Volumetric properties of (water diethanolamine) systems

+

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Yadollah Maham, Tjoon T. Teng, Alan E. Mather, and Loren G. Hepler

Abstract: Densities of completely miscible (water + methyldiethanolamine) and (water + ethyldiethanolamine) systems have been measured over the full range of compositions at temperatures from 25 to 80°C. Results of these measurements have been used in calculating excess molar volumes and partial molar volumes of each component. We have also identified different measures of the thermal expansion of these systems and have calculated some of these derivative quantities. The partial molar volumes and their derivatives with respect to temperature provide a basis for extending our understanding of molecular interactions in these (water + organic) systems. Key words: diethanolamines, excess molar volumes, partial molar volumes, expansivities, aqueous solutions.

Resume : Optrant i des temptratures allant de 25 i 80°C, on a mesurt les densitts des systbmes complbternent miscibles (eau + mtthylditthanolamine) et (eau + tthylditthanolamine) sur I'ensemble des plages de composition. On a utilist ces rtsultats pour calculer les volumes molaires en excbs et les volumes molaires partiels de chacun des composants. On a aussi identifit difftrentes mesures de I'expansion thermique de ces systbmes et on a calcult quelques-unes de ces quantitts dtrivtes. Les volumes molaires partiels et leurs dtrivtes par rapport i la temptrature fournissent une base pour ttendre notre comprChension des interactions dans ces systbmes (eau + compost organique). Mots clks : ditthanolamines, volumes molaires en excbs, volumes molaires partiels, expansivitt, solutions aqueuses. [Traduit par la rtdaction]

Introduction Various (water + alkanolamine) systems are used for removal of acidic gases such as carbon dioxide and especially hydrogen sulfide from gas streams in the natural gas and petroleum industries and are of increasing importance in treating acidic gas streams in several chemical production industries. Knowledge of several properties, including densities at several temperatures, is required for engineering design and for subsequent operations, as summarized by Astarita et al. (1). In addition to the well-established industrial uses of experimental data for these completely miscible (water + alkanolamine) systems, there is interest in using volumetric data in combination with molecular theories or models of solutions to extend our understanding of molecular interactions in (water + organic) systems. Because much of our focus in this paper is on the volumetric properties of an alkanolamine at infinite dilution in water, we cite two theoretical investigations (2, 3) that focussed on the temperature dependence of partial molar Received April 24, 1995.

Y. Maham, T.T. ~ e n g , A.E. ' Mather, and L.G. ~ e ~ l e r . ' Department of Chemistry and Department of Chemical Engineering, University of Alberta, Edmonton, AB T6G 2G2, Canada.

'

Present address: School of Industrial Technology, Universite Sains Malaysia, Penang, Malaysia. Author to whom correspondence may be addressed. Telephone: (403) 492-2762. Fax: (403) 492-823 1.

Can. J. Chem. 73: 1514-1519 (1995). Printed in Canada / Imprimt au Canada

volumes of aqueous solutes. We also call attention to subsequent theory by Yoshimura and Nakahara (4), a useful review by Davis (3,and recent theory by Marcus (6). Some of each of these cited works is devoted to volumetric properties of (water + organic) systems, and some of the theoretical work by Marcus (6) is specifically concerned with volumetric properties of (water + alkanolamine) systems. There have been two recent reports (7, 8) of volumetric properties of (water + alkanolamine) systems. We also call attention to several other reports (7-23) of volumetric properties of (water + organic) systems, which include experimental results or methods of analysis that are related to our work.

Experimental Methyldiethanolamine [CH,N(C,H,OH),, MDEA] and ethyldiethanolamine [C,H,N(C,H,OH),, EDEA] from Aldrich Chemical Company were stated to be 99% and 98+% pure. Results of titrations with standardized hydrochloric acid were consistent with purities slightly better than 99% for both MDEA and EDEA, which were then used as received. Mixtures of these ethanolamines with doubly distilled water were made by mass, with care being taken to minimize exposure to air (carbon dioxide). Densities were measured with an Anton Paar DMA 45 density meter, which was calibrated with dry air and distilled water at each temperature, making use of densities of water from Kell (24). Accuracies of most of our densities are about 1 ( 3 x lo-,) g cm-,, with accuracies of a few densities (especially at the ~. higher temperatures) being about -+(ax lo-$) g ~ m - Temper-

1515

Maham et al.

Table 1. Mole fractions, densities, and excess molar volumes for water (1) + methyldiethanolamine (2, MDEA ) mixtures." 25°C

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X2

0.0000 0.0079 0.0176 0.0364 0.0612 0.0923 0.1322 0.1859 0.2526 0.3021 0.3658 0.5026 0.5653 0.6960 0.7997 0.8989 0.9475 1.OOOO

40°C

30°C

50°C

60°C

70°C

80°C

d

vE

d

vE

d

vE

d

vE

d

vE

d

VE

d

VE

0.997 04 1,001 28 1.006 18 1.014 93 1.024 61 1.034 14 1.042 43 1.048 81 1.052 09 1.05276 1.052 18 1.048 63 1.046 88 1.043 14 1.040 50 1.038 32 1.037 31 1.035 90

0.000 -0.044 -0.101 -0.220 -0.379 -0.570 -0.778 -0.989 -1.154 -1.224 -1.252 -1.144 -1.056 -0.798 -0.558 -0.314 -0.185 0.000

0.995 65 0.999 68 1.004 50 1.012 91 1.022 26 1.031 33 1.039 24 1.045 28 1.048 39 1.04906 1.048 39 1.044 97 1.043 10 1.039 52 1.036 84 1.034 58 1.033 57 1.032 00

0.000 -0.043 -0.101 -0.218 -0.375 -0.561 -0.765 -0.972 -1.136 -1.210 -1.238 -1.145 -1.052 -0.8 14 -0.575 -0.328 -0.201 0.000

0.992 22 0.996 12 1.000 69 1.008 60 1.017 27 1.025 54 1.032 82 1.038 26 1.041 03 1.041 54 1.04074 1.037 20 1.035 50 1.031 80 1.029 12 1.026 87 1.025 86 1.024 45

0.000 -0.044 -0.102 -0.218 -0.369 -0.547 -0.744 -0.943 -1.104 -1.177 -1.203 -1.1 10 -1.032 -0.788 -0.553 -0.308 -0.1 83 0.000

0.998 04 0.991 85 0.996 09 1.003 58 1.01 1 61 1.019 25 1.025 86 1.030 80 1.033 22 1.03364 1.03208 1.029 27 1.027 61 1.024 00 1.021 41 1.019 20 1.018 16 1.016 66

0.000 -0.046 -0.102 -0.216 -0.363 -0.534 -0.722 -0.915 -1.070 -1.143 -1.134 -1.085 -1.01 1 -0.779 -0.555 -0.319 -0.192 0.000

0.983 20 0.986 68 0.990 92 0.997 98 1.005 47 1.012 60 1.018 64 1.023 13 1.025 35 1.02560 1.02476 1.021 28 1.019 62 1.016 06 1.013 38 1.011 38 1.010 38 1.009 00

0.000 -0.043 -0.102 -0.214 -0.356 -0.522 -0.701 -0.885 -1.039 -1.106 -1.136 -1.054 -0.980 -0.75 1 -0.5 18 -0.301 -0.179 0.000

0.977 77 0.98 1 29 0.985 28 0.991 84 0.999 08 1,005 66 1.010 66 1.015 21 1.017 43 1.01764 1.01676 1.013 03 1.011 75 1.008 02 1.005 60 1.003 56 1.002 60 1.001 24

0.000 -0.046 -0.104 -0.21 1 -0.353 -0.5 12 -0.667 -0.858 -1,015 -1.083 -1.113 -1.015 -0.968 -0.725 -0.5 15 -0.295 -0.177 0.000

0.971 80 0.975 36 0.979 01 0.985 31 0.992 04 0.998 12 1.003 29 1.007 12 1.008 87 1.009 12 1.00829 1.004 53 1.003 45 1.000 03 0.997 70 0.995 70 0.994 78 0.993 67

0.000 -0.049 -0.103 -0.208 -0.343 -0.493 -0.657 -0.827 -0.965 -1.033 -1.062 -0.952 -0.915 -0.690 -0.484 -0.265 -0.149 0.000

"Units are g cm-3 for densities (4 and are cm3 mol-' for excess molar volumes (v".

Table 2. Mole fractions, densities, and excess molar volumes for water (1) and ethyldiethanolamine (2, EDEA) + mixtures."

"Units are g cm? for densities (d) and are cm3 mol-' for excess molar volumes (V').

atures of the water bath were stable to +O.OO1° during the time required to measure a density and were known to 0 . 0 l 0 C , as measured with a Guildline platinum resistance thermometer.

in Table 1 for (water + MDEA) systems and in Table 2 for (water + EDEA systems). The excess molar volume is defined by

Results Experimental results (mole fractions and densities) and one kind of derived result (excess molar volume, p)are reported

in which Vm represents the volume of a mixture containing a total of one mole of (water + alkanolamine), x , andx2 are mole

Can. J. Chem. Vol. 73, 1995

Fig. 1. Densities of (water + alkanolamine) systems at 2S°C. DEA (densities from ref. 8) represents diethanolamine. MDEA

Fig. 2. Excess molar volumes of (water + alkanolamine) systems at 25°C. See legend for Fig. 1.

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and EDEA (densities from Tables 1 and 2) represent methyldiethanolamine and ethyldiethanolamine. All of these densities decrease with increasing temperature.

fractions of water and alkanolamine, respectively, and V1* and V2* are the molar volumes of the corresponding pure liquids. Equation [ l ] can also be expressed as

in which M I and M2 represent molar masses of water and alkanolamine, respectively, and d, d,*, and d2* represent densities of a mixture of specified mole fraction, of pure water, and of pure alkanolamine, respectively. The values of vElisted in Tables 1 and 2 were calculated from mole fractions, molar masses, and densities by way of eq. [2]. The general trends of density and vEwith increasing mole fraction of alkanolamine are illustrated in Figs. 1 and 2.

Calculations and discussion

Redlich-Kister coefficients (A,,) are listed in Table 3 for the (water + MDEA) and (water + EDEA) systems. Differentiation of eq. [6] with respect to x2 and combination of the result of differentiation with eqs. [4] and [5] leads to the following equations for the partial molar volumes of water (TI) and of alkanolamine (V,):

Much of our present interest is in the partial molar volume of water at infinite dilution (VI0)in an alkanolamine and in the partial molar volume of an alkanolamine at infinite dilution (V2") in water. We therefore set x2 = 1 in eq. [7] and x2 = 0 in eq. [8] to obtain

The partial molar volume of a component (Ti) is defined by and Differentiation of eq. [ l ] and combination with eq. [3] leads (25, 26) to the following equations for the partial molar volumes of water (TI) and of alkanolamine (V2): -

[41

V, = vE+ v I * - X ~ ( ~ V E I ~ X ~ ) ~ , ~

Equations equivalent to [4] and [5] are presented in the useful review by Davis (5). A convenient way to carry out the differentiations specified in eq. [4] and eq. [5] can begin with equations that will fit the vEresults that are reported in Tables 1 and 2. For this purpose we use equations of the Redlich-Kister form:

Equations [7] and [8] permit calculation of the partial molar volumes of each component (not at infinite dilution) conveniently and with the accuracy that is justified by the accuracy of the experimental data; we have used these equations for this purpose as reported later in this paper. But it should be recognized that the Redlich-Kister equation [6] and its derivative equations [7] and [8] are intended to provide the best overall fit of the data in convenient form with a minimum number of adjustable parameters. It is known, however, that the RedlichKister equation and especially its derivatives do not always provide the best representation of properties of either component at infinite dilution in the other component. Therefore, we

Maham et al

consider two alternatives to eqs. [9] and [lo] for evaluation of VIOand V20. As shown previously (8), the apparent molar volume of water in alkanolamine (V4,1)and the apparent molar volume of alkanolamine in water (V4,2)can be calculated as

Table 3. Redlich-Kister equation fitting coefficents for aqueous mixtures of MDEA and EDEA at different temperatures.

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and

Simple graphical or analytical extrapolation of V4,, to x, = 0 (x, = I) leads to the desired value of 7 , " and similar extrapolation of V4,2 to x, = 0 leads to the desired value of V,". Perron et al. (17) have used an equivalent method based on extrapolation of the "reduced volume" represented by ~ / X , Xto, x2 = 1 or 0 to obtain equally accurate values of partial molar volumes at infinite dilution. The methods of obtaining V2' by way of eq. [lo], extrapolation of V4,,, or extrapolation of VE/x,x2 are all satisfactory and lead to similar results having good accuracy. On the other hand, because we have few VE values for x, near unity (small x,), accuracies of TI0values are less good, especially for those derived from Redlich-Kister coefficients and eq. [9]. The values of V10that we cite later have all been obtained by extrapolation of V4:, values to x, = 0. Before using the equations above with our experimental results for calculation of partial molar volumes, we turn to consideration of thermal expansion. The thermal expansion of a pure substance is often expressed in terms of the coefficient of thermal expansion, defined as a* = (l/V*)(aV*/dT),. It is more convenient for us to omit the (l/V*) and to consider the molar expansivity (E,*) of a pure substance (i) defined as

For a mixture the corresponding definition of the molar expansivity in terms of the molar volume represented by V is

Because we and others have expressed our experimental results in terms of excess molar volumes, it is useful to consider the effect of temperature on the excess volume by differentiating eq. [I] with respect to temperature, defining the excess molar expansivity as

as Similarly, we define a partial molar expansivity (Ei)

and thence obtaining

Differentiation of a well-known equation for the molar volume of a mixture (V = xlVI+ x2\) with respect to temperature and combination with the definitions expressed by eqs. [13]-[15] gives us

All of our VE values are negative (Tables 1 and 2 and Fig. 2), as is common for other completely miscible (water + polar organic) systems. These VE values become less negative with increasing temperature, as is also common. Partial molar volumes of water (TI) and of alkanolamines (V2) can be calculated for all compositions by using the Redlich-Kister coefficients (Table 3) in eqs. [7] and [8]. An illustration of the results of such calculations for the partial molar volumes of MDEA over the complete range of compositions and several temperatures is provided in Fig. 3. Several previous investigators (for examples see refs. 7, 8, 12, 14,21, and 23) have observed similar minima in graphs of against mole fraction (as in Fig. 3) for various alcohols and other polar organics in water. Koga and colleagues (19, 23) have used partial molar vol-

as a relationship between the molar expansivity of the mixture and the partial molar expansivities of the components. - Following earlier investigations (2, 3) of the dependence of VZ0 on temperature in relation to "structure-making" and "structure-breaking" solutes in water, we will be concerned with

v2

Can. J. Chern. Vol. 73, 1995 Table 4. Partial molar volumes" of MDEA and EDEA at infinite dilution in water ( F ) and of water at infinite dilution in MDEA and in EDEA (y).

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t ("C)

"Units of

T(MDEA)

and

y ( i n MDEA)

F(EDEA)

V,"(in EDEA)

are cm' mol-I.

Fig. 3. Partial molar volumes of MDEA in water at several temper80°C. atures. @, 25OC; V, 40°C; Y,60°C; 0,

umes and several other thermodynamic properties as a basis for deducing detailed "pictures" of solute-solute, solute-water, and water-water interactions over ranges of composition for (water + 2-butoxyethanol) and (water + dimethyl sulfoxide) systems. Pagt, Huot, and Jolicoeur (7) have used their collection of thermodynamic properties (volumes, compressibilities, and heat capacities) of the (water + ethanolamine) system as a basis for their ~ i c t u r of e molecular interactions. One of the reasons for undertaking the present investigation and also our earlier investigation (8) of the volumetric properties of other (water + alkanolamine) systems was to obtain some of the data needed for forming similar pictures of molecular interactions in these systems; calorimetric measurements are in progress. Because development of credible pictures along the lines described by Koga (19, 23) and Jolicoeur (7) requires an extensive array of thermodynamic data, we turn now to sim pler analyses that can be carried out with only our presently reported results. Previous investigators of dilute aqueous solutions have used several criteria as a basis for describing some solutes as "structure makers" and other solutes as "structure breakers". One such classification (2, 3) is based on the sign of d2V2"ldT2;a positive sign corresponds to a structure-making solute while a negative sign corresponds to a structure-breaking solute. In Table 4 we list the values of partial molar volumes of MDEA and of EDEA at several temperatures at infinite dilution in water (V,"). Graphs of V," of MDEA and of EDEA against

temperature give straight lines with positive slopes. Values of the slopes dV,"ldT are 0.08 cm3 mol-I K-' for MDEA and 0.10 cm3 mol-I K-I for EDEA. Because of the linearity of v2" against temperature, d2V2"ldT2= 0 within the accuracies of our results over the temperature range 25-80°C, which means (according to the criterion of temperature dependence of partial molar volumes) that these solutes cause no net or overall structure-making or structure-breaking effects in water. It was ~ positive and observed earlier (8) that values of d V , ~ i dare values of d2V201d~2 = 0 for other alkanolamines in water, which led to the same conclusion about these solutes being neither net structure makers nor net structure breakers. Partial molar volumes of water at infinite dilution in MDEA and in EDEA are listed in Table 4. Accuracies of these values do not justify making any statement about d2V10id~2, but it is d V I 0 / d are ~ positive. All of the clear that the first derivatives V," values are smaller than the corresponding molar volumes of pure water (V,*) at the same temperature. This observation is consistent with the idea that the molar volume of pure water is a sum of the "actual" molecular volumes plus the "empty" volume that arises from the hydrogen-bonded "open" structure of liquid water. Partial molar volumes (8) of water at infinite dilution in other alkanolamines at several temperatures are also smaller than corresponding values of V,* and have been interpreted similarly. Sakurai and Nakagawa (18) have measured densities of dilute solutions of water in benzene and in several n-alkanols at several temperatures. They have used these densities and corresponding compositions in evaluating the partial molar volumes of water at infinite dilution (represented here by TI0) in each solvent at several temperatures. Their values of V," for water at infinite dilution in methanol, ethanol, n-propanol, and n-butanol at each temperature from 5 to 45°C are substantially smaller than corresponding values of V,* and are consistent with the interpretation above. We also note that the partial molar volumes of water in alkanols increase with number of atoms of carbon per molecule of alkanol in the sequence ethanol through n-octanol and that the difference between V,* and TI0values decreases with increasing number of atoms of carbon per molecule of alkanol. This effect is sufficiently large that the values of v , " for water in n-octanol are larger than the corresponding values of V, * at the higher temperatures (35 and 45°C). This observation leads us to suggest that our earlier (see above) explanation for values of V," being smaller than corresponding values of V1* is probably incomplete and might even be largely mistaken. The values of TI0reported by Sakurai and Nakagawa (18)

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Maharn et al.

for water in alkanols in the sequence ethanol through n-octanol and also for water in benzene lead to positive values of dVlO/ dT, as also reported here and previously (8) for water in alkanolamines. All of these positive values of d V , " / d ~ a r consistent e with the general observation that dV/dT is positive for most pure substances and most solutions. But they have also reported that d V I 0 / dis ~ negative for water in methanol, for which neither they nor we have any satisfactory explanation. Sakurai and Nakagawa (1 8) have also reported values of V1O for water in benzene that are substantially larger (3-4 cm3 mol-') than corresponding values of V,*. It seems reasonable to suggest that this unusual difference can be explained on the basis of disruption of the "stacked layers structure" of liquid benzene, with a consequent increase in volume. It may also be that a similar explanation involving disruption of reasonably closely packed alkane chains is appropriate for the relatively large values of VI0for water in the larger alkanols. We (1 1, 15) and others (9, 10, 13, 16, 17) have used partial molar volumes (V20)of many organics in water to develop additivity schemes that might contribute to our understanding of organic-water interactions and that are certainly useful for predicting partial molar volumes for organic solutes in water. f few of these investigations (especially ref. 16) have led to additivity schemes for partial molar expansivities. Our further developments along these lines, based on our own and other recently reported volumes and expansivities, will be reported later.

Acknowledgement We thank the Natural Sciences and Engineering Research Council of Canada for grants in support of this and other research on the properties of (water + organic) systems.

References 1. G. Astarita, D.W. Savage, and A. Bisio. Gas treating with chernical solvents. John Wiley & Sons, New York. 1983. 2. L.G. Hepler. Can. J. Chern. 47,4613 (1969). Note that the vertical axis in Fig. 2 of ref. 2 should be labelled v:.

3. J.L. Neal and D.A.I. Goring. J. Phys. Chem. 74,658 (1970). 4. Y. Yoshirnura and M. Nakahara. Bull. Chem. Soc. Jpn. 61, 1887 ( 1988) 5. M.I. Davis. Chern. Soc. Rev. 127 (1993). 6. Y. Marcus. J. Chern. Soc. Faraday Trans. 91,427 (1995). 7. M. Page, J.-Y. Huot, and C. Jolicoeur. Can. J. Chem. 71, 1064 (1993). 8. Y. Maharn, T.T. Teng, L.G. Hepler, and A.E. Mather. J. Solution Chem. 23, 195 (1994). 9. S. Cabani, G. Conti, and L. Lepori. J. Phys. Chern. 76, 1338 ( 1972); 78, 1030 (1974). 10. S. Cabani, G. Conti, and E. Matteoli. J. Solution Chern. 5, 75 1 (1976). 11. 0. Enea, P.P. Singh, and L.G Hepler. J. Solution Chern. 11,719 (1977). 12. G. Roux, G. Perron, and J.E. Desnoyers. J. Solution Chem. 7, 639 (1978). 13. H. Hoiland. J. Solution Chern. 9, 857 (1980). 14. G.C. Benson and 0. Kiyohara. J. Solution Chern. 9,791 (1980). 15. 0. Enea, C. Jolicoeur, and L.G. Hepler. Can. J. Chern. 58, 704 (1980). 16. S. Cabani, P. Gianni, V. Mollica, and L. Lepori. J. Solution Chern. 10,563 (1981). 17. S. Cabani, G. Conti, E. Matteoli, and M.R. Tine. J. Chern. Soc. Faraday Trans. 77, 2385 (1981). 18. M. Sakurai and T. Nakagawa. J. Chern. Therrnodyn. 14, 269 (1982); 16, 171 (1984). 19. J.V. Davies, F.W. Lau, L.T.N. Le, J.T.W. Lai, and Y. Koga. Can. J. Chern. 70,2659 (1992). 20. G. Perron, L. Couture, and J.E. Desnoyers. J. Solution Chern. 21, 433 (1992). 21. G. Perron, F. Quirion, D. Larnbert, J. Ledoux, L. Ghaicha, R. Bennes, M. Privat, and J.E. Desnoyers. J. Solution Chern. 22, 107 (1993). 22. L.E. Strong, M. Bowe, J. White, and K. Abi-Selah. J. Solution Chern. 23,541 (1994). 23. J.T.W. Lai, F.W. Lau, D. Robb, P. Westh, G. Nielsen, C. Trandurn, A. Hvidt, and Y. Koga. J. Solution Chem. 24, 89 (1995). 24. G.S. Kell. J. Chern. Eng. Data, 20,97 (1975). 25. S.E. Wood and R. Battino. Thermodynamics of chemical systems. Cambridge University Press, Cambridge, U.K. 1990. 26. W.E. Acree, Jr. Thermodynamic properties of nonelectrolyte solutions. Academic Press, New York. 1984.

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Yadollah Maham, Tjoon T. Teng, Alan E. Mather, and Loren G. Hepler

Abstract: Densities of completely miscible (water + methyldiethanolamine) and (water + ethyldiethanolamine) systems have been measured over the full range of compositions at temperatures from 25 to 80°C. Results of these measurements have been used in calculating excess molar volumes and partial molar volumes of each component. We have also identified different measures of the thermal expansion of these systems and have calculated some of these derivative quantities. The partial molar volumes and their derivatives with respect to temperature provide a basis for extending our understanding of molecular interactions in these (water + organic) systems. Key words: diethanolamines, excess molar volumes, partial molar volumes, expansivities, aqueous solutions.

Resume : Optrant i des temptratures allant de 25 i 80°C, on a mesurt les densitts des systbmes complbternent miscibles (eau + mtthylditthanolamine) et (eau + tthylditthanolamine) sur I'ensemble des plages de composition. On a utilist ces rtsultats pour calculer les volumes molaires en excbs et les volumes molaires partiels de chacun des composants. On a aussi identifit difftrentes mesures de I'expansion thermique de ces systbmes et on a calcult quelques-unes de ces quantitts dtrivtes. Les volumes molaires partiels et leurs dtrivtes par rapport i la temptrature fournissent une base pour ttendre notre comprChension des interactions dans ces systbmes (eau + compost organique). Mots clks : ditthanolamines, volumes molaires en excbs, volumes molaires partiels, expansivitt, solutions aqueuses. [Traduit par la rtdaction]

Introduction Various (water + alkanolamine) systems are used for removal of acidic gases such as carbon dioxide and especially hydrogen sulfide from gas streams in the natural gas and petroleum industries and are of increasing importance in treating acidic gas streams in several chemical production industries. Knowledge of several properties, including densities at several temperatures, is required for engineering design and for subsequent operations, as summarized by Astarita et al. (1). In addition to the well-established industrial uses of experimental data for these completely miscible (water + alkanolamine) systems, there is interest in using volumetric data in combination with molecular theories or models of solutions to extend our understanding of molecular interactions in (water + organic) systems. Because much of our focus in this paper is on the volumetric properties of an alkanolamine at infinite dilution in water, we cite two theoretical investigations (2, 3) that focussed on the temperature dependence of partial molar Received April 24, 1995.

Y. Maham, T.T. ~ e n g , A.E. ' Mather, and L.G. ~ e ~ l e r . ' Department of Chemistry and Department of Chemical Engineering, University of Alberta, Edmonton, AB T6G 2G2, Canada.

'

Present address: School of Industrial Technology, Universite Sains Malaysia, Penang, Malaysia. Author to whom correspondence may be addressed. Telephone: (403) 492-2762. Fax: (403) 492-823 1.

Can. J. Chem. 73: 1514-1519 (1995). Printed in Canada / Imprimt au Canada

volumes of aqueous solutes. We also call attention to subsequent theory by Yoshimura and Nakahara (4), a useful review by Davis (3,and recent theory by Marcus (6). Some of each of these cited works is devoted to volumetric properties of (water + organic) systems, and some of the theoretical work by Marcus (6) is specifically concerned with volumetric properties of (water + alkanolamine) systems. There have been two recent reports (7, 8) of volumetric properties of (water + alkanolamine) systems. We also call attention to several other reports (7-23) of volumetric properties of (water + organic) systems, which include experimental results or methods of analysis that are related to our work.

Experimental Methyldiethanolamine [CH,N(C,H,OH),, MDEA] and ethyldiethanolamine [C,H,N(C,H,OH),, EDEA] from Aldrich Chemical Company were stated to be 99% and 98+% pure. Results of titrations with standardized hydrochloric acid were consistent with purities slightly better than 99% for both MDEA and EDEA, which were then used as received. Mixtures of these ethanolamines with doubly distilled water were made by mass, with care being taken to minimize exposure to air (carbon dioxide). Densities were measured with an Anton Paar DMA 45 density meter, which was calibrated with dry air and distilled water at each temperature, making use of densities of water from Kell (24). Accuracies of most of our densities are about 1 ( 3 x lo-,) g cm-,, with accuracies of a few densities (especially at the ~. higher temperatures) being about -+(ax lo-$) g ~ m - Temper-

1515

Maham et al.

Table 1. Mole fractions, densities, and excess molar volumes for water (1) + methyldiethanolamine (2, MDEA ) mixtures." 25°C

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X2

0.0000 0.0079 0.0176 0.0364 0.0612 0.0923 0.1322 0.1859 0.2526 0.3021 0.3658 0.5026 0.5653 0.6960 0.7997 0.8989 0.9475 1.OOOO

40°C

30°C

50°C

60°C

70°C

80°C

d

vE

d

vE

d

vE

d

vE

d

vE

d

VE

d

VE

0.997 04 1,001 28 1.006 18 1.014 93 1.024 61 1.034 14 1.042 43 1.048 81 1.052 09 1.05276 1.052 18 1.048 63 1.046 88 1.043 14 1.040 50 1.038 32 1.037 31 1.035 90

0.000 -0.044 -0.101 -0.220 -0.379 -0.570 -0.778 -0.989 -1.154 -1.224 -1.252 -1.144 -1.056 -0.798 -0.558 -0.314 -0.185 0.000

0.995 65 0.999 68 1.004 50 1.012 91 1.022 26 1.031 33 1.039 24 1.045 28 1.048 39 1.04906 1.048 39 1.044 97 1.043 10 1.039 52 1.036 84 1.034 58 1.033 57 1.032 00

0.000 -0.043 -0.101 -0.218 -0.375 -0.561 -0.765 -0.972 -1.136 -1.210 -1.238 -1.145 -1.052 -0.8 14 -0.575 -0.328 -0.201 0.000

0.992 22 0.996 12 1.000 69 1.008 60 1.017 27 1.025 54 1.032 82 1.038 26 1.041 03 1.041 54 1.04074 1.037 20 1.035 50 1.031 80 1.029 12 1.026 87 1.025 86 1.024 45

0.000 -0.044 -0.102 -0.218 -0.369 -0.547 -0.744 -0.943 -1.104 -1.177 -1.203 -1.1 10 -1.032 -0.788 -0.553 -0.308 -0.1 83 0.000

0.998 04 0.991 85 0.996 09 1.003 58 1.01 1 61 1.019 25 1.025 86 1.030 80 1.033 22 1.03364 1.03208 1.029 27 1.027 61 1.024 00 1.021 41 1.019 20 1.018 16 1.016 66

0.000 -0.046 -0.102 -0.216 -0.363 -0.534 -0.722 -0.915 -1.070 -1.143 -1.134 -1.085 -1.01 1 -0.779 -0.555 -0.319 -0.192 0.000

0.983 20 0.986 68 0.990 92 0.997 98 1.005 47 1.012 60 1.018 64 1.023 13 1.025 35 1.02560 1.02476 1.021 28 1.019 62 1.016 06 1.013 38 1.011 38 1.010 38 1.009 00

0.000 -0.043 -0.102 -0.214 -0.356 -0.522 -0.701 -0.885 -1.039 -1.106 -1.136 -1.054 -0.980 -0.75 1 -0.5 18 -0.301 -0.179 0.000

0.977 77 0.98 1 29 0.985 28 0.991 84 0.999 08 1,005 66 1.010 66 1.015 21 1.017 43 1.01764 1.01676 1.013 03 1.011 75 1.008 02 1.005 60 1.003 56 1.002 60 1.001 24

0.000 -0.046 -0.104 -0.21 1 -0.353 -0.5 12 -0.667 -0.858 -1,015 -1.083 -1.113 -1.015 -0.968 -0.725 -0.5 15 -0.295 -0.177 0.000

0.971 80 0.975 36 0.979 01 0.985 31 0.992 04 0.998 12 1.003 29 1.007 12 1.008 87 1.009 12 1.00829 1.004 53 1.003 45 1.000 03 0.997 70 0.995 70 0.994 78 0.993 67

0.000 -0.049 -0.103 -0.208 -0.343 -0.493 -0.657 -0.827 -0.965 -1.033 -1.062 -0.952 -0.915 -0.690 -0.484 -0.265 -0.149 0.000

"Units are g cm-3 for densities (4 and are cm3 mol-' for excess molar volumes (v".

Table 2. Mole fractions, densities, and excess molar volumes for water (1) and ethyldiethanolamine (2, EDEA) + mixtures."

"Units are g cm? for densities (d) and are cm3 mol-' for excess molar volumes (V').

atures of the water bath were stable to +O.OO1° during the time required to measure a density and were known to 0 . 0 l 0 C , as measured with a Guildline platinum resistance thermometer.

in Table 1 for (water + MDEA) systems and in Table 2 for (water + EDEA systems). The excess molar volume is defined by

Results Experimental results (mole fractions and densities) and one kind of derived result (excess molar volume, p)are reported

in which Vm represents the volume of a mixture containing a total of one mole of (water + alkanolamine), x , andx2 are mole

Can. J. Chem. Vol. 73, 1995

Fig. 1. Densities of (water + alkanolamine) systems at 2S°C. DEA (densities from ref. 8) represents diethanolamine. MDEA

Fig. 2. Excess molar volumes of (water + alkanolamine) systems at 25°C. See legend for Fig. 1.

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and EDEA (densities from Tables 1 and 2) represent methyldiethanolamine and ethyldiethanolamine. All of these densities decrease with increasing temperature.

fractions of water and alkanolamine, respectively, and V1* and V2* are the molar volumes of the corresponding pure liquids. Equation [ l ] can also be expressed as

in which M I and M2 represent molar masses of water and alkanolamine, respectively, and d, d,*, and d2* represent densities of a mixture of specified mole fraction, of pure water, and of pure alkanolamine, respectively. The values of vElisted in Tables 1 and 2 were calculated from mole fractions, molar masses, and densities by way of eq. [2]. The general trends of density and vEwith increasing mole fraction of alkanolamine are illustrated in Figs. 1 and 2.

Calculations and discussion

Redlich-Kister coefficients (A,,) are listed in Table 3 for the (water + MDEA) and (water + EDEA) systems. Differentiation of eq. [6] with respect to x2 and combination of the result of differentiation with eqs. [4] and [5] leads to the following equations for the partial molar volumes of water (TI) and of alkanolamine (V,):

Much of our present interest is in the partial molar volume of water at infinite dilution (VI0)in an alkanolamine and in the partial molar volume of an alkanolamine at infinite dilution (V2") in water. We therefore set x2 = 1 in eq. [7] and x2 = 0 in eq. [8] to obtain

The partial molar volume of a component (Ti) is defined by and Differentiation of eq. [ l ] and combination with eq. [3] leads (25, 26) to the following equations for the partial molar volumes of water (TI) and of alkanolamine (V2): -

[41

V, = vE+ v I * - X ~ ( ~ V E I ~ X ~ ) ~ , ~

Equations equivalent to [4] and [5] are presented in the useful review by Davis (5). A convenient way to carry out the differentiations specified in eq. [4] and eq. [5] can begin with equations that will fit the vEresults that are reported in Tables 1 and 2. For this purpose we use equations of the Redlich-Kister form:

Equations [7] and [8] permit calculation of the partial molar volumes of each component (not at infinite dilution) conveniently and with the accuracy that is justified by the accuracy of the experimental data; we have used these equations for this purpose as reported later in this paper. But it should be recognized that the Redlich-Kister equation [6] and its derivative equations [7] and [8] are intended to provide the best overall fit of the data in convenient form with a minimum number of adjustable parameters. It is known, however, that the RedlichKister equation and especially its derivatives do not always provide the best representation of properties of either component at infinite dilution in the other component. Therefore, we

Maham et al

consider two alternatives to eqs. [9] and [lo] for evaluation of VIOand V20. As shown previously (8), the apparent molar volume of water in alkanolamine (V4,1)and the apparent molar volume of alkanolamine in water (V4,2)can be calculated as

Table 3. Redlich-Kister equation fitting coefficents for aqueous mixtures of MDEA and EDEA at different temperatures.

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and

Simple graphical or analytical extrapolation of V4,, to x, = 0 (x, = I) leads to the desired value of 7 , " and similar extrapolation of V4,2 to x, = 0 leads to the desired value of V,". Perron et al. (17) have used an equivalent method based on extrapolation of the "reduced volume" represented by ~ / X , Xto, x2 = 1 or 0 to obtain equally accurate values of partial molar volumes at infinite dilution. The methods of obtaining V2' by way of eq. [lo], extrapolation of V4,,, or extrapolation of VE/x,x2 are all satisfactory and lead to similar results having good accuracy. On the other hand, because we have few VE values for x, near unity (small x,), accuracies of TI0values are less good, especially for those derived from Redlich-Kister coefficients and eq. [9]. The values of V10that we cite later have all been obtained by extrapolation of V4:, values to x, = 0. Before using the equations above with our experimental results for calculation of partial molar volumes, we turn to consideration of thermal expansion. The thermal expansion of a pure substance is often expressed in terms of the coefficient of thermal expansion, defined as a* = (l/V*)(aV*/dT),. It is more convenient for us to omit the (l/V*) and to consider the molar expansivity (E,*) of a pure substance (i) defined as

For a mixture the corresponding definition of the molar expansivity in terms of the molar volume represented by V is

Because we and others have expressed our experimental results in terms of excess molar volumes, it is useful to consider the effect of temperature on the excess volume by differentiating eq. [I] with respect to temperature, defining the excess molar expansivity as

as Similarly, we define a partial molar expansivity (Ei)

and thence obtaining

Differentiation of a well-known equation for the molar volume of a mixture (V = xlVI+ x2\) with respect to temperature and combination with the definitions expressed by eqs. [13]-[15] gives us

All of our VE values are negative (Tables 1 and 2 and Fig. 2), as is common for other completely miscible (water + polar organic) systems. These VE values become less negative with increasing temperature, as is also common. Partial molar volumes of water (TI) and of alkanolamines (V2) can be calculated for all compositions by using the Redlich-Kister coefficients (Table 3) in eqs. [7] and [8]. An illustration of the results of such calculations for the partial molar volumes of MDEA over the complete range of compositions and several temperatures is provided in Fig. 3. Several previous investigators (for examples see refs. 7, 8, 12, 14,21, and 23) have observed similar minima in graphs of against mole fraction (as in Fig. 3) for various alcohols and other polar organics in water. Koga and colleagues (19, 23) have used partial molar vol-

as a relationship between the molar expansivity of the mixture and the partial molar expansivities of the components. - Following earlier investigations (2, 3) of the dependence of VZ0 on temperature in relation to "structure-making" and "structure-breaking" solutes in water, we will be concerned with

v2

Can. J. Chern. Vol. 73, 1995 Table 4. Partial molar volumes" of MDEA and EDEA at infinite dilution in water ( F ) and of water at infinite dilution in MDEA and in EDEA (y).

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t ("C)

"Units of

T(MDEA)

and

y ( i n MDEA)

F(EDEA)

V,"(in EDEA)

are cm' mol-I.

Fig. 3. Partial molar volumes of MDEA in water at several temper80°C. atures. @, 25OC; V, 40°C; Y,60°C; 0,

umes and several other thermodynamic properties as a basis for deducing detailed "pictures" of solute-solute, solute-water, and water-water interactions over ranges of composition for (water + 2-butoxyethanol) and (water + dimethyl sulfoxide) systems. Pagt, Huot, and Jolicoeur (7) have used their collection of thermodynamic properties (volumes, compressibilities, and heat capacities) of the (water + ethanolamine) system as a basis for their ~ i c t u r of e molecular interactions. One of the reasons for undertaking the present investigation and also our earlier investigation (8) of the volumetric properties of other (water + alkanolamine) systems was to obtain some of the data needed for forming similar pictures of molecular interactions in these systems; calorimetric measurements are in progress. Because development of credible pictures along the lines described by Koga (19, 23) and Jolicoeur (7) requires an extensive array of thermodynamic data, we turn now to sim pler analyses that can be carried out with only our presently reported results. Previous investigators of dilute aqueous solutions have used several criteria as a basis for describing some solutes as "structure makers" and other solutes as "structure breakers". One such classification (2, 3) is based on the sign of d2V2"ldT2;a positive sign corresponds to a structure-making solute while a negative sign corresponds to a structure-breaking solute. In Table 4 we list the values of partial molar volumes of MDEA and of EDEA at several temperatures at infinite dilution in water (V,"). Graphs of V," of MDEA and of EDEA against

temperature give straight lines with positive slopes. Values of the slopes dV,"ldT are 0.08 cm3 mol-I K-' for MDEA and 0.10 cm3 mol-I K-I for EDEA. Because of the linearity of v2" against temperature, d2V2"ldT2= 0 within the accuracies of our results over the temperature range 25-80°C, which means (according to the criterion of temperature dependence of partial molar volumes) that these solutes cause no net or overall structure-making or structure-breaking effects in water. It was ~ positive and observed earlier (8) that values of d V , ~ i dare values of d2V201d~2 = 0 for other alkanolamines in water, which led to the same conclusion about these solutes being neither net structure makers nor net structure breakers. Partial molar volumes of water at infinite dilution in MDEA and in EDEA are listed in Table 4. Accuracies of these values do not justify making any statement about d2V10id~2, but it is d V I 0 / d are ~ positive. All of the clear that the first derivatives V," values are smaller than the corresponding molar volumes of pure water (V,*) at the same temperature. This observation is consistent with the idea that the molar volume of pure water is a sum of the "actual" molecular volumes plus the "empty" volume that arises from the hydrogen-bonded "open" structure of liquid water. Partial molar volumes (8) of water at infinite dilution in other alkanolamines at several temperatures are also smaller than corresponding values of V,* and have been interpreted similarly. Sakurai and Nakagawa (18) have measured densities of dilute solutions of water in benzene and in several n-alkanols at several temperatures. They have used these densities and corresponding compositions in evaluating the partial molar volumes of water at infinite dilution (represented here by TI0) in each solvent at several temperatures. Their values of V," for water at infinite dilution in methanol, ethanol, n-propanol, and n-butanol at each temperature from 5 to 45°C are substantially smaller than corresponding values of V,* and are consistent with the interpretation above. We also note that the partial molar volumes of water in alkanols increase with number of atoms of carbon per molecule of alkanol in the sequence ethanol through n-octanol and that the difference between V,* and TI0values decreases with increasing number of atoms of carbon per molecule of alkanol. This effect is sufficiently large that the values of v , " for water in n-octanol are larger than the corresponding values of V, * at the higher temperatures (35 and 45°C). This observation leads us to suggest that our earlier (see above) explanation for values of V," being smaller than corresponding values of V1* is probably incomplete and might even be largely mistaken. The values of TI0reported by Sakurai and Nakagawa (18)

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Maharn et al.

for water in alkanols in the sequence ethanol through n-octanol and also for water in benzene lead to positive values of dVlO/ dT, as also reported here and previously (8) for water in alkanolamines. All of these positive values of d V , " / d ~ a r consistent e with the general observation that dV/dT is positive for most pure substances and most solutions. But they have also reported that d V I 0 / dis ~ negative for water in methanol, for which neither they nor we have any satisfactory explanation. Sakurai and Nakagawa (1 8) have also reported values of V1O for water in benzene that are substantially larger (3-4 cm3 mol-') than corresponding values of V,*. It seems reasonable to suggest that this unusual difference can be explained on the basis of disruption of the "stacked layers structure" of liquid benzene, with a consequent increase in volume. It may also be that a similar explanation involving disruption of reasonably closely packed alkane chains is appropriate for the relatively large values of VI0for water in the larger alkanols. We (1 1, 15) and others (9, 10, 13, 16, 17) have used partial molar volumes (V20)of many organics in water to develop additivity schemes that might contribute to our understanding of organic-water interactions and that are certainly useful for predicting partial molar volumes for organic solutes in water. f few of these investigations (especially ref. 16) have led to additivity schemes for partial molar expansivities. Our further developments along these lines, based on our own and other recently reported volumes and expansivities, will be reported later.

Acknowledgement We thank the Natural Sciences and Engineering Research Council of Canada for grants in support of this and other research on the properties of (water + organic) systems.

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3. J.L. Neal and D.A.I. Goring. J. Phys. Chem. 74,658 (1970). 4. Y. Yoshirnura and M. Nakahara. Bull. Chem. Soc. Jpn. 61, 1887 ( 1988) 5. M.I. Davis. Chern. Soc. Rev. 127 (1993). 6. Y. Marcus. J. Chern. Soc. Faraday Trans. 91,427 (1995). 7. M. Page, J.-Y. Huot, and C. Jolicoeur. Can. J. Chem. 71, 1064 (1993). 8. Y. Maharn, T.T. Teng, L.G. Hepler, and A.E. Mather. J. Solution Chem. 23, 195 (1994). 9. S. Cabani, G. Conti, and L. Lepori. J. Phys. Chern. 76, 1338 ( 1972); 78, 1030 (1974). 10. S. Cabani, G. Conti, and E. Matteoli. J. Solution Chern. 5, 75 1 (1976). 11. 0. Enea, P.P. Singh, and L.G Hepler. J. Solution Chern. 11,719 (1977). 12. G. Roux, G. Perron, and J.E. Desnoyers. J. Solution Chem. 7, 639 (1978). 13. H. Hoiland. J. Solution Chern. 9, 857 (1980). 14. G.C. Benson and 0. Kiyohara. J. Solution Chern. 9,791 (1980). 15. 0. Enea, C. Jolicoeur, and L.G. Hepler. Can. J. Chern. 58, 704 (1980). 16. S. Cabani, P. Gianni, V. Mollica, and L. Lepori. J. Solution Chern. 10,563 (1981). 17. S. Cabani, G. Conti, E. Matteoli, and M.R. Tine. J. Chern. Soc. Faraday Trans. 77, 2385 (1981). 18. M. Sakurai and T. Nakagawa. J. Chern. Therrnodyn. 14, 269 (1982); 16, 171 (1984). 19. J.V. Davies, F.W. Lau, L.T.N. Le, J.T.W. Lai, and Y. Koga. Can. J. Chern. 70,2659 (1992). 20. G. Perron, L. Couture, and J.E. Desnoyers. J. Solution Chern. 21, 433 (1992). 21. G. Perron, F. Quirion, D. Larnbert, J. Ledoux, L. Ghaicha, R. Bennes, M. Privat, and J.E. Desnoyers. J. Solution Chern. 22, 107 (1993). 22. L.E. Strong, M. Bowe, J. White, and K. Abi-Selah. J. Solution Chern. 23,541 (1994). 23. J.T.W. Lai, F.W. Lau, D. Robb, P. Westh, G. Nielsen, C. Trandurn, A. Hvidt, and Y. Koga. J. Solution Chem. 24, 89 (1995). 24. G.S. Kell. J. Chern. Eng. Data, 20,97 (1975). 25. S.E. Wood and R. Battino. Thermodynamics of chemical systems. Cambridge University Press, Cambridge, U.K. 1990. 26. W.E. Acree, Jr. Thermodynamic properties of nonelectrolyte solutions. Academic Press, New York. 1984.