19268
J. Phys. Chem. 1996, 100, 19268-19272
Determination of Self-Association Equilibrium Constants of Ethanol by FTIR Spectroscopy Fanny Schwager, Eva Marand,* and Richey M. Davis Department of Chemical Engineering, Virginia Polytechnic Institute and State UniVersity, Randolph Hall, Blacksburg, Virginia 24060 ReceiVed: May 9, 1996; In Final Form: September 24, 1996X
The self-association of ethanol diluted in CCl4 has been studied by IR spectroscopy. Three OH stretching bands were assigned to monomers, linear dimers, and linear multimers. The self-association was described with two equilibrium constants, one for the formation of dimers, K2, the other for the formation of multimers, KA. These equilibrium constants were determined for ethanol concentration ranging from 0.19 to 0.76 mol L-1 by using a method developed by Coggeshall and Saier. At T ) 25 °C, K2 was found to be equal to 1.08 L mol-1 in terms of molar concentration or 18.4 in terms of molar fraction; KA was found to be equal to 3.52 L mol-1 in terms of molar concentration or 60.0 in terms of molar fraction. The enthalpy of formation for K2 was found to be equal to -4.61 kcal mol-1 and to -4.15 kcal mol-1 for KA.
Introduction In an effort to understand the nature of intermolecular interactions between a water soluble polymer and an alcohol solution, we have examined the solution thermodynamics of the alcoholic solution itself. Although there are number of publications dealing with heat and entropy of mixing of alcoholic solutions,1-3 less reliable information is found about the stoichiometry of the self-association in alcoholic solutions. A better understanding of this stoichiometry would help to predict the physical property changes of certain hydrogen-bonded systems. In particular, formation of hydrogen bonds in a system can lead to higher melting points, boiling points, and the heat of vaporization4 and also to better solubilities of liquid-liquid or liquid-solid mixtures. This latter effect is of particular interest to us. Alcohols are known to highly self-associate via hydrogen bonding.4 The self-association of alcohol is a complicated phenomenon, since many different structures can be formed. Luck and Schrems5 observed IR bands corresponding to free units, cyclic dimers, trimers, and tetramers, linear dimers, and higher multimers. In principle, the formation of each structure should be described by a different equilibrium. To be able to determine the values of these equilibrium constants, the problem has to be simplified. The usual approach2,6-13 has been to develop a model assuming that one or two of the equilibria are predominant in the self-association and that only one or two hydrogen-bonded structures can be detected in the solution. Thus, the predominant chain structure or the more realistic model for the self-association needs to be defined. The nature of the predominant chain structures depends on a number of factors such as the structure of the alcohol, its concentration in a nonpolar or inert medium (for example, carbon tetrachloride or cyclohexane), the nature of the medium, and the temperature. Hydrogen bonding in solutions or blends can be characterized by spectrometric or calorimetric techniques. However, the determination of the self-association equilibrium constants from calorimetric studies is dependent on the type of associated solution model assumed. Spectroscopic measurements, on the other hand, can give direct quantitative information such as the concentration of associated species. In this paper, we focus on the self-association of ethanol diluted in CCl4. Using FTIR spectroscopy, we quantitatively X
Abstract published in AdVance ACS Abstracts, November 1, 1996.
S0022-3654(96)01344-5 CCC: $12.00
measure the concentration of hydrogen-bonded and nonhydrogen-bonded ethanol species and calculate the equilibrium constants of self-association. Experimental Section Spectrometric-grade ethanol was purchased from AAPER alcohol and Chemical Co. and spectrometric-grade carbon tetrachloride from Fisher Scientific and used without further purification. The purity, and more precisely the dryness of ethanol, was verified by infrared spectroscopy before use. This was achieved by performing the infrared spectra of ethanol/ water mixtures at various compositions. A water peak appeared around 3680 cm-1 for water content above 0.5% by volume in ethanol. The absence of a water peak in our mixtures shows that the water content in ethanol was lower than 0.5%. Accurate sample dilutions were performed using a Labsystems micropipet. The infrared spectra were collected with a BIO-RAD FTS 40A spectrometer with a MCTA liquid-nitrogen-cooled detector at a resolution of 2 cm-1. The samples were contained in a demountable precision liquid cell purchased from Harrick Scientific Corporation with two KBr windows and 0.25 mm thickness spacers. The temperature of the sample was controlled by a thermocouple and regulated at (0.1 °C with an OMEGA CN-2011 programmable controller. Each spectrum contained 64 signal-averaged scans. In the case of variable temperature studies, the absence of degradation or leaks in the cell was verified. The area of the band associated with the symmetric and asymmetric CH stretching vibration of the ethanol aliphatic CH2 groups, which is a noninteracting band, was recorded as a function of temperature.14 The area of this band remained constant. The curve fitting of the bands was achieved using a spectrum analysis program, Grams/386, developed by Galactic Industries Corporation. The consistency of the results was within 5%. Results Equilibrium Model. The self-association of ethanol diluted in CCl4 should be described, in principle, by as many equilibrium constants as the number of different structures formed via hydrogen bonding. In the infrared spectra of ethanol, Luck and Schrems5 observed bands corresponding to free units, cyclic dimers, trimers, and tetramers, linear dimers, and higher multimers. To be able to solve this problem mathematically, © 1996 American Chemical Society
Constants of Ethanol
J. Phys. Chem., Vol. 100, No. 50, 1996 19269
Figure 3. IR spectrum of CCl4.
Figure 1. FTIR spectra in the hydroxyl stretching region of ethanol diluted in CCl4 at T ) 50 °C and at ethanol concentrations equal to 0.227, 0.36, 0.76 mol L-1.
Figure 2. FTIR spectra in the hydroxyl stretching region of ethanol diluted in CCl4 at a concentration of ethanol equal to 0.36 mol L-1 and at T ) 50, 60, and 65 °C
we describe the self-association with a simplified model based on the determination of the predominant associated structures. Van Ness et al.1 explained that the existence of cyclic chains beyond a dimer is questionable, since the hydrogen bonds are forming and breaking continually. Linear structures must thus predominate for self-association of alcohols.2,6-13 Since two distinct associated bands are present in the ethanol hydroxyl stretching region (see Figures 1 and 2), at least two equilibrium constants are required to describe the ethanol self-association. Coggeshall and Saier10 and other authors7,14-17 have shown that the self-association can be described by using a model with two equilibrium constants: the first constant corresponding to the formation of dimers and the second constant corresponding to the formation of multimers. This model is consistent with the fact that the formation of a dimer complex is thermodynamically more favored than the addition of a unit to an already existing chain of hydrogen-bonded hydroxyl groups. These association equilibria can be written as linear condensation polymerizations: K2
A1 + A1 798 A2 with
K2 )
φA2 2φA12
KA φ h A1 + Ah 798 Ah+1 (h > 1) with Ka ) φ Ah+1 AhφA1 h + 1
The equilibrium constant written in terms of molar concentrations is in units of (mol/L)-1. The equilibrium constant written in terms of volume fractions is dimensionless. The conversion from (mol/L)-1 to a dimensionless number is accomplished by simply dividing by the molar volume of ethanol. At 25 °C, the molar volume of ethanol is equal to 58.71 cm3 mol-1.
The Diluent. In the study of the self-association of ethanol, measurement of the fraction of hydrogen-bonded hydroxyl groups can be achieved by the quantitative analysis of the FTIR spectrum of the mixture using the Beer-Lambert law. This law can only be applied to bands whose absorbance is less than 1. Since the absorption of the hydroxyl stretching band is very high, ethanol has to be diluted in a solvent that does not form specific interactions with ethanol. The spectrum of pure CCl4, presented in Figure 3, demonstrates that there is zero absorbance in the hydroxyl stretching region ranging from 3700 to 3100 cm-1. Marcus18 demonstrated that there is a possibility that CCl4 interacts with molecules containing hydroxyl groups via the formation of weak hydrogen bonds. However, Coleman and al.14 have shown that this effect does not appear at concentrations above 0.15 mol L-1. Thus, we have restricted our measurements to ethanol concentration in CCl4 greater than 0.15 mol L-1. Hydroxyl Stretching Band. The FTIR spectrum of ethanol diluted in CCl4 in a 0.25 mm path length cell was collected at ethanol concentrations ranging from 0.16 to 0.76 mol L-1 and temperatures ranging from 40 to 65 °C. Figure 1 shows selected spectra in the hydroxyl stretching region at T ) 50 °C for three different ethanol concentrations, while Figure 2 shows selected spectra at a fixed ethanol concentration for three different temperatures. These spectra are given in absolute absorbance units, i.e., absorbance units divided by the concentration of hydroxyl groups. Three main contributions appear in the hydroxyl stretching region: a first narrow band at about 3634 cm-1 and two wider bands at approximately 3500 and 3370 cm-1. The bands characteristic of the hydrogen-bonded hydroxyl groups must appear at frequencies lower than the band characteristic of the free groups, since the strength of the hydroxyl bonds decreases upon hydrogen bond formation. The band at about 3634 cm-1 is thus attributed to the stretching of the free hydroxyl groups. According to Coggeshall and Saier,10 the two bands at 3500 and 3370 cm-1 can be attributed to the ethanol dimers and the multimers, respectively. The hydroxyl stretching bands were curve-fitted into three peaks. Figures 4 and 5 present the variations of the areas with temperature and ethanol concentration. Figure 4 shows that as the temperature increases, the area of the band associated with the free hydroxyl groups slowly increases, whereas the area of the bands characteristic of the hydrogen-bonded species decreases, i.e., the fraction of hydrogen-bonded species decreases as the temperature increases. Figure 5 shows that as the concentration of ethanol in the diluent increases, the fraction of free groups decreases. Figures 4 and 5 also show that the change of area of the bands characteristic of the free and dimer molecules varied only slowly with temperature or ethanol concentration, while the area of the band associated with the multimers changes very fast. These observations can be explained by the differences in the absorptivity coefficients of the bands and also by their temperature and concentration dependence.14 Because of the broadness of the hydrogen-bonded hydroxyl bands and because of the temperature dependence of the
19270 J. Phys. Chem., Vol. 100, No. 50, 1996
Schwager et al.
Figure 4. Plot of the area of the hydroxyl region bands versus temperature for an ethanol/CCl4 mixture. Ethanol concentration ) 0.36 mol L-1.
Figure 6. Graph for the determination of the extinction coefficient 0 extrapolated at the limit c ) 0.
TABLE 1: Values of E0, K2, and γ0 at Each Temperature temp (°C) 40 45 50 55 60 65 5.6146 5.4898 5.3434 5.2776 5.097 5.0751 0 -1 K2 (mol L ) 0.7566 0.6431 0.5989 0.5351 0.4802 0.4295 γ0 (L mol-1) 1.3284 1.5095 1.6910 1.9184 2.0752 2.3048
hydroxyl group concentration, and the fraction of free hydroxyl groups:
(
2 KA ) fFOHcT
(
)
1 -γ K2
(
))
2 2γ γ2 γ - + + K2 2 K2 4
0.5
(3)
where γ is defined as
γ)
Figure 5. Plot of the area of the hydroxyl region bands versus ethanol concentration for an ethanol/CCl4 mixture. Temperature ) 50 °C.
absorptivity coefficients, the fraction of free OH groups cannot be determined directly from the curve fitting of the bands. This has been discussed in detail by Coleman et al.14 Determination of the Equilibrium Constants. The ethanol self-association is best described by two equilibrium constants, the first one describing the formation of dimers, denoted K2, and the second one describing the formation of multimers, denoted KA. Since the absorptivity coefficients of the bands associated with the stretching of the hydrogen-bonded hydroxyl groups cannot be defined, a method described by Coggeshall and Saier10 was employed. Coggeshall and Saier have shown that the molar fraction of chains having h + 1 hydrogen-bonded hydroxyl groups can be written as
(
)
φA1 K2 φA1cKA φAh+1 )h φA φA KA φA
h-1
) hfFOH
K2 (K fOHc )h-1 (1) KA A F T
where φA is the total molar fraction of all the A units contained in the mixture, φA1 is the molar fraction of nonassociated A units in the mixture, φAh is the molar fraction of A units selfassociated into chains of h units, cT is the concentration of A units in the mixture, and fFOH is the fraction of free hydroxyl groups in the mixture; fFOH ) φA1/φA. According to the total mass balance, we have ∞
φAh+1
h)1
φA
∑
)1
(2)
Using eq 2, Coggeshall and Saier derived an expression relating the equilibrium constant KA to the constant K2, the
2(fF0)2cT 1 - fF0
(4)
In the limit of infinite dilution of A units
lim (γ) ) 1/K2 ) γ0
2cTf0
(5)
We first have to determine the fraction of free hydroxyl groups in each mixture. The Beer-Lambert law, IF ) FlcF, relates the intensity of the free hydroxyl band, IF, to the absorbtivity coefficient for the band associated with the free groups, F, the concentration of free hydroxyl groups, cF, and the path length of the sample, l. As the total concentration of hydroxyl groups, cT, tends to zero, all the hydroxyl groups tend to be free and thus cF tends to cT. The value of the absorptivity coefficient as cT approaches zero, 0, is determined from a plot of IF/(cTl) versus cT, for each temperature. We then have IF ) 0lcT. The experimental fraction of free hydroxyl groups can then be calculated using the equation
fFOH )
cF FcFl IF ) ) cT 0cTl 0cTl
(6)
0 was determinated at each temperature, and the experimental fractions of free hydroxyl groups were calculated using eq 6 for each spectrum. Figure 6 illustrates the determination of 0 at T ) 50 °C by using a least-squares fit of the data with a second-order polynomial. The 0 is found to be equal to 5.34 for cT expressed in mol L-1, l in mm, and IF in absorbance units. The results obtained are summarized in Table 1. Now that we have the fraction of free hydroxyl groups, the equilibrium constant for the formation of dimers, K2, can be determined by plotting γ versus c and extrapolating the value
Constants of Ethanol
J. Phys. Chem., Vol. 100, No. 50, 1996 19271
Figure 9. Van’t Hoff plot for the determination of hB for ethanol/ CCl4 mixtures.
Figure 7. Determination of the 1/K2 extrapolated at the limit c ) 0.
The enthalpy of hydroxyl-hydroxyl hydrogen bonding for both self-association equilibria, ∆h2 and ∆hA, can be determined by plotting ln K versus 1/T, where the slope of the line is equal to -∆h/R. These plots are presented in Figures 8 and 9. ∆h2 is the enthalpy for the formation of dimers and ∆hA the enthalpy for the formation of multimers. ∆h2 is found to be equal to -4.61 kcal mol-1 and ∆hA to be equal to -4.15 kcal mol-1. Discussion Coleman et al.14 list approximations for the enthalpy of hydrogen bond formation for different functional groups based on an extensive literature review. For the hydrogen bond formation between hydroxyl groups, they reported ∆h ≈ -5 kcal mol-1. The enthalpy values determined in this study for ethanol are in good agreement with this approximation. The values of the equilibrium constant for the self-association that we have determined can also be compared to those found in the literature. Two different linear chain models are mainly reported: (1) the monomer-linear tetramer model8,19,20 and (2) the monomer-linear chain model where K2 ) K3 ) ... ) K.2,9,13 Table 3 presents the different values of the equilibrium constants obtained for the second model, which seems to be the most realistic and the closest to the monomer-dimermultimer model we have employed in this study. The values of the equilibrium constant found in the literature for a monomer-linear chain model range from 1.59 to 2.79 L mol-1 at T ) 25 °C. At the same temperature, for a monomerdimer-multimer model, we have determined K2 ) 1.08 and KA ) 3.52 L mol-1. Although the average of these two equilibrium constants falls in the range of values found in the literature, it is probably more appropriate to compare only the value of KA with the literature values based on the monomerlinear chain model. We can also compare the equilibrium constants we determined for ethanol diluted in CCl4 to the equilibrium constants
Figure 8. Van’t Hoff plot for the determination of h2 for ethanol/ CCl4 mixtures.
of γ to cT ) 0. Figure 7 shows a least-squares fitting of the data with a second-order polynomial used to determine the equilibrium constant K2 at T ) 50 °C. At this temperature, the equilibrium constant K2 is found to be equal to 0.662 mol L-1 for K2. The values obtained for all temperatures are summarized in Table 1. Substituting the value of K2 previously determined into eq 3 for each concentration leads to the mean value of KA of 2.0 mol L-1 with a standard deviation, σ, equal to 0.1 at T ) 50 °C. The same calculations are carried out over the temperature range varying from 40 to 65 °C. Table 2 lists the results of KA for each temperature. Furthermore, in the narrow temperature range we examine, we can assume that the enthalpy hydrogen bond formation is independent of the temperature. Under that condition, the equilibrium temperature dependence is
[ (
K ) K0 exp -
∆H 1 1 R T T0
)]
(7)
where K0 is the value of the equilibrium constant at T0.
TABLE 2: Values of the Intensity of the Free Hydroxyl Band and of KA (in mol L-1) at Each Temperature and Ethanol Concentration T ) 40 °C
T ) 45 °C
T ) 50 °C
T ) 55 °C
T ) 60 °C
T ) 65 °C
COHa
IF
KA
IF
KA
IF
KA
IF
KA
IF
IF
IF
KA
0.76 0.46 0.36 0.268 0.227 0.182 KAb σc
0.3667 0.2911 0.2621 0.2316 0.2145 0.1884
2.382 2.754 2.819 2.672 2.465 2.285 2.57 0.45
0.3905 0.3111 0.2820 0.2434 0.2201 0.1907
2.143 2.409 2.353 2.263 2.250 2.172 2.26 0.10
0.4027 0.3233 0.2915 0.2497 0.2217 0.1901
1.961 2.108 2.015 1.844 1.960 1.938 1.97 0.13
0.4167 0.3331 0.2972 0.2561 0.2237 0.1915
1.862 1.997 1.949 1.659 1.944 1.906 1.88 0.12
0.4282 0.3420 0.3037 0.2530 0.2242 0.1890
1.705 1.772 1.685 1.623 1.669 1.786 1.71 0.06
0.4423 0.3358 0.3107 0.2565 0.2263 0.1896
1.648 1.976 1.641 1.640 1.725 1.968 1.76 0.16
a
Molarity of hydroxyl groups. b Mean value of KA in terms of molar concentration. c Standard deviation of KA.
19272 J. Phys. Chem., Vol. 100, No. 50, 1996
Schwager et al.
TABLE 3: Self-Association Constants and Association Energies for Ethanol Diluted in CCl4 author Fujiwara9 Sassa2 Littlewood13
method
K L/mol
NMR dilution shift at T ) 34.5 °C K ) 1.59 of the OH band IR measurements at T ) 25 °C K ) 2.79 frequency of the at T ) 25 °C K ) 1.59 proton in NMR
∆H (kcal mol-1)
-7.3 -9.4 ( 1
determined by Whetsel and Lady7 for phenol diluted in CCl4 with the same association model. In this case they calculated K2 ) 1.09 L mol-1and KA ) 2.74 L mol-1. These results appear to be consistent with our values for K2 and KB, since ethanol has a slightly greater propensity to self-associate than phenol, perhaps due to steric factors. Conclusion The self-association of ethanol seems to be best described by two equilibrium constants, one for the formation of dimers, the other for the formation of multimers. Dimer formation appears to be slightly more exothermic than the enthalpy change associated with the addition of an ethanol molecule to an existing multimer unit. This may be true because of the lowered polarizability of the OH bond in the associated units compared to the non-hydrogen-bonded OH groups in the monomers. Furthermore, one would expect the polarizability to change significantly with the degree of association beyond a dimer. To calculate the thermodynamic of mixing of a water soluble polymer in ethanol, we will use these self-association constants. We will also need to determine the interassociation equilibrium constants. This is the topic of part II in our study.21 Acknowledgment. This work was supported by NSF Grant No. DMR-9120004 under the auspices of the National Science
Foundation Science and Technology Center for High Performance Polymeric Adhesives and Composites. References and Notes (1) Van Ness, H. C.; Van Winkle J. Phys. Chem. 1967, 71, 5, 1483. (2) Sassa, Y.; Katayama, T. J. Chem. Eng. Jpn. 1973, 6, 31. (3) Aminabhavi, V. A.; Aminabhavi, T. M.; Balundgi, R. H. Ind. Eng. Chem. Res. 1990, 29, 2106. (4) Vinogradov, S. N.; Linnell, R. H. Hydrogen Bonding; Van Nostrand Reinhold Co.: New York, 1971. Luck, W. A. P. Angew. Chem., Int. Ed. Engl. 1980, 19, 28. (5) Luck, W. A. P.; Schrems, O. J Mol. Stuct. 1980, 60, 333. Luck, W. A. P.; Fritsche, M. Z. Phys. Chem. 1995, 191, 71. (6) Kempter, H.; Mecke, R. K. J. Phys. Chem. 1940, 46, 229. (7) Whetsel, K. B.; Lady, J. H. Spectrometry of Fuels; Friedel, H., Ed.; Plenum Press: London, 1970; Chapter 20. (8) Kopecni, M. M.; Petkovic, D. J. M. Thermochim. Acta 1978, 25, 241. (9) Fujiwara, H.; Ikenoue, T. J. Chem. Soc., Faraday Trans. 1976, 72, 2375. (10) Coggehall, N. D.; Saier, E. L. J. Am. Chem. Soc. 1951, 73, 5414. (11) Prigogine, I.; Defay, R. Thermodynamique Chimique; Desoer, 1950; Chapter 26. (12) Mecke, R. Discuss. Faraday Soc. 1950, 9, 161. (13) Littlewood, A. B; Willmott, F. W. Trans. Faraday Soc. 1966, 62, 3287. (14) Coleman, M. M.; Graf, J. F.; Painter, P. C. Specific Interactions and the Miscibility of Polymer Blends; Technomic: Lancaster, 1991. (15) Yang, X.; Painter, P. C.; Coleman, M. M. Macromolecules 1992, 25, 2156. (16) Coleman, M. M.; Yang, X.; Painter, P. C. Macromolecules 1992, 25, 4414. (17) Coleman, M. M.; Lee, J. Y.; Serman, C. J.; Wang, Z. ; Painter, P. C. Polymer 1989, 30, 1298. (18) Marcus, Y. Introduction to Liquid-State Chemistry; John Wiley and Sons: New York, 1977; p 176. (19) Flechter, A. N.; Heller, C. A. J. Phys. Chem. 1967, 71, 3742. (20) Saunders, M.; Hyne, J. B. J. Chem. Phys. 1958, 29, 1319. (21) Schwager, F; Marand, E.; Davis, R. M. To be submitted.
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