the flow rate employed in the reaction rate studies. The lowest mixing efficiency a t the second electrode was found to be 98.0 f 0.5%. The reaction time was determined to *0.0003 see, indirectly from a knowledge of the reactor volume and the flow rate. The reactor volumes were obtained from Celiano.1’ The flow rates were determined at all temperatures, fluid drive pressures, and in all solvents. It is known that pressure applied to a system affects the electrical resistance of a solution.18 The expected decrease of resistance with increase in pressure was observed to be a linear relationship in all solvents and at temperatures in this study* resistance values were corrected to a reference pressure of 10 psi, at which pressure the initial resistances, resistances> and resistance ratios were determined. In order to Correlate the resistance
+ +
+
The Journal of Physical Chemistry
measurements at each electrode, the eighth electrode was used as a re€erence electrode. The resistances measured a t other electrodes were related to the eighth electrode through resistance ratios. The resistance ratios were determined at every temperature and in every solvent employed in this study. The initial resistance of the metal and ligand solutions, respectively, was determined while flowing through the apparatus at a pressure of 10 psi. The initial resistance after mixing is calculated by the parallel resistance law with the proper dilution factors. I n each solvent system an experimental curve relating concentration of hydrogen ion formed to the resistance of the solution was determined. The experimental calibration curve was based on the assumption made by YIonk, et al., in the determination of the dissociation constant of condensed phosphates, l 9 namely, that the ratio of mobilities and hence conductances of two similar ions are equal to the ratio of their ionic charges. We assumed the mobility of the solvated Cu2+ to be twice that of the solvated first complex, CuAA+, and accordingly made up solutions covering the range of concentrations of products formed in the reaction. Calibration curves were determined for every solvent at all experimental temperatures. A linear calibration curve was found in all solvents, with the exception of those most viscous. In these solvents the experimental calibration curve was concave toward the resistance axis. In order to demonstrate that the concave curvature of the calibration curve had no relation to the hydrolysis between copper ion and the solvent, solutions of increasing concentration of KaC1O4 in the solvent were prepared, and the resistance was measured at the eighth electrode. A plot of resistance of NaC104 exhibited the same curvature. This indicates that measurable hydrolysis of copper ion was not obtained in any experimental solvents.
and Discussion Order of Reaction. The order of reaction of Cu2+ and acetylacetone was evaluated from the van? Hoff equationz0in all solvent systems and found to be overall second order, first order with respect to the concentration of Cu2+,and first order with respect to the (15) 9. R. Cooper and R. P. Barnes, Ind. Enp. Chem., Anal. Ed., 10, 379 (1939). (16)K. Dalaiel, J . Bioi. Chem., 5 5 , 79 (1953~. (17)A. v. Celiano, Thesis, Fordham University, 1960, (18) G. F. Kortum and J. Bockris, “Electrochemistry,” Elsevier Publishing Co., New York, N. Y., 1951. (19) R. w. Jones, C. B. Monk, and C. W. Davies, J . Chem. SOC., 152, 2693 (1949). (20) A. A, Frost R. 0. pearson, “Kmetics and llechanism,,? 2nd ed, John Wiley and Sons, Inc., New York, N. Y., 1961.
RATEOF FORMATION OF MOXOACETYLACETONATOCOPPER(~~) ION
concentration of acetylacetone. The fact that the integrated rate equation could be applied to evaluate the specific rate constant, for all solvent systems, was taken as further evidence that the reaction is over-all second order. The Effect of Hydrogen I o n on the Rate of Complex Formation. The acid dissociation constant of acetylacetonez1a t 0' was found to vary approximately from in H 2 0 to 10-lo in JIeOH. With the concentrations of acetylacetone employed in our experiments, the contribution of hydrogen ion from the dissociation of I I f . Experimenacetylacetone would be less than tally, IIf acetylacetone was not found to have a M measurable effect upon the conductance of a NaC104 in all solvents. Thus, we may conclude that JI acetylacetone in mixed alcoholsolutions of water solvents have a hydrogen ion content of less M. than The rate of formation of the products, in all solvent systems, was measured under identical conditions for two runs, one of which differed only in the initial hydrogen ions added. Table I indicates the measured concentration of products (2) at varying experimental times for the two runs and the difference (A) between the concentrations of products for the runs with and without initial hydrogen ions, respectively.
Table I" A!+---,
Time X 103,
-----103(~+),
sec
Run Ab
Run BC
M
19.64 22.78 44.08 51.15 69.01 80.04 81.13 94.32 108.5
0.201 0.228 0,338 0.370 0.485 0.516 0.553 0.585 0.630
0.196 0.220 0.320 0.351 0.455 0.504 0.523 0.542 0.588
0,005
10aA,
0.008 0.018 0.021 0.030 0.012 0.022 0.040 0.042
Solvent composition: 49.96% MeOH-H20; temperature -10.00'; (Cu2+)o = 4.988 X M; ( H A A E ) ~= 0.9447 X 10-3 M . * (H+)o = lo-* M. (H+)o = 2 X hl.
The value of A a t the beginning of the reaction is within the experimental error of the measured concentration of products, and thus the initial rates of complex formation for the two runs are approximately equal and independent of hydrogen ion. It appears, therefore, that prior ionization of acetylacetone is not involved in the mechanism of complex formation16 but rather a direct combination of the reacting species occurs. As the extent of reaction increases, the value of
1361
A increases indicating that the concentration of products is affected by initial hydrogen ion only insofar as the rate of the reverse reaction is accelerated. Specific Rate Constants. Complex formation can be represented by a stepwise process according to eq 1 and 2 where the equilibrium constant for the first and second complex formation are given by eq 3 and 4, respectively. The integrated rate equation for an irreversible secondorder reactionz0is
k,t
=
2.303 b(a - T ) a - b log a(b - x)
~
where a = initial concentration of Cu2+, b = initial concentration of the enol form of acetylacetone, x = concentration of products measured at time t, and k = specific rate constant for first complex formation. Plottinglog [ ( a - x ) / ( b - x ) ] us. time, we have an equation of the form y = ntx B where the slope is
+
7n
=
ki(a - b) 2.303
(7)
B
=
log ( a / b )
(8)
and the intercept is
The specific rate constants for the first complex formation were determined by graphically evaluating the slope of log [ ( a - z / b - x ) ] us. time and by using eq 7 . Celiano6 has shown that irreversible second-order kinetics may be employed up to 60% completion of the reaction yielding kl which deviates by only 2% from the true value. I n considering the plots of log [(a - x)/ (b - x ) ] us. time for the different solvent systems, linearity was obtained, within experimental error, over the whole experimental concentration-time range studied in solvents of dielectric constant greater than 38. This fact was interpreted to indicate that the measured concentrations of products were only affected by the forward reaction for complex formation. With solvents of lower dielectric constant, we found an upward drift after approximately 60% reaction. dnalysis of the data for the solvent 91.04% EtOH-H20 showed that within 100 msec more hydrogen ion had been formed than the enol initially present. Since the conversion of the keto to the enol form is believed to follow the mechanism given by eq 5 , the change of an appreciable amount of the keto to the enol form could not possibly occur in the experimental time range of our study. In all probability, therefore, the upward drift may be due to the second complex formation reaction of Cu(AA)+ with the enol form first and then (21) P. S. Gentile, 1083 (1963).
M.Cefola, and A. V. Celiano, J . Phys.
Chem., 67,
Volume 70,Number 6 May 1966
1362
R. BARILE,n,I. CEFOLA, P. GENTILE,AND A. CELIANO
by interaction with the keto form especially in solvents of lower dielectric constants. Table .I1 lists the specific rate constants and the conditions under which they were determined.
Boltzmann's constant, ZA = ionic charge, e = electronic charge, and T = absolute temperature. Applying the above equation to the reaction of copper ion with the enol form of acetylacetone and neglecting the polar nature of the latter, the rate constant, ICl, measured at an ionic strength of 0.025 is taken as equal to the rate constant at zero ionic strength, klO. For a reaction between an ion and a polar molecule, the influence of ionic strength on the specific rate constant has been ~ h o ~to nbe ~practically ~ , ~ nil ~ below an ionic strength of 0.10. Ignoring the polar character of the enol form does not essentially change the basic nature of the relation of log ICo with the dielectric constant which follows
Table 11: Specific Rate Constants for First Complex Formation Wt
70
%
alcohol
D
enol
49.58MeOH 50.42MeOH 49,60 MeOH 49.60 MeOH 49.80MeOH 46.37 MeOH 49.96MeOH 49.96MeOH 49.96 MeOH 49.96nleOH 49.96 MeOH 70.37MeOH 70.37 MeOH 70.37 MeOH 70.37 MeOH 87.33MeOH 87.33 hIeOH 87.33 MeOH 87.56MeOH 87.56 MeOH 79.95 MeOH 79.95 MeOH 69.86 MeOH 69.86 MeOH 91.02 EtOH 91,02 EtOH 91.04EtOH 91.04 EtOH 91.04EtOH 91.04EtOH 69.70 PrOH 69.70PrOH 80.06 EtOH 80.06EtOH 18.20 EtOH 18.20EtOH
63.02 62.74 66.50 66.50 62.84 68.21 66.31 66.31 66,31 66.31 66.31 55.02 55.02 51.93 51.93 42.30 44.72 44.72 47.24 47.24 51.93 51.93 58.52 58.52 36.55 36.55 -34.36 34.36 32.31 32.31 35.85 35.85 38.05 38.05 76.87 76.87
49.83 50.41 48.43 48.43 50.00 46.02 48.70 48.70 48.70 48.70 48.70 63.88 63.88 63.90 63.90 72.75 75,36 75.36 77.33 77.33 72.19 72.19 63.70 63.70 86.17 86.17 85.05 85.05 83.42 83.42 77.77 77.77 77.84 77.84 32.89 32.89
Temp,
lO3a.
OK
M
273.16 273.16 263.16 263.16 273.16 263.16 263.16 263.16 263.16 263.16 263.16 263.16 263.16 273.16 273.16 273.16 263.16 263.16 253.16 253.16 253.16 253.16 253.16 283.16 253.16 253.16 263.16 263.16 273.16 273.16 273.16 273.16 273.16 273.16 273.16 273.16
5.041 5.070 5.063 5.063 4.989 5.002 4.966 4.993 4.988 2.494 4.986 4.986 4.986 4.986 4.986 4.986 4.986 4.986 4.999 4.999 4.475 4.475 4.475 4.475 4.337 4.337 5.263 4.503 4.995 4.995 5.058 5.064 4.974 4.974 5.183 5.183
10*b, M
10 -3k, ,I4 -1
sec
0.968 2.49 1.97 0.677 1.052 2 . 0 1 0.806 1.85 0.856 2.63 0.904 2 . 0 3 0.844 1.72 1.81 0.947 0.947 2.00 0.943 1.78 1.73 0.943 1.978 2.20 1.903 2.24 1.904 3.51 1.904 3.42 3.078 3.62 3.284 2 . 4 5 2.844 2 . 5 4 3.192 1 . 7 3 3.180 1 . 7 7 1.59 2.682 2.719 1.56 2.523 1.41 1.49 2.512 3.958 2.28 3.968 3.24 3.433 7.29 3.403 7.25 3.347 13.9 3.354 14.0 1.16 2.682 2.803 1.16 2.943 4.33 2.934 4.35 0.709 2.16 1.87 0.417
Efect of Solvent on the Specific Rate Constant. Considering the reaction of ionic species with neutral molecules, Laidler and Eyring,22using the theory of absolute reaction rates, showed that d(log kn) .-....-__- d(l/D)
%$(;A
E:*)
(9)
where ICo = specific rate constant at zero ionic strength, D = macroscopic dielectric constant, RA = radius of ionic species, RM*= radius of activated complex, k = The Journal of Physical Chemistry
log
k1O
= A(;)
+B
Figures 1-3 are the plots of log lcln 2 5 , 2 6 us. 1/D at 0, -10, and -20°, respectively. Treating the data by the method of least squares, the equations were derived
t
=
log kt
=
1 21.81 D
+ 3.067 at t
=
0"
(11)
1 log klo = 18.77 D
+ 2.960 at t = -10"
(12)
1 log kI0 = 20.96 D
+ 2.799 at t
(13)
=
-20"
From Figures 1-3 the plots of log k1° us. 1/D are linear over the range of 1/D from 0.0125 to 0.0250 and then rise sharply. The upward deviation from linearity begins a t different dielectric constants depending upon whether the solvent system is EtOH-HSO or MeOHHzO. This seems to imply the existence of some factor(s), dependent on the mole fraction of alcohol, as the contributing cause for the nonlinear behavior beyond a certain dielectric constant. Furthermore, deviations from linearity appear to be smaller at the lower temperatures when compared a t values of t = 0, -10, and -20'. Thus, there is also reason to believe that deviation from linearity is influenced by some dielectric constant dependent factor. (22) K. J. Laidler and H. Eyring, Ann. N. Y . Acad. Sci., 39, 303 (1940). (23) J. N. BrZnsted and W. F. K. Wynne-Jones, Trans. Faraday Soc., 25, 59 (1929). (24) A. Long, J. McDevitt, and P. Dunkle, J . Phys. Colloid Chem., 55, 819 (1951). (25) The values of the specific rate constants are for the average values of those in Table 11. (26) Values of klo in 98.76% MeOH-Hz0 were obtained by interpolating the data of Celiano.
RATEOF FORMATION OF MONOACETYLACETONATOCOPPER(~~) ION
4 201
3.*0i
LINEAR
. *
3 007
Figure 1. Log
k10 as
S L O P E : 21 8 1
YEOM ETOH
-
Hz0
H20
a function of 1 / D a t 0"
4 20
4 00 3 80
3 60 3 40
1363
I t is a known fact30 that the axially coordinated HzO molecules in such a distorted octahedron are replaced at a faster rate than the equatorially situated HzO molecules. Thus, the occupation of an axial position by an alcohol molecule should result in a larger rate constant. A factor dependent upon dielectric constant, which could account for the upward deviation from linearity, is the instability of ionic species in solvents of low dielectric constant (D < 35). Separation of Energy of Activation. I n comparing reactions in the gas state and in solution one would like to compare activation energies of the gas state with those in solution which are independent of the properties of the solution. Since the rate constant is a function of temperature, dielectric constant, and ionic strength in ~ o l u t i o n , ~the ~ -energy ~~ of activation and other thermodynamic properties of activation are functions of these parameters. Svirbely and Warner33described a method of separating the temperature and dielectric effects on the energy of activation. For a system at zero ionic strength, one may write log Lo = f(D,T)
3 2c
(14)
Obtaining the general differential expression
3 oc
[TI,
6 log
d log ICo =
2 80 I O
12
Figure 2.
14
Log
16
k10 as
18
20
22
24
2 6
a function of 1/D a t
28.
30
32
- 10".
kO
dT
7 1
+ [6 log ICo
dD (15)
T
dividing t'hrough by dT, and mult.iplying by 2 . 3 ~ we ~ ~ , obtain
4.20
2.3RT2[
4.00
-1
d log ICo dT
=
2.3RT2[-]
6 log IC0
6T
D
+
2 . 3 R T6 2log [ 7ICo] dD - (16)
3.80
T ~ T 3.6 0
Equation 16 can simply be stated as
/ .
3.40
/./'
3.20
/'
(Ea)m
L I N E A R S L O P E : 20.96
*
3.00
M E O H - H20 ETOH
-nlo
2.80 1.0
Figure 3.
1.2
1.4
1.6
1.8
2.0
k.2
2.4
2.6
2.8
3.0
3.2
Log k10 as a function of 1/Dat -20".
Data on the coordination of metal ions in alcoholwater solvents have indicated that the fully coordinated aquo complex is not found when stoichiometric amounts of HzO are available for the metal ion. For Co2+ in EtOH-HzOZ7, Dy3+ in MeOH-Hz02*, and Cu2+ in EtOH-Hz0,29 the hexaaquo complex is found exclusively a t concentrations of HZO greater than 10 A I .
=
(Ea) D
+ (EJT
(17)
where (E,)Fc is the energy of activation at a fixed composition, the Arrhenius activation energy, (E,) is the contribution to the energy of activation a t a fixed dielectric constant, and (Ea)Tis the contribution to the energy of activation at a constant. temperature. I n (27) C. K. Jorgensen, Acta Chem. Scand., 8, 176 (1954). (28) J. Bjerrum and C. K. Jorgensen, ibid., 7, 953 (1953). (29) N. J. Friedman and R. A. Plane, Inorg. Chem., 2, 11 (1963). (30) L. DeMaeyer and K. Kustin, Ann. Rec. Phys. Chem., 14, 8 (1963). (31) E. S. Amis and V. K. La Mer, J . Am. Chem. Soc., 61, 905 (1939). (32) W. J. Svirbely and J. Lander, ibid., 60, 1616 (1938). (33) W. J. Svirbely and J. C. Warner, ibid., 57, 1883 (1935)
Volume 70, .Turnher 6
May 1966
R. BARILE,AI. CEFOLA,P. GENTILE,AND A. CELIANO
1364
previous ( E a ) D was evaluated by using isodielectric solvents at different temperatures. (EB) was obtained by subtracting ( E J Dfrom ( E a ) ~ Cwhich is evaluated by the Arrhenius equation. To eliminate the extra weight placed upon a point in using isodielectric solvents, an analytical method of evaluating (Ea)D was adopted from the work of Cefola, Gentile, and C e l i a n ~ . Instead ~~ of using isodielectric solvents, a function of the dielectric constant is chosen which gives a linear relationship with log k' over the range of dielectric constants of interest. At each temperature, an equation of the form log kO = Af(D) B is obtained. For a fixed dielectric constant log kO can be calculated at each temperature at which the above expression has been evaluated, then can be obtained. In this work log k10 is a linear function of 1/D over the range of D = 40 to 80. Equations 11-13 represent these linear functions a t 0, -10, and -20', respectively. In order to demonstrate the additivity (Ea117 = ( E a ) F C , ( E a ) D , (Ea)T, and ( E a ) F C of ( E d D are evaluated for t = -10 and solvents of D = 40, 50, 60, 70, and 80. (E,)FC was evaluated by using the Arrhenius expression
+
+
where the rate constants are evaluated using eq 11 and 13 a t 0 and -20' for t,he fixed compositions corresponding to D = 40,50,60,70, and 80 at - 10'. (Ea)Dis given by the expression
which is equivalent to
Log klo is determined at 0 and -20' using eq 11 and 13 forD = 40,50,60,70, and80, and [blogkl'/b(l/T)]D is evaluated for each D and (Ea) is calculated. ( E a ) T is given by the expression
The Journal of Physical Chemistry
which is equivalent to
dD/dT is evaluated by the data of Akerlof35 and [b log k?/b(1/D)IT is the least-squares slope of the equation of log k? vs. 1/D for t = -10' derived from eq 11and 13 a t 0 and -20'. Table 111 contains the tabulation of (Ea)T,(Ea)D, and (Ea)Fc for each D. ( E a ) T -k Table 111: Energy of Activation for the Formation of Monoacetylacetonatocopper(I1) Ion a t Constant Temperature, Fixed Dielectric Constant, and Fixed Composition as a Function of Dielectric Constant of XleOH-H20 Mixtures a t - 10"
+
(JUT, koal/mole
(EdTs kcal/mole
(E~D, kcal /mole
5.48 5.28 5.10 4.94 4.82
(Ea)D,
D 40 50 60 70 80
4.56
0.918
4.50
0.775
4.47 4.43 4.40
0.633
0.507 0.417
( E d FC , kcal/mole
5.50 $- 0.02 5.27 5.08 4.92 4.81
- 0.01 - 0.02 - 0.02 - 0.01
The additivity of (Ea)=and ( E a ) D is found to be within *20 cal/mole. (Ea)Dvaries only slightly with dielectric constant, but (Ea)Tis a linear function of log D over the range of solvent compositions in which log k? is linear with 1/D. Thus, the variation of the Arrhenius activation energy with a change in solvent composition is due mainly to the variation of the contribution to the energy of activation at a constant temperature with solvent composition.
Acknowledgment. We are grateful to the Atomic Energy Commission for support of this work under Contract, AT(30-1)-906. (34) P. S, Gentile, hf. Cefola, and A . V. Celiano, J . Phys. Chem., 67, 1447 (1963). (35) G. Akerlof, J . A m . Chem. Soc., 54, 4125 (1932).
