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Thermodynamic analysis of the mutual solubilities of hydrocarbons and water
Fluid Phase Equilibria 186 (2001) 185–206
Thermodynamic analysis of the mutual solubilities of hydrocarbons and water Constantine Tsonopoulos∗ 18 Dorothy Drive, Morristown, NJ 07960, USA Received 6 December 2000; accepted 20 April 2001
Abstract The analysis of mutual solubilities and calorimetric heats of solution carried out for normal alkanes and water close to 298 K [Fluid Phase Equilib. 156 (1999) 21] is extended to normal alkylcyclohexanes, linear 1-alkenes, and normal alkylbenzenes. Extensive solubility data are available for alkylbenzenes, but relatively little is known about alkylcyclohexanes and alkenes in water. All of these hydrocarbons are more soluble than the corresponding alkanes, but are less volatile than the alkanes (their Henry’s constants descending in the order alkanes > alkenes > alkylcyclohexanes > alkylbenzenes). The solubility minimum for hydrocarbons in water is confirmed by calorimetric data for C6 –C9 alkylbenzenes (∼291 K) and cyclohexane (298.5 K). It appears that the heat capacity of solution is independent of temperature and increases linearly with carbon number, in the descending order alkanes > alkylcyclohexanes > alkylbenzenes. In the absence of calorimetric data, the relatively limited solubility data for alkenes in water do not allow a reliable determination of the solubility minimum or of the heat capacity of solution. As is the case for water in alkanes, the solubility of water in hydrocarbons at 298 K is relatively insensitive to carbon number (CN), but, unlike that in alkanes and alkylcyclohexanes, the solubility of water in alkenes and alkylbenzenes decreases slightly with increasing CN. Less is known about the heat of solution, but for each family it appears to be independent of temperature and CN, covering the range 24 kJ mol−1 (alkylbenzenes) to 35 kJ mol−1 (alkanes and alkylcyclohexanes). The latter is a better measure of the hydrogen bond energy in hydrocarbon/water systems, since alkanes and alkylcyclohexanes have the least affinity for water. This affinity is measured by the heat of hydrophobic interaction, which makes a negative contribution to the heat of solution, and therefore, as observed, the heat of solution of water in alkenes (33 kJ mol−1 ) and alkylbenzenes is smaller than that in alkanes and alkylcyclohexanes. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Hydrocarbon solubility; Hydrocarbon Henry’s constant; Water solubility; Heat of solution
∗ Tel.: +1-973-540-9229. E-mail address: [email protected] (C. Tsonopoulos).
0378-3812/01/$20.00 © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 5 2 0 - 9
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Fig. 1. P–T diagram of n-decane/water (from [4]).
1. Introduction This paper completes the thermodynamic analysis of the mutual solubilities with water of four families of hydrocarbons for which we have presented new data, especially at high temperatures [2–4]: normal alkanes; alkylcyclohexanes, and alkylbenzenes; and linear 1-alkenes. The binaries of these hydrocarbons with water exhibit type III phase behavior, an example of which is given in Fig. 1 for n-decane/water [4]. The thermodynamic analysis, which began with the simplest family, normal alkanes [1], focuses on temperatures closer to 298 K than to the three-phase critical temperature (the highest temperature at which the hydrocarbon-rich liquid phase can exist, which is 569.3 K for n-decane/ water). The importance of hydrocarbon/water mutual solubilities to the design and operation of process equipment in refineries and petrochemical plants was discussed in [2] and briefly in [1]. In water pollution abatement, in addition to the hydrocarbon solubility in water, it is important to know the volatility of
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the hydrocarbons, which typically is expressed by Henry’s constants. Although Henry’s constants are a function of temperature, the key measure of the hydrocarbon volatility in water pollution abatement is given by their Henry’s constant at 298.15 K. However, the maximum temperature of interest in water pollution abatement can exceed 400 K. On the hydrocarbon-rich side, the maximum temperature of interest is the three-phase critical end point temperature. The high-temperature range was emphasized in our earlier publications [2–4]; here we focus on temperatures generally below 400 K and examine the mutual solubilities, the Henry’s constants for hydrocarbons in water (at 298.15 K), and the heats of solution as a function of carbon number.
2. Mutual solubilities of hydrocarbons and water As noted earlier, the phase behavior of all the binaries examined here is similar to that illustrated in Fig. 1. A point below the three-phase equilibrium curve represents equilibrium between one liquid phase and the vapor, while a point above the line represents equilibrium between the hydrocarbon-rich and water-rich liquid phases. All three phases are at equilibrium at P3 , the three-phase equilibrium pressure. Because the mutual solubilities are only weakly pressure-dependent [2], the mutual solubilities generally are measured at P slightly above P3 (if the vapor phase is of no interest). The two mutual solubilities have a significantly different dependence on carbon number, as well as on temperature; that is, the two heats of solution are drastically different. The solubility of hydrocarbons in water goes through a minimum (where the heat of solution is zero), while that of water in hydrocarbons increases monotonically with increasing temperature. We will examine the solubility and heat of solution separately for hydrocarbons in water and water in hydrocarbons. First we will consider the solubility (and Henry’s constant for hydrocarbons in water) at 298 K, and then the heat of solution.
3. Solubility of hydrocarbons in water 3.1. Solubility at 298 K The solubility of hydrocarbons in water at 298 K drops steeply with increasing CN. As shown in Fig. 2, at a given carbon number, the normal alkanes are the least soluble and the normal alkylbenzenes the most soluble. The solubility of normal alkylbenzenes is known accurately up to C12 [5–7] and the data suggest some curvature in the solubility dependence on CN ln xhc = 4.25097 − 1.59463CN −
14.89081 CN
(1)
Much less is known about the solubility of the other two families of hydrocarbons. For alkylcyclohexanes, experimental data at 298 K are available only for cyclohexane and methylcyclohexane [5]; to augment this limited information, we used extrapolations based on the fit of higher-temperature data for ethylcyclohexane [3] and n-butylcyclohexane [4,8] — which will be discussed in a later section. The resulting dependence of the solubility on CN is judged as approximate ln xhc = −3.74419 − 1.27431CN
(2)
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Fig. 2. Solubility of hydrocarbons in water at 298.15 K. Lines calculated with Eqs. (1)–(3).
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In the case of linear 1-alkenes, the solubility dependence on CN was based on the experimental data for C5 , C6 , and C8 [5]; and the value for C4 calculated with the parameters in Table 4 of [4] ln xhc = −2.24515 − 1.54381CN
(3)
More solubility data at ∼298 K for CN > 6 will be most helpful in establishing reliably the CN dependence of the solubilities of alkylcyclohexanes and 1-alkenes in water. Fig. 2 indicates that, at a given CN, an alkylcyclohexane is more soluble than an 1-alkene in water, and of course both are more soluble than the corresponding alkane. This enhancement in the solubility is due to two different effects. In the case of the 1-alkenes, it is reasonable to assume that most of the enhancement is due to some weak specific interaction between the -bond and the water molecules. The much higher solubility of the alkylbenzenes is likely due to the formation of weak hydrogen bonds between the aromatic -electrons and the water molecules, as suggested by Atwood et al. [9] and others. But there is no such specific interaction that could explain why alkylcyclohexanes are more soluble than the corresponding alkanes. When the solubilities are plotted versus the liquid molar volume of the hydrocarbon, as in Fig. 3, it becomes clear that it is the higher density or lower molar volume (at a given CN) of the alkylcyclohexanes that makes them more soluble. The more compact alkylcyclohexane can fit more easily in a solvent (water) cavity than the less dense alkane. At constant density or molar volume, alkylcyclohexanes are about as soluble as the alkanes, alkenes are more soluble, and the alkylbenzenes are the most soluble. But the enhancement in the solubility of the alkylbenzenes is much less than that in Fig. 2, because part of the apparent enhancement in Fig. 2 is due to the even higher density of the alkylbenzenes. 3.2. Henry’s constants at 298 K To predict the distribution of hydrocarbons between the vapor and the water-rich liquid phase, either because we need to know how much hydrocarbon is in the air or to carry out distillation calculations (as in modeling sour water strippers), we need the volatility of the hydrocarbons in water. This typically is expressed by their Henry’s constant in water. Henry’s constants have been calculated in our previous work up to high temperatures, using rigorous thermodynamic relationships [2–4]. However, at 298 K it is permissible to simplify the calculation and set the Henry’s constant equal to the hydrocarbon’s vapor pressure [28] divided by its solubility in water s yhc P ∼ Phc Hhc,w ∼ = = xhc xhc
(4)
The resulting values, even for benzene, the most soluble of the hydrocarbons examined, are within 2% of the value calculated properly by extrapolating to infinite dilution and introducing fugacity coefficients [2–4]. Our results for the Henry’s constants at 298.15 K are plotted in Fig. 4. The values for normal alkanes (most volatile) and alkylbenzenes (least volatile) are considered reliable (within ∼10%), but those for alkylcyclohexanes and 1-alkenes are uncertain. Comparisons were made with three compilations of Henry’s constants. The most recent one by Shiu and Ma [10] gives recommendations only for the C6 –C10 normal alkylbenzenes, in good agreement with those in Fig. 4, while Yaws et al. [11] recommend values for all four families. For normal alkylbenzenes, [11] is within 10% for C6 –C11 and perhaps 10–15% low for C12 . However, for normal alkanes, [11]
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Fig. 3. Solubility of hydrocarbons in water at 298.15 K vs. the liquid molar volume of the hydrocarbons at 298.15 K.
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Fig. 4. Henry’s constants for hydrocarbons in water at 298.15 K.
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recommends the erratic values plotted in Fig. 4. It should be noted that the older review of Mackay and Shiu [12] agrees with the C6 –C10 alkane values in Fig. 4. The two reviews [11,12] do not shed any light on the recommendation for alkylcyclohexanes: they only report the experimental values for cyclohexane and methylcyclohexane. It should be noted that the corner in the dashed line at C7 is due to the vapor pressure of cyclohexane, which (unlike that of benzene) is much lower than the value that one would obtain by extrapolating the vapor pressures of C7 +alkylcyclohexanes to C6 . Finally, for linear 1-alkenes, comparing only the experimental data, [11] is 25% low for C6 and 35% low for C8 , while [12] calculated the value for 1-butene (not shown in Fig. 4) erroneously as 4150 MPa (versus the correct value of 1300 ± 100 MPa) because it divided the vapor pressure of 1-butene by its solubility at atmospheric pressure (rather than at P3 ). 3.3. Heat of solution Generally, it is accepted that the heat of solution includes two effects: a positive heat of cavitation and a negative heat of hydrophobic interaction between the hydrocarbon and water. These two effects cancel each other at Tmin , the temperature at which the hydrocarbon solubility goes through a minimum, with the heat of cavitation becoming the dominant effect at T > T min . The relationship between solubility and heat of solution is given by h¯ i ∂ ln xi ∼ (5) = ∂T RT2 P h¯ i , the heat of solution, is the difference between the enthalpy of the hydrocarbon i in solution and the enthalpy of the pure hydrocarbon h¯ i = h¯ i (in solution) − hi (pure hc)
(6)
Thus, h¯ i = h¯ Ei , the partial molar excess enthalpy of component i. Gill et al. [13,14] have measured the heat of solution of C6 –C9 normal alkylbenzenes and cyclohexane in water from 288.15 to 308.15 K, using a flow-microcalorimetric technique. Gill’s measurements have established that the heat of solution is a linear function of temperature (see Fig. 3 in [1]); therefore, the heat capacity of solution (or the partial molar excess heat capacity) is constant. Such a linear dependence was also assumed in [1] for the normal alkanes, although Gill et al. [14] only measured the heat of solution at 288.15 and 298.15 K for n-pentane and n-hexane. The values of c¯p from the data of Gill et al. are plotted in Fig. 5. Integration of Eq. (5), where h¯ i is expressed as a linear function of temperature, leads to Eq. (7) B + C ln T T where c¯p = RC and h¯ = −RB + RCT (and R = 8.314 472 J K−1 mol−1 ). ln xhc = A +
(7)
3.3.1. Normal alkylbenzenes The data for normal alkylbenzenes suggest that the heat capacity of solution is a linear function of CN: Normal alkylbenzenes : c¯p = (215 + 50[CN − 6]) J K−1 mol−1
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Fig. 5. Calorimetric data for the heat capacity of solution.
Furthermore, the solubility minimum at ∼291 K for alkylbenzenes (with a slight increase in Tmin with increasing CN) is firmly established by the calorimetric data of Gill et al. [13,14] and is confirmed by solubility data [5–7]; especially those of Bohon and Claussen [15], which give T min = (290 ± 1) K. It was therefore felt, especially at T < 400 K, that the solubility of normal alkylbenzenes should be reasonably well estimated with Eq. (7), with parameter C determined from the heat capacity of solution, B from the heat of solution being 0 at 291 K, and A from the solubility at 298.15 K given by Eq. (1).
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Fig. 6. Solubility of C6 –C12 normal alkylbenzenes in water.
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The results for C6 –C12 normal alkylbenzenes are shown in Fig. 6. No data points are shown for benzene, but the dashed line is the regression of the extensive data [2,5,6,16–19] with Eq. (7) — with adjustable A, B, and C. The agreement with the direct fit of the solubility data (which also led to a T min = 291 K) is excellent up to at least 350 K. For the higher alkylbenzenes, the plotted solubility data also support the thermodynamic calculations. 3.3.2. Normal alkylcyclohexanes Gill’s et al. [14] calorimetric results for cyclohexane in water at first appear to be in significant conflict with the solubility data. Both the heat capacity of solution, 360±30 J K−1 mol−1 , and Tmin , 298.5 K, appear reasonable, as they are between the corresponding values for alkanes and alkylbenzenes. However, our fit of the solubility data gave a c¯p = 261 J K−1 mol−1 and T min = 283.5 K, and thus it appeared that there was a definite conflict between calorimetric and solubility data. It is just as likely, though, that the discrepancy is due to the limited data above 298 K. Gill’s value for cyclohexane was accepted and the CN dependence was estimated by interpolating between the values for alkanes and alkylbenzenes in Fig. 5 Normal alkylcyclohexanes :
c¯p = (360 + 32[CN − 6]) J K−1 mol−1
In addition, it was assumed that T min = 298.5 K for all alkylcyclohexanes. These two calorimetric results were combined with the solubility data at 298.15 K, Eq. (2), to give the parameters in Table 1, which were then used to calculate the solubilities of alkylcyclohexanes in water that are plotted in Fig. 7. As can be seen for C6 and C7 , the calorimetric data (solid lines) are arguably better than the fit of the solubility data (dashed lines). For C8 and C10 the solubility values at 298.15 K were determined
Table 1 Solubility of hydrocarbons in water with Eq. (7) Hydrocarbon
A
B
C
Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene Pentylbenzene Hexylbenzene Cyclohexane Methylcyclohexane Ethylcyclohexane Butylcyclohexane 1-Hexene
−180.368 −221.739 −263.220 −304.679 −346.295 −387.920 −429.463 −301.366 −328.666 −355.422 −409.630 −268.791
7524.83 9274.79 11024.75 12774.71 14524.67 16274.64 18024.60 12924.45 14073.29 15222.13 17519.81 11353.70
25.8585 31.8721 37.8858 43.8994 49.9130 55.9266 61.9402 43.2980 47.1467 50.9954 58.6928 38.4871
Benzenea Cyclohexanea Methylcyclohexanea 1-Hexenea
−192.4824 −219.863 −491.070 −276.423
8053.106 8893.78 22132.10 11833.54
27.67472 31.3744 70.9150 39.5126
a
Values of the parameters determined in the direct fit of the solubility data with Eq. (7).
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Fig. 7. Solubility of C6 –C10 normal alkylcyclohexanes in water.
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by fitting the solubility data, and thus there is closer agreement between calorimetric and solubility data. 3.3.3. Linear 1-alkenes Perhaps surprisingly, less is known about the solubility of alkenes in water than that of alkylcyclohexanes. In the absence of calorimetric data, a guess would have to be made about c¯p and Tmin . A reasonable assumption would be that these values should be between the corresponding ones for alkylcyclohexanes and alkylbenzenes, but that can indirectly be confirmed only for 1-hexene. For 1-octene, the calorimetric approach works reasonably well if the solubility at 298 K is adjusted from 0.43 to about 0.55 mppm, while our data [4] for 1-decene are clearly suspect. For the solubility of 1-alkenes in water, see discussion and Fig. 3 in [4].
4. Solubility of water in hydrocarbons 4.1. Solubility at 298 K It was shown in [1] that the solubility of water in alkanes at 298 K is relatively insensitive to CN. This is also true of the hydrocarbon families examined here, but with significant differences. First, on the basis of limited experimental evidence, it can be concluded that water is less soluble in alkylcyclohexanes than in the corresponding alkanes; and that the water solubility increases with CN, as it does for alkanes. On the other hand, water is significantly more soluble in alkenes and alkylbenzenes, but the water solubility in both decreases with increasing CN. Fig. 8 collects all the data for the solubility of water in the four hydrocarbon families. In the case of alkylbenzenes, Fig. 8 includes data for multibranched alkylbenzenes to emphasize that xw in a given family is little affected by branching. New data sources are those for the water solubility in propene [22,23] and in 1-butene [24]. All other data sources have already been given: 1-alkenes [4]; alkylcyclohexanes [2–5,8]; alkylbenzenes [2–5,8,16,17,20,21]. The dependence of the solubility of water on CN is given by ln xw =
A + B CN C + CN
(8)
The parameters A, B, C for each family are listed in Table 2. Fig. 8 suggests that the solubility of water in all four families of hydrocarbons, which in the CN range of interest decreases in the order Table 2 Solubility of water in hydrocarbons at 298.15 K with Eq. (8)
Alkylbenzenes 1-Alkenes Alkylcyclohexanes Alkanes [1]
A
B
−78.1518 4.6649 −102.4415 −79.6677
−7.9107 −7.3894 −6.7228 −6.6547
C 15.7423 −0.3834 11.9077 9.5470
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Fig. 8. Solubility of water in hydrocarbons at 298.15 K.
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alkylbenzenes > alkenes > alkanes > alkylcyclohexanes, is approaching the same limiting value for CN 10. When water solubility is plotted versus the liquid molar volume of the hydrocarbon, the solubilities in alkanes and alkylcyclohexanes move closer together. At a given CN, water is slightly less soluble in the more dense alkylcyclohexane than in the alkane, because water can less readily dissolve in the more dense solvent. However, density plays a smaller role than in the solubility of hydrocarbons in water (see Figs. 2 and 3), because the solubility of water in hydrocarbons is governed by a different effect, which will be discussed in the following section. 4.2. Heat of solution The relationship between solubility and heat of solution is given by Eqs. (5) and (6). However, here h¯ i is the enthalpy of water in solution and hi is the enthalpy of pure liquid water. Unlike the heat of solution of hydrocarbons in water, the heat of solution of water in hydrocarbons is always positive and nearly is the same for all members of a hydrocarbon family. Nilsson [25] confirmed that c¯p ≈ 0 from measuring the heat of solution of water in benzene at 298.15 and 308.07 K (and in n-decane at 298.15 and 313.14 K). He also confirmed that h¯ is independent of CN, at least for alkanes, from measurements on water dissolved in C7 –C12 normal alkanes (see also [1]). These calorimetric results are supported by solubility data for water in C6 –C12 alkylbenzenes [2–4]. Although there are no calorimetric data for water in alkylcyclohexanes and alkenes (except for the questionable result of Reid et al. for water in cyclohexane [26]), the solubility data support the conclusion that h¯ is largely independent of temperature and CN and has the following approximate values: Alkylcyclohexanes (and alkanes) :
h¯ = 35 ± 1 kJ mol−1
Alkenes : h¯ = 33 ± 1 kJ mol−1 Alkylbenzenes :
h¯ = 24 ± 1 kJ mol−1
These values are close to the energy of a ‘normal’ hydrogen bond, which is in the range 20–40 kJ mol−1 (5–10 kcal mol−1 ). This suggests that the major effect in dissolution of n water molecules is the breaking of n hydrogen bonds, which to a good approximation is independent of both temperature and CN. If we accept that h¯ is constant, then c¯p = 0 and integration of Eq. (5) gives ln xw = A +
B T
(9)
This simple equation fits the data remarkably well to within ∼50 K of the three-phase critical temperature. ¯ Table 3 lists the parameters of Eq. (9) obtained from the calorimetric heat of solution (B = − h/R) and the solubility at 298.15 K (calculated with Eq. (8) and the parameters in Table 2). 4.2.1. Alkylbenzenes In the case of alkylbenzenes, the calorimetric data ( h¯ = 24 kJ mol−1 ) give a good fit of the solubility data up to ∼373 K, but a higher heat of solution is required to fit the solubility data at much higher temperatures.
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Table 3 Solubility of water in hydrocarbons with Eq. (9)a CN
Alkylbenzenesb A
4 5 6 7 8 9 10 11 12
3.90513 3.80334 3.72924 (3.64502)c 3.57573 (3.50609)c 3.44155
Alkylcyclohexanes B
−2886.53 −2886.53 −2886.53 −2886.53 −2886.53 −2886.53 −2886.53
A
6.12043 (6.21193)c 6.32846 (6.32520)c 6.34262
1-Alkenes B
A
B
−4209.53 −4209.53 −4209.53 −4209.53 −4209.53
6.44349 (6.31980)c 6.21794 (6.19970)c 6.19355 (6.13508)c 6.10316
−3968.98 −3968.98 −3968.98 −3968.98 −3968.98 −3968.98 −3968.98
a Parameter B = − h¯ w /R, where h¯ w is assumed to be the same for each family; A = ln xw,298 − B/298.15, where xw,298 is the experimental value. b Best fit of high-temperature solubility data with B determined from h¯ w = (25.6+0.4[CN−6]) kJ mol−1 ; or by introducing a small heat capacity of solution, (8 + 2[CN − 6])J K−1 mol−1 , setting the heat of solution at 298.15 K equal to 24 kJ mol−1 , and using Eq. (7). c Interpolated xw,298 with Eq. (8) and parameters in Table 2.
This is illustrated in Fig. 9, where the solubility of water in n-butylbenzene (open symbols; [5,21]) and 1,3-diethylbenzene (solid symbols; [4,5,8,27]) has been plotted up to the three-phase critical temperature for the 1,3-diethylbenzene system (583 K). The solubility in the normal C10 alkylbenzene has been measured up to 373 K, and in that range a single line, using the calorimetric heat of solution, fits the solubility data very well. The data of Englin et al. in [5] for both isomers suggest that the solubility of water is about 4% more soluble in the C10 isomer, a difference that is less than the uncertainty of the solubility measurements. However, to fit the solubility data at higher temperatures, perhaps to within ∼50 K of three-phase critical temperature, we need a higher heat of solution — for C10 alkylbenzenes, 27.2 kJ mol−1 . (To fit xw up to the three-phase critical temperature, 583 K, it is necessary to use the more complex equation derived in [3]; Eq. (6)). Because this higher heat of solution does not give the best fit of the low-temperature data, it is preferable to make the heat of solution for water in alkylbenzenes a weak function of temperature (and CN) by introducing a small heat capacity of solution (about 4% of the value for alkylbenzenes in water) that increases with CN Alkylbenzenes :
c¯p = (8 + 2[CN − 6]) J K−1 mol−1
If we focus our attention to temperatures closer to 298 K, the “calorimetric” heats of solution are recommended; these values are listed in Table 3. 4.2.2. Alkylcyclohexanes Fig. 10 is a plot of the solubility of water in alkylcyclohexanes up to 448 K: C6 [2,5]; C7 [8]; C8 [3]; C10 [4,8]. This Fig. also includes the lines calculated with Eq. (9) and the parameters in Table 3 for C6 and C10 . In this case, the calorimetric heat of solution, 35 kJ mol−1 , is in good agreement with the solubility
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Fig. 9. Solubility of water in C10 alkylbenzenes.
data up to at least 423 K. Furthermore, the calculations support reasonably well the CN dependence of xw . 4.2.3. 1 Alkenes Fig. 11 collects the data for the solubility of water in C4 –C10 1-alkenes. The single calculated line for 1-hexene (with Eq. (9) and the parameters in Table 3) appears to adequately represent the temperature (and the weak CN) dependence of the water solubility in all alkenes. Thus, using a heat of solution equal to 33 kJ mol−1 works well for water in 1-alkenes up to at least 423 K.
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Fig. 10. Solubility of water in alkylcyclohexanes.
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Fig. 11. Solubility of water in 1-alkenes.
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5. Conclusions and recommendations The thermodynamic analysis of the mutual solubilities of normal alkanes and water [1] has been expanded to include other “type III” (see Fig. 1) hydrocarbon binaries: normal alkylbenzenes, normal alkylcyclohexanes, and linear 1-alkenes. At 298 K, the solubility of hydrocarbons in water drops steeply with CN, while the solubility of water in hydrocarbons is very weakly dependent on CN. There are two contributions to the heat of solution: a positive heat of cavitation and a negative heat of hydrophobic interaction. On the water-rich side, there is a definite minimum in the solubility (Figs. 6 and 7), in the range ∼291 K (alkylbenzenes) to ∼303 K (alkanes), where the two contributions cancel each other, with the heat of cavitation becoming the dominant effect at T > T min . The heat of solution for hydrocarbons in water is a linear function of temperature, thus giving a constant heat capacity of solution (Fig. 5). The solubility of water in hydrocarbons increases monotonically with temperature (Figs. 9–11), because the predominant effect here is the breaking of hydrogen bonds between the water molecules. Thus, the heat of solution is approximately equal to the hydrogen bond energy, which is large, positive, and changes little with temperature ( c¯p ≈ 0) or CN. The best measure of the hydrogen bond energy is provided by the heat of solution of water in alkanes and alkylcyclohexanes, 35 kJ mol−1 . It decreases to 24 kJ mol−1 for water in alkylbenzenes, where the high-temperature solubility data suggest a weak dependence of the heat of solution on temperature and CN. Among hydrocarbons, alkanes and alkylcyclohexanes (more generally, cycloalkanes) have the least affinity for water. The differences in solubility between alkanes and alkylcyclohexanes are largely due to differences in density. Alkylcyclohexanes are more soluble than alkanes in water because they are denser (they have a lower molar volume) and can thus more readily dissolve in the cavities of the solvent (water). However, the water solubility decreases slightly with increasing density, because water can less readily dissolve in a more dense solvent (hydrocarbon). Alkanes and alkylcyclohexanes (and other cycloalkanes) must therefore have the smallest (in absolute sense) heat of hydrophobic interaction. Since this makes a negative contribution to the heat of solution, the heat of solution of water in these two families must be larger than in other hydrocarbons. In the case of the solubility of water in hydrocarbons, the decrease in the heat of solution by ∼2 kJ mol−1 for alkenes and ∼11 kJ mol−1 for alkylbenzenes is a measure of the difference between the respective heats of hydrophobic interaction with water and that for alkanes and alkylcyclohexanes. The much stronger interaction between alkylbenzenes and water is likely due to the formation of weak hydrogen bonds between water and the -electrons of the aromatic ring [9]. A weaker form of that interaction, between water and the -bond of alkenes, may account for the ∼2 kJ mol−1 difference between alkenes and alkanes or alkylcyclohexanes. As noted in [1], it is hoped that the recommendations reached here for the mutual solubilities of hydrocarbons and water, and for the Henry’s constant at 298.15 K for hydrocarbons in water (Fig. 4), will be useful both in engineering application and theoretical investigations. It is also hoped that more experimental investigations will be undertaken, especially for water with C8 + alkylcyclohexanes and 1-alkenes. A relatively clear picture of how mutual solubilities depend on carbon number and temperature should provide the basis for developing molecular models and simulations that will explain at least some of the observations summarized in the previous paragraphs. It may then be possible to develop a reliable predicitive model for the mutual solubilities of water with any hydrocarbon.
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List of symbols A, B, C parameters of Eqs. (7) and (9) CN number of carbon atoms cp heat capacity h enthalpy (heat) h¯ i partial molar enthalpy ¯hEi partial molar excess enthalpy Hhc,w Henry’s constant for hydrocarbon in water; Eq. (4) P pressure s Phc vapor pressure of hydrocarbon R gas constant T absolute temperature Tmin temperature of minimum hydrocarbon solubility x liquid mole fraction Greek letters c¯p heat capacity of solution ¯ h enthalpy (heat) of solution Subscripts hc w 3
property of hydrocarbon property of water three-phase equilibrium property
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
C. Tsonopoulos, Fluid Phase Equilib. 156 (1999) 21–33. C. Tsonopoulos, G.M. Wilson, AIChE J. 29 (1983) 990–999. J.L. Heidman, C. Tsonopoulos, C.J. Brady, G.M. Wilson, AIChE J. 31 (1985) 376–384. I.G. Economou, J.L. Heidman, C. Tsonopoulos, G.M. Wilson, AIChE J. 43 (1997) 535–546. D.G. Shaw (Ed.), Hydrocarbons with Water and Seawater: Part I. Hydrocarbons C5 to C7 Part II. Hydrocarbons C8 to C36 , Vols. 37 and 38, IUPAC Solubility Data Series, Pergamon Press, Oxford, 1989. W.E. May, S.P. Wasik, M.M. Miller, Y.B. Tewari, J.M. Brown-Thomas, R.N. Goldberg, J. Chem. Eng. Data 28 (1983) 197–200. J.W. Owens, S.P. Wasik, H. DeVoe, J. Chem. Eng. Data 31 (1986) 47–51. H.-J. Ng, C.-J. Chen, Mutual Solubility in Water–Hydrocarbon Systems, Gas Processors Association Research Report 150, Tulsa, OK, 1995. J.R. Atwood, F. Hamada, K.D. Robinson, G.W. Orr, R.L. Vincent, Nature 349 (1991) 683–684. W.-Y. Shiu, K.-C. Ma, J. Phys. Chem. Ref. Data 29 (2000) 41–130. C. Yaws, H.-C. Yang, X. Pan, Chem. Eng. (1991) 179–185. D. Mackay, W.-Y. Shiu, J. Phys. Chem. Ref. Data 10 (1981) 1175–1199. S.J. Gill, N.F. Nichols, I. Wadsö, J. Chem. Thermodyn. 7 (1975) 175–183. S.J. Gill, N.F. Nichols, I. Wadsö, J. Chem. Thermodyn. 8 (1976) 445–452. R.L. Bohon, W.F. Claussen, J. Am. Chem. Soc. 73 (1951) 1571–1578. F.E. Anderson, J.M. Prausnitz, Fluid Phase Equilib. 32 (1986) 63–76. H. Chen, J. Wagner, J. Chem. Eng. Data 39 (1994) 470–474.
206 [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
C. Tsonopoulos / Fluid Phase Equilibria 186 (2001) 185–206 R.L. Stevenson, D.S. LaBrancio, T.A. Beaton, M. Thies, Fluid Phase Equilib. 93 (1994) 317–336. K. Chandler, B. Eason, C.L. Liotta, C.A. Eckert, I&EC Res. 37 (1998) 3515–3518. H. Chen, J. Wagner, J. Chem. Eng. Data 39 (1994) 475–479. H. Chen, J. Wagner, J. Chem. Eng. Data 39 (1994) 679–684. R.M. Gentry, V.H. Gunther, Oil Gas J. 53 (1955) 131–132. W.R. Parrish, A.G. Pollin, T.W. Schmidt, in: Proceedings of the 61st Gas Processing Association Annual Convention, 1982, pp. 164–170. T.W. Leland Jr., J.J. McKetta Jr., K.A. Kobe, Ind. Eng. Chem. 47 (1955) 1265–1271. S.-O. Nilsson, J. Chem. Thermodyn. 18 (1986) 877–884. D.S. Reid, M.A.J. Quickenden, F. Franks, Nature 224 (1969) 1293–1294. R.P. Guerrant, M.S. Thesis, The Pennsylvania State University, University Park, 1964. T.E. Daubert, R.L. Rowley, et al., DIPPR® Data Compilation of Pure Compound Properties, 2000, http://dippr.byu.edu.
Thermodynamic analysis of the mutual solubilities of hydrocarbons and water Constantine Tsonopoulos∗ 18 Dorothy Drive, Morristown, NJ 07960, USA Received 6 December 2000; accepted 20 April 2001
Abstract The analysis of mutual solubilities and calorimetric heats of solution carried out for normal alkanes and water close to 298 K [Fluid Phase Equilib. 156 (1999) 21] is extended to normal alkylcyclohexanes, linear 1-alkenes, and normal alkylbenzenes. Extensive solubility data are available for alkylbenzenes, but relatively little is known about alkylcyclohexanes and alkenes in water. All of these hydrocarbons are more soluble than the corresponding alkanes, but are less volatile than the alkanes (their Henry’s constants descending in the order alkanes > alkenes > alkylcyclohexanes > alkylbenzenes). The solubility minimum for hydrocarbons in water is confirmed by calorimetric data for C6 –C9 alkylbenzenes (∼291 K) and cyclohexane (298.5 K). It appears that the heat capacity of solution is independent of temperature and increases linearly with carbon number, in the descending order alkanes > alkylcyclohexanes > alkylbenzenes. In the absence of calorimetric data, the relatively limited solubility data for alkenes in water do not allow a reliable determination of the solubility minimum or of the heat capacity of solution. As is the case for water in alkanes, the solubility of water in hydrocarbons at 298 K is relatively insensitive to carbon number (CN), but, unlike that in alkanes and alkylcyclohexanes, the solubility of water in alkenes and alkylbenzenes decreases slightly with increasing CN. Less is known about the heat of solution, but for each family it appears to be independent of temperature and CN, covering the range 24 kJ mol−1 (alkylbenzenes) to 35 kJ mol−1 (alkanes and alkylcyclohexanes). The latter is a better measure of the hydrogen bond energy in hydrocarbon/water systems, since alkanes and alkylcyclohexanes have the least affinity for water. This affinity is measured by the heat of hydrophobic interaction, which makes a negative contribution to the heat of solution, and therefore, as observed, the heat of solution of water in alkenes (33 kJ mol−1 ) and alkylbenzenes is smaller than that in alkanes and alkylcyclohexanes. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Hydrocarbon solubility; Hydrocarbon Henry’s constant; Water solubility; Heat of solution
∗ Tel.: +1-973-540-9229. E-mail address: [email protected] (C. Tsonopoulos).
0378-3812/01/$20.00 © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 5 2 0 - 9
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Fig. 1. P–T diagram of n-decane/water (from [4]).
1. Introduction This paper completes the thermodynamic analysis of the mutual solubilities with water of four families of hydrocarbons for which we have presented new data, especially at high temperatures [2–4]: normal alkanes; alkylcyclohexanes, and alkylbenzenes; and linear 1-alkenes. The binaries of these hydrocarbons with water exhibit type III phase behavior, an example of which is given in Fig. 1 for n-decane/water [4]. The thermodynamic analysis, which began with the simplest family, normal alkanes [1], focuses on temperatures closer to 298 K than to the three-phase critical temperature (the highest temperature at which the hydrocarbon-rich liquid phase can exist, which is 569.3 K for n-decane/ water). The importance of hydrocarbon/water mutual solubilities to the design and operation of process equipment in refineries and petrochemical plants was discussed in [2] and briefly in [1]. In water pollution abatement, in addition to the hydrocarbon solubility in water, it is important to know the volatility of
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the hydrocarbons, which typically is expressed by Henry’s constants. Although Henry’s constants are a function of temperature, the key measure of the hydrocarbon volatility in water pollution abatement is given by their Henry’s constant at 298.15 K. However, the maximum temperature of interest in water pollution abatement can exceed 400 K. On the hydrocarbon-rich side, the maximum temperature of interest is the three-phase critical end point temperature. The high-temperature range was emphasized in our earlier publications [2–4]; here we focus on temperatures generally below 400 K and examine the mutual solubilities, the Henry’s constants for hydrocarbons in water (at 298.15 K), and the heats of solution as a function of carbon number.
2. Mutual solubilities of hydrocarbons and water As noted earlier, the phase behavior of all the binaries examined here is similar to that illustrated in Fig. 1. A point below the three-phase equilibrium curve represents equilibrium between one liquid phase and the vapor, while a point above the line represents equilibrium between the hydrocarbon-rich and water-rich liquid phases. All three phases are at equilibrium at P3 , the three-phase equilibrium pressure. Because the mutual solubilities are only weakly pressure-dependent [2], the mutual solubilities generally are measured at P slightly above P3 (if the vapor phase is of no interest). The two mutual solubilities have a significantly different dependence on carbon number, as well as on temperature; that is, the two heats of solution are drastically different. The solubility of hydrocarbons in water goes through a minimum (where the heat of solution is zero), while that of water in hydrocarbons increases monotonically with increasing temperature. We will examine the solubility and heat of solution separately for hydrocarbons in water and water in hydrocarbons. First we will consider the solubility (and Henry’s constant for hydrocarbons in water) at 298 K, and then the heat of solution.
3. Solubility of hydrocarbons in water 3.1. Solubility at 298 K The solubility of hydrocarbons in water at 298 K drops steeply with increasing CN. As shown in Fig. 2, at a given carbon number, the normal alkanes are the least soluble and the normal alkylbenzenes the most soluble. The solubility of normal alkylbenzenes is known accurately up to C12 [5–7] and the data suggest some curvature in the solubility dependence on CN ln xhc = 4.25097 − 1.59463CN −
14.89081 CN
(1)
Much less is known about the solubility of the other two families of hydrocarbons. For alkylcyclohexanes, experimental data at 298 K are available only for cyclohexane and methylcyclohexane [5]; to augment this limited information, we used extrapolations based on the fit of higher-temperature data for ethylcyclohexane [3] and n-butylcyclohexane [4,8] — which will be discussed in a later section. The resulting dependence of the solubility on CN is judged as approximate ln xhc = −3.74419 − 1.27431CN
(2)
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Fig. 2. Solubility of hydrocarbons in water at 298.15 K. Lines calculated with Eqs. (1)–(3).
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In the case of linear 1-alkenes, the solubility dependence on CN was based on the experimental data for C5 , C6 , and C8 [5]; and the value for C4 calculated with the parameters in Table 4 of [4] ln xhc = −2.24515 − 1.54381CN
(3)
More solubility data at ∼298 K for CN > 6 will be most helpful in establishing reliably the CN dependence of the solubilities of alkylcyclohexanes and 1-alkenes in water. Fig. 2 indicates that, at a given CN, an alkylcyclohexane is more soluble than an 1-alkene in water, and of course both are more soluble than the corresponding alkane. This enhancement in the solubility is due to two different effects. In the case of the 1-alkenes, it is reasonable to assume that most of the enhancement is due to some weak specific interaction between the -bond and the water molecules. The much higher solubility of the alkylbenzenes is likely due to the formation of weak hydrogen bonds between the aromatic -electrons and the water molecules, as suggested by Atwood et al. [9] and others. But there is no such specific interaction that could explain why alkylcyclohexanes are more soluble than the corresponding alkanes. When the solubilities are plotted versus the liquid molar volume of the hydrocarbon, as in Fig. 3, it becomes clear that it is the higher density or lower molar volume (at a given CN) of the alkylcyclohexanes that makes them more soluble. The more compact alkylcyclohexane can fit more easily in a solvent (water) cavity than the less dense alkane. At constant density or molar volume, alkylcyclohexanes are about as soluble as the alkanes, alkenes are more soluble, and the alkylbenzenes are the most soluble. But the enhancement in the solubility of the alkylbenzenes is much less than that in Fig. 2, because part of the apparent enhancement in Fig. 2 is due to the even higher density of the alkylbenzenes. 3.2. Henry’s constants at 298 K To predict the distribution of hydrocarbons between the vapor and the water-rich liquid phase, either because we need to know how much hydrocarbon is in the air or to carry out distillation calculations (as in modeling sour water strippers), we need the volatility of the hydrocarbons in water. This typically is expressed by their Henry’s constant in water. Henry’s constants have been calculated in our previous work up to high temperatures, using rigorous thermodynamic relationships [2–4]. However, at 298 K it is permissible to simplify the calculation and set the Henry’s constant equal to the hydrocarbon’s vapor pressure [28] divided by its solubility in water s yhc P ∼ Phc Hhc,w ∼ = = xhc xhc
(4)
The resulting values, even for benzene, the most soluble of the hydrocarbons examined, are within 2% of the value calculated properly by extrapolating to infinite dilution and introducing fugacity coefficients [2–4]. Our results for the Henry’s constants at 298.15 K are plotted in Fig. 4. The values for normal alkanes (most volatile) and alkylbenzenes (least volatile) are considered reliable (within ∼10%), but those for alkylcyclohexanes and 1-alkenes are uncertain. Comparisons were made with three compilations of Henry’s constants. The most recent one by Shiu and Ma [10] gives recommendations only for the C6 –C10 normal alkylbenzenes, in good agreement with those in Fig. 4, while Yaws et al. [11] recommend values for all four families. For normal alkylbenzenes, [11] is within 10% for C6 –C11 and perhaps 10–15% low for C12 . However, for normal alkanes, [11]
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Fig. 3. Solubility of hydrocarbons in water at 298.15 K vs. the liquid molar volume of the hydrocarbons at 298.15 K.
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Fig. 4. Henry’s constants for hydrocarbons in water at 298.15 K.
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recommends the erratic values plotted in Fig. 4. It should be noted that the older review of Mackay and Shiu [12] agrees with the C6 –C10 alkane values in Fig. 4. The two reviews [11,12] do not shed any light on the recommendation for alkylcyclohexanes: they only report the experimental values for cyclohexane and methylcyclohexane. It should be noted that the corner in the dashed line at C7 is due to the vapor pressure of cyclohexane, which (unlike that of benzene) is much lower than the value that one would obtain by extrapolating the vapor pressures of C7 +alkylcyclohexanes to C6 . Finally, for linear 1-alkenes, comparing only the experimental data, [11] is 25% low for C6 and 35% low for C8 , while [12] calculated the value for 1-butene (not shown in Fig. 4) erroneously as 4150 MPa (versus the correct value of 1300 ± 100 MPa) because it divided the vapor pressure of 1-butene by its solubility at atmospheric pressure (rather than at P3 ). 3.3. Heat of solution Generally, it is accepted that the heat of solution includes two effects: a positive heat of cavitation and a negative heat of hydrophobic interaction between the hydrocarbon and water. These two effects cancel each other at Tmin , the temperature at which the hydrocarbon solubility goes through a minimum, with the heat of cavitation becoming the dominant effect at T > T min . The relationship between solubility and heat of solution is given by h¯ i ∂ ln xi ∼ (5) = ∂T RT2 P h¯ i , the heat of solution, is the difference between the enthalpy of the hydrocarbon i in solution and the enthalpy of the pure hydrocarbon h¯ i = h¯ i (in solution) − hi (pure hc)
(6)
Thus, h¯ i = h¯ Ei , the partial molar excess enthalpy of component i. Gill et al. [13,14] have measured the heat of solution of C6 –C9 normal alkylbenzenes and cyclohexane in water from 288.15 to 308.15 K, using a flow-microcalorimetric technique. Gill’s measurements have established that the heat of solution is a linear function of temperature (see Fig. 3 in [1]); therefore, the heat capacity of solution (or the partial molar excess heat capacity) is constant. Such a linear dependence was also assumed in [1] for the normal alkanes, although Gill et al. [14] only measured the heat of solution at 288.15 and 298.15 K for n-pentane and n-hexane. The values of c¯p from the data of Gill et al. are plotted in Fig. 5. Integration of Eq. (5), where h¯ i is expressed as a linear function of temperature, leads to Eq. (7) B + C ln T T where c¯p = RC and h¯ = −RB + RCT (and R = 8.314 472 J K−1 mol−1 ). ln xhc = A +
(7)
3.3.1. Normal alkylbenzenes The data for normal alkylbenzenes suggest that the heat capacity of solution is a linear function of CN: Normal alkylbenzenes : c¯p = (215 + 50[CN − 6]) J K−1 mol−1
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Fig. 5. Calorimetric data for the heat capacity of solution.
Furthermore, the solubility minimum at ∼291 K for alkylbenzenes (with a slight increase in Tmin with increasing CN) is firmly established by the calorimetric data of Gill et al. [13,14] and is confirmed by solubility data [5–7]; especially those of Bohon and Claussen [15], which give T min = (290 ± 1) K. It was therefore felt, especially at T < 400 K, that the solubility of normal alkylbenzenes should be reasonably well estimated with Eq. (7), with parameter C determined from the heat capacity of solution, B from the heat of solution being 0 at 291 K, and A from the solubility at 298.15 K given by Eq. (1).
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Fig. 6. Solubility of C6 –C12 normal alkylbenzenes in water.
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The results for C6 –C12 normal alkylbenzenes are shown in Fig. 6. No data points are shown for benzene, but the dashed line is the regression of the extensive data [2,5,6,16–19] with Eq. (7) — with adjustable A, B, and C. The agreement with the direct fit of the solubility data (which also led to a T min = 291 K) is excellent up to at least 350 K. For the higher alkylbenzenes, the plotted solubility data also support the thermodynamic calculations. 3.3.2. Normal alkylcyclohexanes Gill’s et al. [14] calorimetric results for cyclohexane in water at first appear to be in significant conflict with the solubility data. Both the heat capacity of solution, 360±30 J K−1 mol−1 , and Tmin , 298.5 K, appear reasonable, as they are between the corresponding values for alkanes and alkylbenzenes. However, our fit of the solubility data gave a c¯p = 261 J K−1 mol−1 and T min = 283.5 K, and thus it appeared that there was a definite conflict between calorimetric and solubility data. It is just as likely, though, that the discrepancy is due to the limited data above 298 K. Gill’s value for cyclohexane was accepted and the CN dependence was estimated by interpolating between the values for alkanes and alkylbenzenes in Fig. 5 Normal alkylcyclohexanes :
c¯p = (360 + 32[CN − 6]) J K−1 mol−1
In addition, it was assumed that T min = 298.5 K for all alkylcyclohexanes. These two calorimetric results were combined with the solubility data at 298.15 K, Eq. (2), to give the parameters in Table 1, which were then used to calculate the solubilities of alkylcyclohexanes in water that are plotted in Fig. 7. As can be seen for C6 and C7 , the calorimetric data (solid lines) are arguably better than the fit of the solubility data (dashed lines). For C8 and C10 the solubility values at 298.15 K were determined
Table 1 Solubility of hydrocarbons in water with Eq. (7) Hydrocarbon
A
B
C
Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene Pentylbenzene Hexylbenzene Cyclohexane Methylcyclohexane Ethylcyclohexane Butylcyclohexane 1-Hexene
−180.368 −221.739 −263.220 −304.679 −346.295 −387.920 −429.463 −301.366 −328.666 −355.422 −409.630 −268.791
7524.83 9274.79 11024.75 12774.71 14524.67 16274.64 18024.60 12924.45 14073.29 15222.13 17519.81 11353.70
25.8585 31.8721 37.8858 43.8994 49.9130 55.9266 61.9402 43.2980 47.1467 50.9954 58.6928 38.4871
Benzenea Cyclohexanea Methylcyclohexanea 1-Hexenea
−192.4824 −219.863 −491.070 −276.423
8053.106 8893.78 22132.10 11833.54
27.67472 31.3744 70.9150 39.5126
a
Values of the parameters determined in the direct fit of the solubility data with Eq. (7).
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Fig. 7. Solubility of C6 –C10 normal alkylcyclohexanes in water.
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197
by fitting the solubility data, and thus there is closer agreement between calorimetric and solubility data. 3.3.3. Linear 1-alkenes Perhaps surprisingly, less is known about the solubility of alkenes in water than that of alkylcyclohexanes. In the absence of calorimetric data, a guess would have to be made about c¯p and Tmin . A reasonable assumption would be that these values should be between the corresponding ones for alkylcyclohexanes and alkylbenzenes, but that can indirectly be confirmed only for 1-hexene. For 1-octene, the calorimetric approach works reasonably well if the solubility at 298 K is adjusted from 0.43 to about 0.55 mppm, while our data [4] for 1-decene are clearly suspect. For the solubility of 1-alkenes in water, see discussion and Fig. 3 in [4].
4. Solubility of water in hydrocarbons 4.1. Solubility at 298 K It was shown in [1] that the solubility of water in alkanes at 298 K is relatively insensitive to CN. This is also true of the hydrocarbon families examined here, but with significant differences. First, on the basis of limited experimental evidence, it can be concluded that water is less soluble in alkylcyclohexanes than in the corresponding alkanes; and that the water solubility increases with CN, as it does for alkanes. On the other hand, water is significantly more soluble in alkenes and alkylbenzenes, but the water solubility in both decreases with increasing CN. Fig. 8 collects all the data for the solubility of water in the four hydrocarbon families. In the case of alkylbenzenes, Fig. 8 includes data for multibranched alkylbenzenes to emphasize that xw in a given family is little affected by branching. New data sources are those for the water solubility in propene [22,23] and in 1-butene [24]. All other data sources have already been given: 1-alkenes [4]; alkylcyclohexanes [2–5,8]; alkylbenzenes [2–5,8,16,17,20,21]. The dependence of the solubility of water on CN is given by ln xw =
A + B CN C + CN
(8)
The parameters A, B, C for each family are listed in Table 2. Fig. 8 suggests that the solubility of water in all four families of hydrocarbons, which in the CN range of interest decreases in the order Table 2 Solubility of water in hydrocarbons at 298.15 K with Eq. (8)
Alkylbenzenes 1-Alkenes Alkylcyclohexanes Alkanes [1]
A
B
−78.1518 4.6649 −102.4415 −79.6677
−7.9107 −7.3894 −6.7228 −6.6547
C 15.7423 −0.3834 11.9077 9.5470
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Fig. 8. Solubility of water in hydrocarbons at 298.15 K.
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alkylbenzenes > alkenes > alkanes > alkylcyclohexanes, is approaching the same limiting value for CN 10. When water solubility is plotted versus the liquid molar volume of the hydrocarbon, the solubilities in alkanes and alkylcyclohexanes move closer together. At a given CN, water is slightly less soluble in the more dense alkylcyclohexane than in the alkane, because water can less readily dissolve in the more dense solvent. However, density plays a smaller role than in the solubility of hydrocarbons in water (see Figs. 2 and 3), because the solubility of water in hydrocarbons is governed by a different effect, which will be discussed in the following section. 4.2. Heat of solution The relationship between solubility and heat of solution is given by Eqs. (5) and (6). However, here h¯ i is the enthalpy of water in solution and hi is the enthalpy of pure liquid water. Unlike the heat of solution of hydrocarbons in water, the heat of solution of water in hydrocarbons is always positive and nearly is the same for all members of a hydrocarbon family. Nilsson [25] confirmed that c¯p ≈ 0 from measuring the heat of solution of water in benzene at 298.15 and 308.07 K (and in n-decane at 298.15 and 313.14 K). He also confirmed that h¯ is independent of CN, at least for alkanes, from measurements on water dissolved in C7 –C12 normal alkanes (see also [1]). These calorimetric results are supported by solubility data for water in C6 –C12 alkylbenzenes [2–4]. Although there are no calorimetric data for water in alkylcyclohexanes and alkenes (except for the questionable result of Reid et al. for water in cyclohexane [26]), the solubility data support the conclusion that h¯ is largely independent of temperature and CN and has the following approximate values: Alkylcyclohexanes (and alkanes) :
h¯ = 35 ± 1 kJ mol−1
Alkenes : h¯ = 33 ± 1 kJ mol−1 Alkylbenzenes :
h¯ = 24 ± 1 kJ mol−1
These values are close to the energy of a ‘normal’ hydrogen bond, which is in the range 20–40 kJ mol−1 (5–10 kcal mol−1 ). This suggests that the major effect in dissolution of n water molecules is the breaking of n hydrogen bonds, which to a good approximation is independent of both temperature and CN. If we accept that h¯ is constant, then c¯p = 0 and integration of Eq. (5) gives ln xw = A +
B T
(9)
This simple equation fits the data remarkably well to within ∼50 K of the three-phase critical temperature. ¯ Table 3 lists the parameters of Eq. (9) obtained from the calorimetric heat of solution (B = − h/R) and the solubility at 298.15 K (calculated with Eq. (8) and the parameters in Table 2). 4.2.1. Alkylbenzenes In the case of alkylbenzenes, the calorimetric data ( h¯ = 24 kJ mol−1 ) give a good fit of the solubility data up to ∼373 K, but a higher heat of solution is required to fit the solubility data at much higher temperatures.
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Table 3 Solubility of water in hydrocarbons with Eq. (9)a CN
Alkylbenzenesb A
4 5 6 7 8 9 10 11 12
3.90513 3.80334 3.72924 (3.64502)c 3.57573 (3.50609)c 3.44155
Alkylcyclohexanes B
−2886.53 −2886.53 −2886.53 −2886.53 −2886.53 −2886.53 −2886.53
A
6.12043 (6.21193)c 6.32846 (6.32520)c 6.34262
1-Alkenes B
A
B
−4209.53 −4209.53 −4209.53 −4209.53 −4209.53
6.44349 (6.31980)c 6.21794 (6.19970)c 6.19355 (6.13508)c 6.10316
−3968.98 −3968.98 −3968.98 −3968.98 −3968.98 −3968.98 −3968.98
a Parameter B = − h¯ w /R, where h¯ w is assumed to be the same for each family; A = ln xw,298 − B/298.15, where xw,298 is the experimental value. b Best fit of high-temperature solubility data with B determined from h¯ w = (25.6+0.4[CN−6]) kJ mol−1 ; or by introducing a small heat capacity of solution, (8 + 2[CN − 6])J K−1 mol−1 , setting the heat of solution at 298.15 K equal to 24 kJ mol−1 , and using Eq. (7). c Interpolated xw,298 with Eq. (8) and parameters in Table 2.
This is illustrated in Fig. 9, where the solubility of water in n-butylbenzene (open symbols; [5,21]) and 1,3-diethylbenzene (solid symbols; [4,5,8,27]) has been plotted up to the three-phase critical temperature for the 1,3-diethylbenzene system (583 K). The solubility in the normal C10 alkylbenzene has been measured up to 373 K, and in that range a single line, using the calorimetric heat of solution, fits the solubility data very well. The data of Englin et al. in [5] for both isomers suggest that the solubility of water is about 4% more soluble in the C10 isomer, a difference that is less than the uncertainty of the solubility measurements. However, to fit the solubility data at higher temperatures, perhaps to within ∼50 K of three-phase critical temperature, we need a higher heat of solution — for C10 alkylbenzenes, 27.2 kJ mol−1 . (To fit xw up to the three-phase critical temperature, 583 K, it is necessary to use the more complex equation derived in [3]; Eq. (6)). Because this higher heat of solution does not give the best fit of the low-temperature data, it is preferable to make the heat of solution for water in alkylbenzenes a weak function of temperature (and CN) by introducing a small heat capacity of solution (about 4% of the value for alkylbenzenes in water) that increases with CN Alkylbenzenes :
c¯p = (8 + 2[CN − 6]) J K−1 mol−1
If we focus our attention to temperatures closer to 298 K, the “calorimetric” heats of solution are recommended; these values are listed in Table 3. 4.2.2. Alkylcyclohexanes Fig. 10 is a plot of the solubility of water in alkylcyclohexanes up to 448 K: C6 [2,5]; C7 [8]; C8 [3]; C10 [4,8]. This Fig. also includes the lines calculated with Eq. (9) and the parameters in Table 3 for C6 and C10 . In this case, the calorimetric heat of solution, 35 kJ mol−1 , is in good agreement with the solubility
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Fig. 9. Solubility of water in C10 alkylbenzenes.
data up to at least 423 K. Furthermore, the calculations support reasonably well the CN dependence of xw . 4.2.3. 1 Alkenes Fig. 11 collects the data for the solubility of water in C4 –C10 1-alkenes. The single calculated line for 1-hexene (with Eq. (9) and the parameters in Table 3) appears to adequately represent the temperature (and the weak CN) dependence of the water solubility in all alkenes. Thus, using a heat of solution equal to 33 kJ mol−1 works well for water in 1-alkenes up to at least 423 K.
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Fig. 10. Solubility of water in alkylcyclohexanes.
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Fig. 11. Solubility of water in 1-alkenes.
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5. Conclusions and recommendations The thermodynamic analysis of the mutual solubilities of normal alkanes and water [1] has been expanded to include other “type III” (see Fig. 1) hydrocarbon binaries: normal alkylbenzenes, normal alkylcyclohexanes, and linear 1-alkenes. At 298 K, the solubility of hydrocarbons in water drops steeply with CN, while the solubility of water in hydrocarbons is very weakly dependent on CN. There are two contributions to the heat of solution: a positive heat of cavitation and a negative heat of hydrophobic interaction. On the water-rich side, there is a definite minimum in the solubility (Figs. 6 and 7), in the range ∼291 K (alkylbenzenes) to ∼303 K (alkanes), where the two contributions cancel each other, with the heat of cavitation becoming the dominant effect at T > T min . The heat of solution for hydrocarbons in water is a linear function of temperature, thus giving a constant heat capacity of solution (Fig. 5). The solubility of water in hydrocarbons increases monotonically with temperature (Figs. 9–11), because the predominant effect here is the breaking of hydrogen bonds between the water molecules. Thus, the heat of solution is approximately equal to the hydrogen bond energy, which is large, positive, and changes little with temperature ( c¯p ≈ 0) or CN. The best measure of the hydrogen bond energy is provided by the heat of solution of water in alkanes and alkylcyclohexanes, 35 kJ mol−1 . It decreases to 24 kJ mol−1 for water in alkylbenzenes, where the high-temperature solubility data suggest a weak dependence of the heat of solution on temperature and CN. Among hydrocarbons, alkanes and alkylcyclohexanes (more generally, cycloalkanes) have the least affinity for water. The differences in solubility between alkanes and alkylcyclohexanes are largely due to differences in density. Alkylcyclohexanes are more soluble than alkanes in water because they are denser (they have a lower molar volume) and can thus more readily dissolve in the cavities of the solvent (water). However, the water solubility decreases slightly with increasing density, because water can less readily dissolve in a more dense solvent (hydrocarbon). Alkanes and alkylcyclohexanes (and other cycloalkanes) must therefore have the smallest (in absolute sense) heat of hydrophobic interaction. Since this makes a negative contribution to the heat of solution, the heat of solution of water in these two families must be larger than in other hydrocarbons. In the case of the solubility of water in hydrocarbons, the decrease in the heat of solution by ∼2 kJ mol−1 for alkenes and ∼11 kJ mol−1 for alkylbenzenes is a measure of the difference between the respective heats of hydrophobic interaction with water and that for alkanes and alkylcyclohexanes. The much stronger interaction between alkylbenzenes and water is likely due to the formation of weak hydrogen bonds between water and the -electrons of the aromatic ring [9]. A weaker form of that interaction, between water and the -bond of alkenes, may account for the ∼2 kJ mol−1 difference between alkenes and alkanes or alkylcyclohexanes. As noted in [1], it is hoped that the recommendations reached here for the mutual solubilities of hydrocarbons and water, and for the Henry’s constant at 298.15 K for hydrocarbons in water (Fig. 4), will be useful both in engineering application and theoretical investigations. It is also hoped that more experimental investigations will be undertaken, especially for water with C8 + alkylcyclohexanes and 1-alkenes. A relatively clear picture of how mutual solubilities depend on carbon number and temperature should provide the basis for developing molecular models and simulations that will explain at least some of the observations summarized in the previous paragraphs. It may then be possible to develop a reliable predicitive model for the mutual solubilities of water with any hydrocarbon.
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List of symbols A, B, C parameters of Eqs. (7) and (9) CN number of carbon atoms cp heat capacity h enthalpy (heat) h¯ i partial molar enthalpy ¯hEi partial molar excess enthalpy Hhc,w Henry’s constant for hydrocarbon in water; Eq. (4) P pressure s Phc vapor pressure of hydrocarbon R gas constant T absolute temperature Tmin temperature of minimum hydrocarbon solubility x liquid mole fraction Greek letters c¯p heat capacity of solution ¯ h enthalpy (heat) of solution Subscripts hc w 3
property of hydrocarbon property of water three-phase equilibrium property
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