7002 Methyl 1,3-Dioxolane-2-carboxylate. Attempts to prepare 1,3dioxolane-2-carboxylic acid or its methyl ester from glyoxylic acid and ethylene glycol and from methyl dichloroacetate and the sodium salt of ethylene glycol were unsuccessful, but we later learned that the former method has been made to'work by Newman and Chen.36 Our successful method began by bubbling excess ozone through a solution of 8.5 g (85 mmol) of 2-vinyl-1,3-dioxolane'2 in 100 ml of methanol at -15". The resulting solution was added t o 150 ml of 5 % aqueous sodium hydroxide and 42 g (180 mmol) of silver oxide. After 1 hr of rapid stirring the solution was filtered and the filtrate extracted with 100 ml of ether. Excess carbon dioxide was bubbled into the aqueous layer which was then evaporated to dryness at 20 mm pressure. The 26.5 g of white solid was extracted with hot methanol and the filtered methanol solution evaporated to dryness, leaving 10.5 g of white crystals whose nmr spectrum in deuterium oxide indicated the presence of equimolar amounts of sodium formate (6 7.2) and sodium 1,3-dioxolane-2carboxylate [6 2.78 (s, 4, CH,) and 3.88 ppm (s, 1, CH)].a7 Enough 18 N sulfuric acid was added t o 7.5 g of an equimolar mixture of sodium formate and sodium 1,3-dioxolane-2-carboxylate in 20 ml of water at 0" to give a pH of 2. The solution was quickly extracted twice with 100-ml portions of ether to which ethereal diazomethane was added until the yellow color persisted for 1 hr. Distillation of the magnesium sulfate dried solution gave 3.1 g of methyl 1,3-dioxolane-2-carboxylate:9 9 . 4 2 pure by glpc (6-ft DEGS column); bp 87-88' (24 mm); nmr (CC1,) 6 5.22 (s, 1, CH), 4.00 (br s, 4, CH2), 3.70 ppm (s, 3, CH3);3s ir (neat) in order of decreasing intensity 1740, 1130, 1222, 940, 1035, 2955, 1292, 1420, and 2900 cm-'. Kinetics. The following changes were made in the kinetic procedure used previously. A Perkin-Elmer grating spectrophotometer, Model 337, was used with 0.05 mm IR Trans I1 (36) M. S.Newman and F. Chen, The Ohio State University, personal communication, 1971. (37) Chemical shifts downfield from the carbon-bound protons of internal tert-butyl alcohol. (38) Chemical shifts downfield from internal tetramethylsilane.
cells. Under these conditions, the extinction coefficient for MeOH, which was found to follow eq 3, was somewhat smaller than that
(108.8 - 5.98[NaOMe])M--' cm-'
E ~ ~ ~=o H
(3)
obtained previously. The runs at 60" were carried out by using a 2-ml sealed ampoule for each point. Ester concentrations were in the range 0.55-0.98 M and sodium methoxide concentrations in the range 0.36-0.62 M . pK Determinations. The pK of tetrahydrofuran-2-carboxylic acid was determined by measuring the pH in a potentiometric titration against standard aqueous sodium hydroxide using a Radiometer titrator (ABUl, PHM26c, SBR2c, and type C electrode). The other two acids were used in the form of their sodium salts, which were titrated rapidly with standard acid (although reference data on other acetals show that no significant amount of hydrolysis of the acetal linkages would have occurred even under more acidic conditions). The ionic strengths at which the pH values were measured were in the range 0.005-0.020 M . The observed pH was taken to be -log a H + and ionic activity coefficients were assumed to obey the Davies equation ( i . e . , eq 4 at 35"). In
calculating the pK values proper allowance was made for the fact that the hydrogen ion concentrations were not negligible compared to the concentrations of the acid and its anion. The sodium salts used were prepared by recrystallizing from alcohol the products of the reaction of aqueous sodium hydroxide with the corresponding methyl esters. A weighed amount of each sodium salt was dissolved in deuterium oxide containing a known concentration of fert-butyl alcohol, the ratios of the areas of the strongest nmr peaks were found to agree with the calculated value, and no nmr peaks due to impuritiescould be seen.
Acknowledgment. We are indebted to Dr. Wendel ~i~ for carrying out preliminary studies on this investigation.
Effect of Solvent on the Ground States and Transition States in the Reactions of 2,4,6-Tri-tert-butylphenoxyl with Phenols L. R. Mahoney" and M . A. DaRooge
Contribution from the Ford Motor Company, Dearborn, Michigan Receiced M a y 13, 1971
48121.
Abstract: The absolute rate constants for the hydrogen atom transfer reaction of the 2,4,6-tri-tert-butylphenoxyl radical with phenols in various solvent systems have been determined a t 30 a n d 60". T h e Henry's law constants for phenol a n d 1,3,5-tri-tert-butylbenzene which h a d previously been shown to be a good model for the solution properties of the free radical have been determined by transpiration techniques. Utilizing infrared spectroscopy, the activity coefficients of Prigogine for the specific hydrogen bonding interactions of phenol with solvent have been determined. T h e results of these kinetic a n d solution property studies have been combined and subjected t o a detailed analysis based upon activity coefficients. This type of analysis provided a detailed description of the partial molal energy changes resulting f r o m the transfer of the activated complex, free radical, a n d phenol from carbon tetrachloride to other solvent systems. T h e findings suggest that the mechanism of the reaction involves a prior equilibrium formation o f a hydrogen-bonded free radical-phenol complex, followed by hydrogen a t o m transfer within the complex. I t is shown that this mechanism accounts for the abnormally low activation energies observed for hydrogen a t o m transfer between oxy1 radicals a n d is consistent with the A factors observed for such reactions. Finally, the effect of solvent on such reactions is not consistent with the activated complex being polar in nature.
important reaction in An systems For
a number of free-radical is the transfer of hydrogen atoms between the mechanism Of the Oxy phenolic inhibition of hydrocarbon oxidation involves Journal of the American Chemical Society
the rapid and often reversible transfer of hydrogen atoms between p h e n o x y and peroxy free r a d i c a l s . ' (1) For a review, cf, L. R. Mahoney, Angew. Chem. Irit. Ed. Engl., 8, 547 (1969).
1 94:20 1 October 4, 1972
7003
The synergistic behavior of mixtures of phenols as antioxidants depends upon the transfer of hydrogen atoms between hindered and nonhindered phenoxy radicals. Kinetic studies in nonpolar solvents have revealed that the rates of these processes (1) possess very low temperature coefficients, i.e., low apparent activation ene r g i e ~ , ~and - j (2) are greatly accelerated by the presence of electron-donating substitutents on the phenolic moiety; empirical correlations with a+ values yield p values comparable to those observed in reactions in which carbonium ions are formede6-* With the exception of a study of the effect of solvent upon the ratio of rate constants for the reaction of polystyrenyl peroxy radicals with styrene and with phenolsg the effects of polar solvents on the rates of these reactions have not been reported. Two requirements must be satisfied in order to interpret, in terms of the transition state theory, the effect of solvent upon the rate of a bimolecular freeradical reaction. First of all, absolute rate constants for the reaction must be obtained. As Walling and Wagner emphasized'O data obtained from the usual competitive techniques show only the effect of medium on the difference in free energy of the transition states involved. A second requirement is a knowledge of the effect of solvent on the ground-state properties of the reactants. If this latter requirement is not fulfilled solvent effects upon the reactants and the transition states may not be separated. Both of these requirements are satisfied by the system chosen for the present study. The absolute rate constants for the hydrogen atom transfer reaction of 2,4,6tri-tert-butylphenoxyl with phenols may be directly determined by means of stop-flow techniques" and the heat of formation of the radical in a variety of solvents has been determined by direct calorimetric measurements. ] The determination of absolute rate constants in the same solvents with the additional experimental determination of the effect of solvent on the ground states of the phenolic hydrogen donor and a model compound for the radical has allowed a quantitative estimate to be made of the effect of solvent upon the free-energy contents of the activated complexes in the reactions.
Results and Discussion Kinetic Study. A systematic study of the effect of solvent on the rates of reaction of the 2,4,6-tri-tertbutylphenoxy free radical, A with phenolic compounds was carried out. A series of substituted phenols was studied in pure carbon tetrachloride and pure benzene as solvents at 30 and 60". The reaction with unsub1 ,
(2) L. R. Mahoney and M. A . DaRooge, J . Amer. Chem. SOC.,89, 5619 (1967). (3) L. R. Mahoney and M. A. DaRooge, ibid., 92, 4063 (1970). (4) R . W. Kreilick and S. I. Weissman, ibid., 88, 2645 (1966). (5) J. A. Howard, W. J. Schwalm, and I'/i(p/~)"
(10)
where (p/c)O and (pic)' are the Henry's law constants in mm M-I for the phenol in carbon tetrachloride and in the second solvent, respectively. The mole fractions of phenolic compounds in the vapor phase over their dilute solutions in pure CCld and in pure benzene at 60" were determined utilizing a modification of the transpiration technique of Andon, et aI.,l5 and the Henry's law constants were determined (14) A . J. Parker, J . Chem. Soc., A , 220 (1966). (15) R. J. L. Andon, J. D. Cox, and E. F. G. Herrington, J . Chem. Soc., 3188 (1954).
94:20 J October 4 , 1972
7005 Table II. Summary of Solution Properties of Phenols Substituent
Solvent
4-H
A. Substituted Phenols in CCl, and CEHE OYSBE at 60" ARB,kcal/mol at 30"
CCI, C6He
cc14
4-t-Bu 3,5-Mez 3-Carboethoxy
CeH6 CCla CEHE CCl4 C6He
1 .oo 0.35 i 0.02 1 .oo 0 . 3 2 f 0.02 1.oo 0.36 f 0.02 1 .oo 0.21 f 0.01
6.23 4.48 6.82 5.23 7.58 6.30 8.34 8.17
oYSBH(Cakd)at 30" 1 .oo 0.27 1 .oo 0.28 1.00 0.23 1 .oo 0.20
f 0.06 f 0.04 f 0.08 f 0.06 f 0.18 f 0.05 f 0.07 f 0.16
f 0.02 f 0.02
f 0.02 f 0.01
B. Phenol in CC14-CH,CN and CC14-C4H802Mixtures OY'EH
30 O
Solvent"
60'
1 .oo 0.14 i 0.01 0.081 f 0.007 0.037 i 0.003 0.035 f 0.002 0.017 i 0.001 1 .oo 0.20 i 0.02 0.120 f 0.005 0.027 i 0.001 0.023 i 0.001 0.0087 i 0.0006 C.
I .oo 0.18 i 0.01 0.064 i 0.005 0.047 f 0.002 0.034 i 0.002 0.028 i 0.005 1 .oo 0.19 f 0.01 0.082 f 0.008 0.044 i 0.004 0.030 f 0.002 0.015 i 0.001
Phenol in CC1,-CH3CN and CC14-C4HsOlMixtures [oysEHb
Solvent0
a
30
60 O
I .oo 0.32 f 0.01 0.17 f 0.01 0.097 f 0.004 1 .oo 0.38 f 0.02 0.193 i 0.006 0.11 i 0.01
1 .oo 0.52 i 0.02 0.28 f 0.01 0.14 i 0.01 1 .oo 0.67 f 0 . 0 4 0.260 f 0.004 0.16 f 0.01
The number preceding the chemical formula denotes the mcle fraction of components in the solvent mixture, the remainder being CCI,.
from plots of pressure of the phenols in the vapor phase us. their molar concentration in solution. The values of O T ~ B H at 60" calculated by means of eq 10 are summarized in Table 11, part A. Also included in the table are values of the partial molar enthalpies of solution at high dilution of the phenols at 25" in pure carbon tetrachloride and pure benzene determined by solution calorimetry. Based on the assumption that the differences in the partial molar enthalpies of solution at infinite dilution in carbon tetrachloride and benzene are relatively constant in the temperature range of 25-50', the values of OyS~Hat 30" were calculated and are summarized in Table 11, part A. The values of O Y ~ B H for phenol in the mixed solvents carbon tetrachloride-acetonitrile and carbon tetrachloride-dioxane at 30 and 60" were calculated from the Henry's law constants and eq 10 and are presented in Table 11, part B. Specific Hydrogen Bonding Interactions. In addition to the relatively weak solvent interaction due to dipolar effects, a phenolic compound, BH, is capable of strong specijic hydrogen-bonded interactions with the solvent. The change in the standard chemical potential on the transfer of BH from the reference solvent to the second solvent, S, may be divided into two parts,I6 i.e. P'BH
=
P'BH
+ RT In ['ySBH]* + RT In
[OYSBHlH
(1 1)
The activity coefficient ['YSBH]* accounts for all interactions which affect the standard chemical potential of BH except specific hydrogen bonding. The activity coefficient ['YsBHIH represents the effect on the change of the chemical potential due to specific hydrogen bonding interactions and is defined by the expression
where [BH] and [BH.S] are the concentrations of free and hydrogen-bonded phenol as determined by spectroscopic techniques.'' Combining eq 12 and 16 we may write 1 kS ___-
- 'ySA.['ySBH]*
oY sx + ko This expression allows a direct estimate to be made of the solvation of the activated complex compared to the sum of the solvation of the free radical and the residual phenolic moiety. Infrared studies of solutions of CC1,-CH3CN and CC14-C4H40, containing phenol were utilized for the determination of the concentration of free and hy[oYsBH]H
(17) Under conditions of sufficiently high dilution such that the activity coefficients of BH and S approximate unity, eq 12 may be replaced by
(16) I. Prigogine and R. Defay, "Chemical Thermodynamics," D. H. Everett, Translator, Wiley, New York, N. Y.,1954, pp 409-436.
Mahoney, DaRooge
Reactions of 2,4,6-Tri-tert-bulylphenoxyl
7006 Table 111. Summary of Activity Coefficient Ratios for the Reaction of 2,4,6-Tri-tert-butylphenoxyl with Phenols
A. Substituted Phenols in CCl, and CaHa OYSA, o y s , , / o Y s x + - ~ .
Substituent ~~~~
~~
~~~~
30 '
Solvent. ~
~
4-t-Bu
~
~~
~
~~
3,5-Mez 4-H 3-Carboethoxy
~~~~~
~
~
~~
~
1 .o 0.52 i 0.06 1 .o 0.46 + 0 . 0 5 1 .o 0.48 i 0.05 1.0 0.33 i 0.04
1.0 CCI, 1 .o C6H6 1 .o CC14 1 .O CaH6 1 .o CCla 1 .o C6H6 1 .o CCli I .O CsHe
7
30 '
60
1 .o CCI, 0.036CHaCN 0.088 CH3CN 0.170CHaCN 0,381 CH&N 0.648CHsCN 0.820CH3CN 1 .o CCl, 0.0226 CdHg02 0.0564C1Hg02 0.1120C4H~02 0.260C4H802 0.530C4HsO?
,oYsBH/oy"~~_-7
Y.*, 5
0-
7
60'
1 .o 1.9 i 0.4 1 .o 2.0 i 0.4 1 .o 1.8 & 0.3 1 .o 1.7 C 0.3
i 0.03
i 0.09 i 0.09 i 0.04
[OySBEJ*/OysX*t-.--,
30 '
60 '
30"
60 '
1 .o 0.34 i 0.03 0.19 z!z 0.02 0.10 i 0.01 0.052 i 0.006 0.034 i 0.003 0.030 i 0.003 1 .o 0.20 0.02 0.13 i 0.01 0.049 i 0.004 0.038 i 0.003 0.017 i 0.001
1 .o 0.39 i 0.03 0.22 i 0.02 0.11 i 0.01 0.06 zt 0.006 0.025 i 0.003 0.032 i 0.003 1 .o 0 . 2 2 5 0.04 0.26 I-t 0.03 0.089 + 0.008 0.042 i 0.04 0.028 i 0.002
1 .o 1.06 i 0.12 1.12 i 0.19 1.03 i 0.15
1 .o 0.75 i 0.09 0.79 3 0.10 0.79 & 0.12
1 .o 0.54 i 0.08 0.68 I 0 . 0 7 0.47 i 0.10
1 .o 0.59 i 0.13 1 . 0 0 x 0.08 0.56 zt 0.09
Solvent.
oysxi-~-
~~
1 .o 0.56 1 .o 0.77 1 .o 0.56 1 .o 0.31
B. Phenol in CCII-CH~CNand CCla-C:H802 Mixtures +SA
OYSA, /
1 .o 1.8 i 0.2 1 .o 2.1 t 0.4 1 .o 1 . 6 i 0.4 1 .o 1.5 x 0.3 Y"a,
7---o
^I
!O' T.Sx'--
__._
30'
60
0.72 i 0 . 1 1 0.61 r 0.11 0.92 i 0.15 0.86 5 0.13 1 .o
0.61 I 0 . 0 7 0.94 I 0.16 0 . 5 3 1: 0 . 0 8 0.94 & 0 . 1 3 1 .o
0.25 i 0.05 0.12 i 0.04 0 . 6 3 I 0.06
0.47 0.51 0.64
-ir I
zt
0.07 0.09 0.10
6 Number preceding the chemical formula denotes the mole fraction of component in the solvent mixture. the remainder being CCIL Values of [oYs€3H]H derived from eq 17.
drogen-bonded phenol at 30 and 60". The infrared analysis did not allow the concentration of free phenol to be accurately determined at mole fractions of the donor solvents greater than 0.11 for dioxane and 0.17 for acetonitrile. The values of ['YSBHIH obtained from the study are summarized in Table 11, part C. Solution Properties of 1,3,5-Tri-tert-butylbenzene. In the earlier calorimetric study1*it was observed that the enthalpy changes at 25" for the transfer of A . from a state of high dilution in carbon tetrachloride to states of high dilution in a series of solvents are equal ( 1 0 . 5 kcal/niol) to the enthalpy changes for 1,3,5-tri-tertbutylbenzene (TTB). From those results it was suggested that TTB could serve as a good model compound for the solution properties of A . . Within the validity of this assumption the changes in the chemical potentials will be equal and 0
9
Y'A.
=
(14)
@YsTTB
Accordingly we have determined the mole fraction of TTB in the vapor phase at 60" above 0.1 M solution in carbon tetrachloride, benzene, and 0.65 mole fraction CH,CN. The values of "T'TTB calculated from eq 15 were equal to 1.0, 2.0 i. 0.1, and 6.0 =t0.5, respectively. The fact that the values of ' Y ~ T T B exceed unity is consistent with the observed endothermicity of the transfer measured at 25". Benzene as Solvent. In Table 111, part A, are summarized the values of @ y S@~y S.B H / @ y S x at 30 and 60" in benzene for phenol and a number of substituted phenols. Although the values of the individual rate constants, ks and k @ ,increase by a factor of 100 in the series 3-carboethoxyphenol to 4-tert-butylphenol their ratios, @Y~.&. O T S E ~ / ~ Y X = ,are relatively constant for all phenols. The values of @ y s/ ~" y, S ~ are = also insensitive to temperature and are relatively constant with
*
Journal of the American Chemical Society
change of substituent. Since the value of O y s . ~is. constant we conclude that the solvation of the activated complexes in benzene relative to CCl, as measured by "y'x* is insensitice t o the remote substituent on thc phenolic moiety. Utilizing the value of OySTTB and eq 14 the values of' " T ~ x +were calculated for the substituted phenols from the ratios of "ysx*/"ySA, . Within experimental uncertainties the values of o ~ are ~ equal ~ to * unity for the substituted phenols. Thus, the free energies of the activated complexes are cinchanged upon transfer from carbon tetrachloride to benzene and the rate difference in the two solvents is solely determined by the extent of solvation of the reactant molecules. Mixtures of Carbon Tetrachoride-Acetonitrile and Carbon Tetrachloride-Dioxane as Solvents. The values of the ratios @ySa, 'ySB&Sx +, 0ys.A. (Oycn~I)*/@ySs =, and @ T ~/OySx * , rt for the reaction of phenol in the mixed solvents carbon tetrachloride-acetonitrile and carbon tetrachloride-dioxane at 30 and 60" are summarized in Table 111, part B. In all cases the values of "T'A. ' ~ ' B H / @ y s X + decrease with increasing concentrations of acetonitrile and dioxane. From the values of Oys~. (Oyr"~~)*/@ySx+ it is clear that virtually all of this decrease up to mole fractions of 0.17 acetonitrile and 0.11 dioxane'8 is due to the specific hydrogen bonding of phenol with added donor solvent. Moreover. the solvations of the activated complexes are accurately described by the sum of the solvations of the free radical and the residual solvation of the phenol, i.e., "y'.~ ( @ y s ~ H ) *is equal to oysx *. At the higher mole fractions of the added solcents where values of ["ys:RH]" are not experimentally ob(18) Due to the possible occurrence of reaction 6 the values of dioxane mixtures may be low by as much a s ii factor of two.
a *!;A i ,nys~a/o-ySx* or all
1 94:20 1 October 4, I972
7007 tainable but values of OySBH have been determined, the values of O ~ S A/OySx . =i= have been calculated and are found to be somewhat less than unity in all cases. Utilizing the value of " ~ ' T T B and eq 12 the value of oysx+ is found to be on the order of 10 in 0.54 M CH3CN at 60". Thus, the activated complex is less strongly solvated in this polar solvent mixture than in carbon tetrachloride. Nature of the Activated Complex in Hydrogen Atom Transfer from Phenolic Compounds. As pointed out in the introductory statement the rates of reaction of oxy radicals with phenolic compounds are characterized by very low activation energies and by large rate effects due to the presence of remote substituents of phenolic moiety. In the following section the results of the present study of the effects of solvent upon the activated complex in regard to these two characteristics will be discussed. The values of OySA. ( o y s ~ H ) * / =io= yins ~carbon tetrachloride-acetonitrile mixtures (cf. Table 111, part B), were found to be unity. This result suggests that the specific hydrogen bonding interactions of the reactant phenol with solvent have been replaced in the activated complex by specific hydrogen bonding interactions with the free radical, i.e., the activated complex resembles a hydrogen-bonded free radical-molecule complex. The addition of the reversible formation of hydrogen-bonded free-radical complexes to eq 2 leads to the scheme BH
+ A . )JBHA.
BHA.
BHA
.BHA I _ B.
+ HA
(15)
(16)
(17)
where BHA and . BHA represent the hydrogen-bonded complexes of A . with BH and B. with AH. Under conditions such that the rate-controlling step in the formation of B. l 9 is the transfer reaction 16 and where ki6
