Excess Heat Capacity Surfaces for Water-Alkanol Mixtures by the UNIQUAC Model

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Water-Alkanol Mixtures by the UNIQUAC Model YASAR DEMIREL

1 University of Nebraska - Lincoln From the SelectedWorks of YASAR DEMIREL 1995 Excess Heat Capacity Surfaces for Water-Alkanol Mixtures by the UNIQUAC Model YASAR DEMIREL H Paksoy Available at:

Ind. Eng. Chem. Res. 1996,34, 921-927 92 1 Excess Heat Capacity Surfaces for Water-Alkanol Mixtures by the UNIQUAC Model Yagar Demirel* and Halime 6.

2 Ind. Eng. Chem. Res. 1996,34, Excess Heat Capacity Surfaces for Water-Alkanol Mixtures by the UNIQUAC Model Yagar Demirel* and Halime 6. Paksoyt Department of Chemical Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia Hydroorganic mixtures are industrial solvents that can serve as media to solubilize either water in hydrocarbon or a hydrophobic substance in water. In many cases the solubilizing capability is obtained via a homogeneous complex aqueous mixtures containing an alcohol. Since excess heat capacity, CF, is very sensitive to structural changes in mixtures, concentration and temperature dependence of CE have been calculated by using the UNIQUAC model for the mixtures methanol(l)-water(%, ethanol(l)-water(2), and l-propanol(l)-water(2). The temperature-dependent parameters of the model estimated directly from CF data at more than one different isotherm are used in the calculations. The overall deviations between the calculated and experimental data points change in the range %, which indicates the satisfactory representation of CE data by the model for engineering calculations. The temperature range of experimental data for the mixtures is and K. Surfaces of reduced, apparent, and partial molar excess heat capacities are also derived. The concentration and temperature dependencies of these functions suggest the existence of transitions of microstructure in the water-rich region, qualitatively similar to micellization. The surface of these thermodynamic functions facilitates a better understanding of thermodynamic properties and association of alcohol-water mixtures over a whole or certain concentration and temperature range. Such thermodynamic surfaces may be represented satisfactorily by the UNIQUAC model at low pressures. Introduction The thermodynamic properties of alkanol-water mixtures attracted a high degree of attention among the researchers. Complicated systems such as microemulsions depend significantly on the characteristic properties of alcohol in water, and the study of such mixtures is essential due to their numerous applications in many fields, such as biology, pharmacy (Attwood and Florence, 19831, and many biochemical reactions (Tanford, 1973). One of the industrial applications that received by far the most attention is the use of microemulsions for enhanced oil recovery (Shah and Schecter, 1977). One fast-growing field of research is the study of systems where the hydrophilic and hydrophobic balance can be adjusted to obtain the necessary solubilization in chemical or separation processes (Grolier et al., 1986). For some time, the surfactant has been considered a key constituent in such systems; however, recent studies have emphasized the important role played by the alcohol. This behavior is merely the consequence of the typical self-association of alcohol in aqueous as well as in nonaqueous solutions (Roux-Desgranges et al., 1986). Surfactant-containing aqueous solutions are recognized as micellar or microemulsion systems, and their basic property is the formation of local microheterogeneities. As the surfactants are needed in large quantity and are expensive, the surfactant agent is replaced by a solvent with a right hydrophilic character, such as alcohols, carboxylic acids, or amines. Such mixtures are practical t Faculty of Art and Science, University of Cukurova, Adana 01330, Turkey. *To whom all correspondence should be addressed. E- mail: FACAllE@SAUPMOO.BITNET $09.00/0 solvents with complex concentration and temperature dependence that affects the behavior of dissolved species (Franks and Desnoyers, 1985; Roux et al., 1980). The studies of alcohol dilute aqueous mixtures have evidenced the important changes in partial molar properties (especially heat capacities) of alcohols that indicates the structural changes taking place at certain concentrations (Page et al., 1993; Perron et al., 1993). Sharper changes at lower temperature suggest that liquid water may retain some character of icelike structure (Franks and Desnoyers, 1985). A simple and reliable way of treating quantitatively the thermodynamics of such systems is needed (Roux et al., 1980). As Deiters (1993) suggests, for a quite long time models based on activity coefficients have been the preferred method for the calculation of thermodynamic properties of associating mixtures. Such models are capable of a high degree of accuracy and usually do not create numerical problems at low pressures. The UNI- QUAC model is based on activity coefficients and widely used in estimating the thermodynamic properties of various types of mixtures including highly nonideal, partially miscible, and associating systems (Abrams and Prausnitz, 1975; Demirel and Gecegormez, 1989). In a previous study, temperature-dependent interaction energy parameters of the UNIQUAC model were estimated using excess heat capacity, C:, data at more than one different isotherm to correlate such data. The mathematical technique used in the parameter estimation, variance of the fit of C: data, and the sensitivity analysis of the model are discussed in detail elsewhere (Demirel and Gecegormez, 1989, 1991; Demirel et al., 1992; Demirel and Paksoy, 1992). The mixtures considered in this study and the deviations obtained from the correlation of C; data are shown in Table 1. The American Chemical Society

922 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 Table 1. Deviations between the Experimental and Calculated Excess Heat Capacity, CF, Data by the WQUAC Model system reference n T("C) DCCF) 1.

3 922 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 Table 1. Deviations between the Experimental and Calculated Excess Heat Capacity, CF, Data by the WQUAC Model system reference n T("C) DCCF) 1. methanol(l)-water(2) Benson and D'Arcy, Ogawa and Murakami, " 2. ethanol(l)-water(2) Benson and DArcy, Ogawa and Murakami, a 3. l-propanol(l)-water(2) Benson and D'Arcy, Ogawa and Murakami, a Overall deviation. 6.52" deviations are obtained from the following equation: 1 (1) where n shows the number of data points at each isotherm. As Table 1 indicates, direct correlation of Cf data by the UNIQUAC model yields reasonably low deviations. The overall deviations for the whole temperature range are in the range %. Therefore an attempt has been made to calculate the concentration and temperature dependence of CE surfaces to show the feasibility of the UNIQUAC mode? in studying the structural changes in the associating mixtures. Excess Heat Capacity Surfaces The rate of change of excess Gibbs free energy, ge, with respect to temperature, T, is proportional to the excess enthalpy, he, and is given by the Gibbs-Helmholtz equation at constant pressure, P, and liquid mole fraction, x: parameters in the following form were used: a21 = d, + ddt (5) a12 = d, + d,/t Here a21 and a12 are the interaction energy parameters in kelvin. Terms dl and d3, in kelvin, and d2 and d4, in P, are the coefficients related to the parameters alj. This form of the temperature dependency is especially appropriate in obtaining derivative expressions, such as he and CE, from the original expression for ge. The UNIQUAE model contains a pure-component structural parameter q. Anderson and Prausnitz (1978) slightly modified the UNIQUAC model and introduced new values of surface parameters q' for alcohols and water, to be used in the residual part of the model. The temperature-dependent parameters were estimated directly from Cf data at more than one different isotherm. The importance of the temperature-dependent parameters in the UNIQUAC model and the estimation of the parameters are discussed in detail elsewhere (Demirel and Gecegormez, 1989; Demirel and Paksoy, 1992). Using eq 4, the dependence of concentration and temperature of CE and various derived functions were calculated as surfaces. One of them is the molar heat capacity of the mixture, Cp,m,calculated by where COp,i represents the molar heat capacity of the pure liquid i, and x1 is the mole fraction of alkanol. The reduced excess heat capacity, CfIx1x2 and temperature derivative of it, a(ce /xlx2)/at are also derived. The apparent moyar heat capacities of alkanol, C*p,i, were expressed by the equation C*p,1= [C,,, - (1 - xl)cop,2]/x1 The partial molar excess heat capacities of alkanol, were calculated from Differentiating the expression for he, obtained from the UNIQUAC model and given elsewhere (Demirel and Gecegormez, 19891, with respect to temperature: c; = (ahe/at)p,x (3) gives an expression for excess heat capacity Cf in terms of the UNIQUAC notation: where tu = exp(-ajt) 0, = xiq'i/cxiq'i In the UNIQUAC model, the temperature-dependent Most of the changes occurring in aqueous organic mixtures are in the water-rich region. Molar excess heat capacities tend to attenuate the changes at both ends of the mixture. Partial and apparent molal quantities do not suffer from this drawback and reflect more readily the characteristic interactions and structural changes in the water rich region (Roux et al., 1980). Results and Discussion The temperature-dependent parameters and molecular interaction area parameters of the UNIQUAC model used in the calculations are given elsewhere (Demirel and Paksoy, 1992). Pure-component molar heat capacities are taken from Miller et al. (1976). The temperature ranges used in the excess heat capacity calculations are K for methanol-water and ethanolwater, and K for l-propanol-water. These temperatures, as seen from the Table 1, are slightly outside the temperature range of the experimental data used in estimating the parameters, for better representation of the thermodynamic surfaces,

4 Ind. Eng. Chem. Res., Vol. 34, No. 3, a X1 Y 1 a b b X Figure 1. Concentration and temperature dependence of excess heat capacity surfaces. (a) methanol(l)-water(2) for K (b) ethanol(l)-water(2) for K (c) l-propanol(l)-water(2) for K. since the UNIQUAC model with temperature-dependent parameters are capable of extrapolation as well as interpolation of experimental data (Abrams and Prausnitz, 1975; Demirel and Gecegormez, 1989). The concentration and temperature dependence of the C Figure 2. Concentration and temperature dependence of molar heat capacity of mixtures. (a) methanol(l)-water(2) for K (b) ethanol(u-water(2) for K (c) l-propanol(l)-water(2) for K. excess heat capacity and molar heat capacity of the mixtures in the whole mole fraction range are shown in Figures 1 and 2, respectively. Such surfaces clearly reveal the simultaneous effect of the concentration and

5 924 Ind. Eng. Chem. Res., Vol. 34, No. 3, a o.2w 0.8 T[Kl X s Figure 3. Concentration and temperature dependence of reduced heat capacity. (a) methanol(l)-water(2) for K. (b) ethanol(l)-water(2) for O.K (c) 1-propanol(1)-water: (2) for K. the temperature on CE and Cp,m. As the number of carbon atoms in the afcohol increases, humps in the water-rich region becomes less steep with increasing alcohol concentration. This effect is different at both ends of temperature intervals. The overall shape of the X1 0.4 Figure 4. Concentration and temperature dependence of temperature derivative of reduced heat capacity in the water-rich region: (a) methanol(1)-water(2) for K (b) ethanol- (U-water(2) for K (c) l-propanol(l)-water(2) for K. surfaces are consistent with the tendency of change of isothermal experimental data with respect to concentration and temperature for the mixtures studied (Benson

and D'Arcy, 1982; Simonson et al., 1987; Ogawa and Murakami, 1986). The reduced excess heat capacity for the whole concentration range is shown in Figure 3.

6 and D'Arcy, 1982; Simonson et al., 1987; Ogawa and Murakami, 1986). The reduced excess heat capacity for the whole concentration range is shown in Figure 3. The reduced excess heat capacity is related to the apparent quantity, C*,,i and molar quantity, Cop,i Ind. Eng. Chem. Res., Vol. 34, No. 3, Reduced excess thermodynamic quantities are thus equivalent to apparent molar quantities in dilute regions at both ends of the mole fraction scale and put an equal weight on interactions over the whole mole fraction range (Perron et al., 1993). The sharp changes of the reduced heat capacity surfaces in the water-rich region are shown in Figure 3. The temperature derivatives of the reduced excess heat capacities in the waterrich region are shown in Figure 4. The concentration dependence of C;/XIXZ and temperature derivative of it, ~~(C;IX~X~)I~T suggest the existence of transition in the water-rich region, qualitatively similar to micellization that is the result of a reinforcement of hydrophobic hydration due to strong hydrogen-bonding interactions of the polar groups in water. These sharp changes also suggest that alcohols that can form clathrates with water (solvent-shared association complexes), undergo a microphase transition at about 0.02 mole fraction for all the three mixtures studied. This transition in the water-rich region cannot be related to the critical demixing since the sharpness and magnitudes of the changes decrease as the temperature is increased (Perron et al., 1993). This property is clearly seen in Figure 5. Alcohols are major components of microemulsions (Prince, 1977). As Roux et al. (1980) pointed out, there could be a relationship between the action of the alcohol in stabilizing the microemulsion and the microheterogeneity of its aqueous mixtures. Several possible factors can contribute to the microheterogeneity of these solutions, such as the hydrophobic character of the molecule, the tendency for the system to unmix, the geometry of the molecule, and the nature of the polar group. The concentration and temperature dependences of apparent and partial molar excess heat capacities in the water-rich region are shown in Figures 5 and 6, respectively. While apparent molal heat capacities of most hydrophobic solutes decrease in a rather regular way from infinite dilution to the pure liquid (Roux et al., 19781, these mixtures behave like other alcohols; C*,,& goes through a maximum or hump before decreasing rapidly to the molar heat capacity of the alcohol. The hump seems to be related to the relaxational part of the heat capacity and is an indication of strong concentration fluctuations or microheterogeneity in the mixture (Perron and Desnoyers, 1981). A similar trend can also be seen for CE,l in Figure 6. This effect increases with a hydrophobic character of the alcohol. The hydrophobic hydration, as measured by the magnitude of C*,i - Cop,i increases in the order methanol < ethanol.c 1-propanol and so does the magnitude of the humps. The effect is also larger at low temperature with all mixtures (Roux et al., 1980). The changes that take place in the alcohol-water mixtures are better seen from the concentration dependence of C*,,i shown in Figure 5. The values of C*,,,change very rapidly for a mole fraction of around b T[K] X m Figure 5. Concentration and temperature dependence of apparent molar heat capacity in the water-rich region: (a) methanol- (Wwater(2) for K (b) ethanol(l)-water(2) for K (c) l-propanol(l)-water(2) for K and then tend to the value of the pure alcohol. The sudden change in C*,i is usually associated with the micellization process (Row et al. 1980).

926 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 a b -looi,y 300 X1 Y m,.r. 305 0.4 0.4 with water.

7 926 Ind. Eng. Chem. Res., Vol. 34, No. 3, 1995 a b -looi,y 300 X1 Y m,.r with water. Most of the studies on alcohol-water mixtures strongly suggest, as is confirmed once more in this thermodynamic study, the existence of timeaverage clathrate hydrates in the water-rich region, and the collapsing of this structure when the ratio of alcohol to water exceeds that of clathrates (Roux et al., 1980; Perron and Desnoyers, 1981; Costas and Patterson, 1985; Grolier et al., 1986). This transition is the result of two effects: (1) the increase in the structure of water due to the existence of time-average clathrates, (2) the acid-base type of interactions between the alcohol and water (Roux et al., 1980). Conclusion Homogeneous systems containing water and alcohol are of great interest from both a practical and theoretical point of view. Their thermodynamic properties can empirically be adjusted for specific uses by thermodynamic-model calculations. The surfaces of the excess heat capacity and its derivatives, such as reduced, apparent, partial molar quantities, with respect to concentration and temperature are represented satisfactorily by the temperature-dependent parameters of the UNIQUAC model at low pressure. Both the waterrich region and the whole concentration range are considered. The temperature intervals are K for methanol-water and ethanol-water, and K for 1-propanol-water mixtures. The concentration dependence of aqueous alcohol can be interpreted as follows: (a) When an alcohol is added to water at infinite dilution, the acid-base interaction with water reinforces the normal hydrophobic hydration. (b) As the concentration of alcohol is increased, hydrophobic interaction between alcohol molecules tends to decrease the hydrophobic hydration. (c) As the structure around the alcohol collapses, the alcohol molecules rearrange themselves in a way such as to minimize contacts of the hydrophobic chains with water. As further alcohol is added, it dissolves preferentially with their hydrophobic chains in the microphases and the partial molar quantity remains essentially constant. These are in line with the conclusions derived earlier by Roux et al. (1980). Excess heat capacity and its derivatives are very sensitive to structural changes in mixtures. The concentration and temperature dependence of these functions may help to achieve some understanding of the microorganization resulting from molecular interactions and present the unique advantage of revealing, almost quantitatively in concentration and temperature terms, where the structural changes take place. The UNI- QUAC model, with the temperature-dependent parameters estimated from accurate excess heat capacity data, may be one effective tool of treating quantitatively and qualitatively the thermodynamics of these fluctuating mixtures. o.lv Acknowledgment C X1 0.4 Figure 6. Concentration and temperature dependence of partial molar excess heat capacity in the water-rich region. (a) methanol- (Wwater(2) for K (b) ethanol(l)-water(2) for K (c) l-propanol(l)-water(2) for K. Microheterogeneity in aqueous organic systems is observed mostly with systems that can hydrogen bond The authors thank Data Processing Center of King Fahd University of Petroleum & Minerals for the computational facilities provided. Nomenclature uv = UNIQUAC binary energy interaction parameters related to ti, K CF = excess heat capacity, J K-l mol-'

C:,l = partial molar excess heat capacity, J K-l mol-' dl, ds = UNIQUAC parameters related to ag, K dz, dq = UNIQUAC parameters related to ai, K2 ge = excess Gibbs energy, J mol-l he = excess

8 C:,l = partial molar excess heat capacity, J K-l mol-' dl, ds = UNIQUAC parameters related to ag, K dz, dq = UNIQUAC parameters related to ai, K2 ge = excess Gibbs energy, J mol-l he = excess enthalpy of mixing, J mo1-l n = number of experimental CF data points at a specified isothermal temperature q' = molecular interaction area parameter P = total pressure, Pa R = gas constant, J K-l mol-l T = absolute temperature, K xi = liquid phase mole fraction component i Greek Symbols rq = UNIQUAC binary parameters eq 4 8i = area fraction of component i in residual contribution to the activity coefficient Subscripts exptl = experimental calcd = calculated ij = component Superscripts E = excess o = pure-component value * = apparent molar value Literature Cited Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116. Anderson, T. F.; Prausnitz, J. M. Application of the UNIQUAC Equation to Calculation of Multicomponent Phase Equilibria 1. Vapour-Liquid Equilibria. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 552. Attwood, D.; Florence, A. I. Surfactant Systems, Their Chemistry, Pharmacy and Biology; Chapman and Hall: New York, Benson, G. C.; DArcy, P. J. Excess Isobaric Heat Capacities of Water-n-Alcohol Mixtures. J. Chem. Eng. Data, 1982,27, 439. Costas, M.; Patterson, D. Heat Capacities of Water+Organic- Solvent Mixtures. J. Chem. SOC., Faraday Trans ,81, Deiters, U. K. Application of an EOS Chain Association Theory to the Calculation of Thermodynamic Properties of (Alkane+l- Alkanol) Mixtures. Fluid Phase Equilib. 1993, 89, 229. Demirel, Y.; Gecegormez, H. Simultaneous Correlation of Excess Gibbs Energy and Enthalpy of Mixing by the UNIQUAC Equation. Can. J. Chem. Eng. 1989, 67, 455. Demirel, Y.; Gecegormez, H. Simultaneous Representation of Excess Enthalpy and Vapor-Liquid Equilibrium Data by the NRTL and UNIQUAC Models. Fluid Phase Equilib. 1991, 65, 111. Ind. Eng. Chem. Res., Vol. 34, No. 3, Demirel Y.; Paksoy, H. 6. Calculation of Excess Heat Capacities for Liquid Mixtures. Thermochim. Acta 1992, 198, 329. Demirel, Y.; Paksoy, H. 0.; Gecegormez, H. Correlation of Heats of Mixing Data by the NRTL and UNIQUAC Models. Part 2. Prediction of Calorimetric Properties. Thermochim. Acta 1992, 194, 343. Franks, F.; Desnoyers, J. E. Alcohol-Water Mixtures Revisited. In Water Science Reviews; Franks, F., Ed.; Cambridge University Press: Cambridge, 1985; Vol. 1. Grolier, J-P. E.; Roux-Desranges, G.; Roux, A. H. Thermodynamics of Complex Aqueous Systems. Fluid Phase Equilib. 1986, 30, 157. Miller, Jr., J. W.; Schorr, G. R.; Yaws, C. L. Physical & Thermodynamic Properties-Part 20. Methanol, Ethanol, Propanol and Butanol. Chem. Eng. 1976,83, 119. Ogawa, 0.; Murakami, S. Excess Isobaric Heat Capacities for Water+Alkanol Mixtures at K. Thermochim. Acta 1986, 109, 145. Page, M.; Huot, J.-Y.; Jolicoeur, C. A Thermodynamic Investigation of Aqueous 2-Methoxyethanol. J. Chem. Thermodyn. 1993,25, 139. Perron, G.; Desnoyers, J. E. Heat Capacities and Volumes of Interaction Between Mixtures of Alcohols in Water at K. J. Chem. Thermodyn. 1981,13, Perron, G.; Quirion, F.; Lambert, D.; Ledoux, J.; Ghaicha, L.; Bennes, R.; Privat, M.; Desnoyers, J. E. Thermodynamic Properties of Aqueous Organic Mixtures Near the Critical Demixing: Cases of 2,6 Dimethylpyridine and 2. Isobutoxyethanol. J. Solution Chem. 1993,22, 107. Prince, L. M. Microemulsions, Theory and Practice: Academic Press: New York, Roux, G.; Perron, G.; Desnoyers, J. E. Model Systems for Hydrophobic Interactions: Volumes and Heat Capacities of n-alkoxyethanols in Water. J. Solution Chem. 1978, 7, 639. Roux, G.; Roberts, D.; Perron, G.; Desnoyers, J. E. Microheterogeneity in Aqueous-Organic Solutions: Heat Capacities, Volumes and Expendabilities of Some Alcohols, Aminoalcohol and Tertiary Amines in Water. J. Solution Chem. 1980, 9, 629. Roux-Desgranges, G.; Grolier, J.-P. E.; Villamanan, M. A.; Casanova, C. Role of Alcohol in Microemulsions Volumes and Heat Capacities in the Continuous Phase Water-n-Butanol-Toluene of Reverse Micelles. Fluid Phase Equilib. 1986,25, 209. Shah, D. O., Schecter, R. S., Eds. Improved Oil Recovery by Surfactant and Polymer Flooding; Academic Press: New York, Simonson, J. M.; Bradley, D. J.; Busey, R. H. Excess Molar Enthalpies and the Thermodynamics of (Methanol+Water) to 573 K and 40 MPa. J. Chem. Thermodyn. 1987,19,479. Tanford, C. The Hydrophobic Effects; Wiley-Interscience: New York, Received for review June 7, 1994 Revised manuscript received October 3, 1994 Accepted November 21, 1994@ Abstract published in Advance ACS Abstracts, February 15, 1995.

Calculations of thermodynamic derivative properties from the NRTL and UNIQUAC models

University of Nebraska - Lincoln From the SelectedWorks of YASAR DEMREL 1997 Calculations of thermodynamic derivative properties from the NRTL and UNQUAC models YASAR DEMREL Available at: https://works.bepress.com/yasar_demirel/61/