J. Chem. SOC., Faraday Trans. I, 1986,82, 2435-2457 Thermodynamic Properties of Binary Alcohol-Hydrocarbon Systems Alf Pettersson, Paul Saris and Jar1 B. Rosenholm" Department of Physical Chemistry, Abo Akademi, SF-20500 Abo 50, Finland Head-space gas chromatography has been used to determine the partial vapour pressures of the components of seven binary alcohol-hydrocarbon systems at 298.15 K. The chain lengths of the alcohols were chosen to record the differences between a long-chain alcohol (decan- 1-01) and intermediate homologues (pentan- 1-01 and butan- 1-01). The hydrocarbon solvents chosen (n-octane, cyclohexane and benzene) offer the possibility to extract the contribution of ring closure and aromaticity. The accuracy of the activities were controlled applying a commonly used thermodynamical consistency test.Theexcess Gibbs freeenergies werecombined with previously determined excess enthalpies to obtain the molar excess entropy of solution and the partial molar entropies of the components. The results suggest that the mixtures can be grouped into three concentration regions with significantly different properties. First, in the dilute alcohol solutions the hydrogen- bonding equilibria determine the properties of the system. The influence of the apolar interaction also contributes significantly to the energetic state of the system. Secondly, in the mid-concentration range the hydrogen bonding seems to be of only secondary importance, while the apolar interaction is gaining enhanced importance. In this range the benzene-hydroxy group interaction seems to deviate drastically from the normal behaviour of alcohol-hydrocarbon systems.Thirdly, in dilute hydrocarbon systems the interaction seems to be purely apolar in nature, erasing the previous difference between the aromatic and saturated hydrocarbon systems. ~~~ -~ ~ -~~ The importance of the hydrogen-bonding equilibria to the properties of a multitude of living and technical systems has for a long time been acknowledged. Alcohols may be considered as favourable models for hydrogen-bonded systems. Many of the properties recorded suggest a division into short-chain alcohols (methanol to propanol) with a large association constant1 and to long-chain alcohols, which on steric grounds show a reduced association tendency. Butanol and pentanol are considered intermediate in character.In many investigations it is fortuitous to compare the influence of a solute or the solvent on the hydrogen-bond network with the effect produced when the temperature is increased. It is possible to convert the shift induced by the solute to a temperature effect on the pure The hydrophobicity of the alcohols offers another common and useful way to study the extent of the hydrogen bond association: when diluting alcohols in inert hydrocarbons it may be assumed that the disruption of hydrogen bonds dominates the properties of the Recently a few authors have indicated that hydrogen bonding makes an important contribution to the thermodynamic properties only in the most dilute region.5* For most solutions the structural compatibility of the alcohol hydrocarbon residue with the solvent molecules is more i m p ~ r t a n t .~ ? The present investigation reports the Gibbs free energy and the entropy as well as the partial molar enthalpies of seven alcohol-hydrocarbon systems. The alcohols were chosen to record the difference between a long-chain alcohol and the intermediate homologues. The hydrocarbon solvents offer the possibility to extract the contribution of aromaticity to the parameters considered. The influence of breaking the cyclohexane 24352436 Thermodynamics of Alcohol-Hydrocarbon Systems ring is also given. The systems investigated should thus provide a picture of the relative importance of the polar and apolar interactions for the state of the systems. The entropy should be successful in recording the structural state of the system.Experimental Chemicals The alcohols used were: butan-1-01 (Merck AG, p.a. grade), pentan-1-01 (Merck AG, p.a. grade), and decan-1-01 (Merck AG, pro synthesis). The hydrocarbons were: benzene (Merck AG, p.a. grade), cyclohexane (Merck AG, p.a. grade), and n-octane (Fluka AG, puriss.). All the alcohols were distilled before use and molecular sieve pellets (Merck AG, 0.4 nm) were added to the mid-fraction used in order to remove residual traces of water. For the same reasons metallic sodium was added to the hydrocarbon liquids. The final water content, as determined by a Karl-Fisher titrator (Metrohm 652 KF-Coulometer), was 0.02% by weight for butan-1-01, 0.01 1 % for pentan-1-01, 0.01 % for decan-1-01, 0.0012% for benzene, 0.001 % for cyclohexane and 0.001 ;< for n-octane.Instrumentation The vapour pressures of the components were analysed with a Hewlett-Packard 5730A gas chromatograph equipped with an f.i.d. detector and an HP 7672A automatic sampler unit. The sampler was controlled with an HP 19400A sampler/event control module and the results were recorded using an HP 3390A integrator. The temperature (298.15 0.10 K) of the closed sampler box was measured at the vial to be analysed. In order to minimize the influence of possible temperature gradients on the gas-liquid equilibrium in the vials, the time between two successive samplings was programmed to be considerably longer than the retention time of the components. Care was also taken to ‘wash’ the syringe between the samplings so that no residual traces from previous injections could be detected.When running the binary solutions containing butanol, a 0.7 m x 1 /8 in? stainless steel column packed with 10% Carbowax 20 M on 80-100 mesh Gas-Chrom Q was used. The oven temperature was 368 K. The other solutions were analysed with Porapak Q, 150-200 mesh packed in a stainless steel column of the same dimensions. In these cases the oven temperature was kept at 503 K, except for the decanol-octane samples, for which a temperature of 513 K was chosen. The injection port was kept at 523 K and the f.i.d. detector at 573 K. Ultra-pure helium was used as a carrier gas with a flow rate of 30 cm3 min-l and a pressure of 3 bar. The pressures of hydrogen and air were optimized to give the largest peak areas and the least tailings possible.The pressures used were 0.85 bar and 1.8 bar, respectively. Measurements The activities of the components were determined as the relative integrated gas chromatogram peak areas of the sample to the reference. Although this procedure neglects some contribution from non-ideality it has been found that the non-ideality of the sample vapour and the pure liquid vapour tend to ~ a n c e l . ~ To ensure maximal accuracy several reference samples of the pure liquids were run in the beginning, the middle and at the end of a sample series. The experimental points were smoothed in order to make the activities approach the Raoult’s slope. When analysing the decanol systems it was found that the vapour pressure of decanol was too low to get reliable activities. Therefore the Gibbs-Duhem law was applied to calculate the activity factor of decanol t 1 in = 2.54 cm.A .Pettersson, P . Saris and J. B. Rosenholm 2437 from the activity factors of the hydrocarbons by integration. In estimating the activity factor for the most dilute solution we utilized the standard method of using a temporary lower limit.1° Originally 14 cm3 of the samples were mixed gravimetrically in order to reduce weighing errors although only 0.5 cm3 was used in the experiments. The gas volume taken from the head space of the 2 cm3 vials was 0.1 cm3. The consistency of the rational activity coefficients calculated were checked using the integral test in the way suggested by Gmehling and 0nken.ll The test involves a comparison of the areas of the plot of In [f(alcohol)/f(hydrocarbon)] us.x(alcoho1) above ( A ) and below ( B ) the abscissa using the following equation The following deviations were found : butanol-benzene (2.3 % ), butanokyclohexane (9.9 % ), pentanol-benzene (1.2:4 ), pentanokyclohexane (2.8 % ), decanol-benzene (0.6% ), decanol-cyclohexane (1 .O% ), and decanol-octane (0.7% ). The test suggests that the activities measured for all the systems may be considered thermodynamically consistent. Some care should, however, be taken when using the activities of the butanol-cyclohexane system owing to the somewhat too high deviation percentage level observed. There are very few publications on the activities of the components of binary alcohol-hydrocarbon systems.Gmehling and Onken have tabulated the vapour pressures of the butanol-benzene, butanol-cyclohexane and decanol-cyclohexane systems. l1 When recalculated to the excess Gibbs free energy of solution our results agree with theirs within 20%. However, since their number of data points was small and the data failed the consistency test, we consider our results to be of higher accuracy. Recently Sjoblom and Henriksson have published activities of pentanol mixed with benzene at 293 K using a similar head-space gas chromatography technique.12 Since they provided no information of the activity of the hydrocarbon component we could not compare the thermodynamic consistency of their activities. Probably the most reliable activities obtained with an alternative technique have been reported by French and Stokes on the butanol- cyclohexane system at 298 K.139 l4 It was found that both our partial molar excess Gibbs free energy of the butanol and our enthalpy function [H~/x(butanol)x(cyclohexane)] agree very well with their results.Since our thermodynamic consistency test indicated some uncertainty for this particular system, the comparison suggests that some doubt may be laid on our activities of cyclohexane for this system. Results Gibbs Free Energy In reporting the results we first compare the properties of the alcohols when mixed with benzene (fig. 1) and cyclohexane (fig. 2), respectively. This provides an opportunity to study the influence of lengthening the chain on the property investigated, keeping the solvent and the functional group the same.Finally we illustrate the effect imposed by the change of solvent, keeping the chain length of the alcohol (decanol) the same (fig. 3). In fig. 1 (a)-3 (a) the molar excess Gibbs free energies are plotted against mole fraction of the alcohols. The figures also include partial molar excess Gibbs free energies (the chemical potentials) for the alcohols (b) and the hydrocarbons (c), respectively, plotted against the mole fraction of the alcohols. As described in the previous section, the partial molar free energies are obtained directly from the measurements. This option reduces considerably the error which would be introduced if they were derived from the molar excess Gibbs free energy of the system! In our case the latter function has been calculated by summation of the contributions of the components.2438 Thermodynamics of Alcohol-Hydrocarbon Systems 200 0 0 0.2 0. 4 0. 6 0. 8 1. 0 x (alcohol) 10000 L 1000 - 800 - 3 - I 2 600 - W E u c, 1 400 - 4 I - 0 6000 --. v c- u w 4000 2000 0 0 0.2 0.4 0.6 0.8 1.0 x(alcoho1) Fig. l ( a ) and (b). For description see opposite.A . Pettersson, P. Saris and J . B. Rosenholrn 2439 3000 1000 0 0 0.2 0.4 0.6 0.0 1.0 x(alcoho1) Fig. 1. (a) The molar excess Gibbs free energies for (a) butanol-, (A) pentanol- and (a) decanol-benzene systems at 298.15 K us. the mole fraction of alcohol and the partial molar excess Gibbs free energies of the alcohols (b) and benzene (c). For all the solutions the molar excess Gibbs free energy is positive with the maximum shifted slightly towards solutions poor in alcohol [x(alcohol) z 0.41. The maximum values vary between the limits of ca.1.2 and 0.78 kJ mol-1 found for the benzene systems. The most important feature of the GZ curves [fig. 1 (a)-3(a)] is that the spacing between them changes at both extremes of concentration. When the alcohols are diluted with the hydrocarbons the partial molar excess Gibbs free energies (the excess chemical potentials) remain close to zero in the x(alcoho1) = 0.8- 1.0 range. For the solutions poorer in alcohol a successive deviation towards positive energies is registered. For the same solvent the deviation is largest for butanol, while octane produces the largest effect when mixed with decanol. The partial molar excess free energies of the hydrocarbons increase monotonically over the whole concentration range, but show a saturation tendency for the dilute solutions.The magnitude of the differences found follow the trend given for the excess Gibbs free energies of the alcohols. The limiting values of the plots are given in table 1. Enthalpy In fig. 4 we have collected the partial molar enthalpies for all the systems discussed. They have been calculated from the molar excess enthalpies published in another context6 by stepwise derivation and smoothed when possible to averages of three consecutive points. The equations used were where A = alcohol and HC = hydrocarbon.2440 Thermodynamics of Alcohol-Hydrocarbon Systems 0 D.2 0. 4 0. 6 0.8 1.0 x (alcohol) 10000 8000 6000 w u 4000 2000 0 0 0.2 0.4 0.6 0.8 1.0 x(alcoho1) Fig.2(a) and (b). For description see opposite.A . Pettersson, P. Saris and J . B. Rosenholm 244 1 1000 0 0 0.2 0.4 0.6 0.8 1.0 x( alcohol) Fig. 2. (a) The molar excess Gibbs free energies for (0) butanol-, (A) pentanol- and (0) decanokyclohexane systems at 298.15 K us. the mole fraction of alcohol and the partial molar excess Gibbs free energies of the alcohols (b) and cyclohexane (c). The influence of the alcohol chain length on the enthalpic state of the components is very small [fig. 4(a) and (b)]. The largest effects are recorded when varying the hydrocarbon liquids mixed with decanol [fig. 4(c)]. Accordingly, these systems also produce the highest maximal molar excess enthalpy of solution of ca. 1.30 kJ mol-l (benzene system), 0.66 kJ mol-1 (cyclohexane system) and 0.50 kJ mol-1 (octane system).6 The corresponding values for the pentanol and butanol systems are only ca.100 (cyclohexane) - 200 (benzene) J mol-l lower. Note, however, that the sequence is opposite as compared with the molar excess Gibbs free energies! The partial molar excess enthalpies are largest for decanol mixed with benzene, while the partial enthalpies observed for the saturated hydrocarbon mixtures are much the same [fig. 4 (c)]. For the latter systems a significant contribution from decanol is obtained only for solutions with x(decano1) = 0-0.1. For the benzene mixtures the corresponding concentration range extends to x(decano1) = 0.3 [fig. 4(a)]. The partial molar excess enthalpy of the hydrocarbons increases smoothly with alcohol concentration. There is, however, a significant exothermal shift in the partial molar excess enthalpy of both benzene and cyclohexane when the mole fraction of decanol exceeds 0.9.For octane this effect is not observed. Since the enthalpies reported by FrenchI4 did not exhibit any exothermal parts in the dilute region a relatively high uncertainty is suggested for the limiting hydrocarbon values given in table 1. Entropy All the molar entropies are expressed as ‘entropy function’ calculated by applying the Gibbs-Helmholtz equation expressed in the form (4) The negative sign was used for the entropy function in order to obtain the energetically favourable and unfavourable contributions to the state of the system directed in the same -TSE = GR-H” 81 F A R 12442 Thermodynamics of Alcohol-Hydrocarbon Systems 1000 800 4 - I 2 600 W E u 400 200 0 0 0.2 0.4 0.6 0.8 1.0 x( decanol) 10000 8000 - 2 6000 13 *.u W W 4000 2000 0 0 0.2 0.4 0.6 0.8 1.0 x( decanol) Fig.3(a) and (6). For description see opposite.3000 - I - E" 2 2000 n w ._ v u 1000 0 A . Pettersson, P. Saris and J . B. Rosenholm r 2443 0 0.2 0.4 0-6 0.8 1.0 x(decano1) Fig. 3. (a) The molar excess Gibbs free energies for (*) octane-, (0) cyclohexane- and (A) benzenedecanol systems at 298.15 K us. the mole fraction of decanol and the partial molar excess Gibbs free energies of decanol (6) and the hydrocarbons (c). Table 1. The limiting excess Gibbs free energies, excess enthalpies and excess entropies of alcohols in hydrocarbons and hydro- carbons in alcohols, respectively, at 298.15 K" mixture GE H E b - TSE /kJ mol-l /kJ mol-l /kJ mol-l alcohols butanol in benzene 10 pentanol in benzene 8 decanol in benzene 5 butanol in cyclohexane 12 pentanol in cyclohexane I1 decanol in cyclohexane 9 decanol in octane 8 hydrocarbons benzene in butanol 4.0 benzene in pentanol 3 .2 benzene in decanol 2.2 cyclohexane in butanol 4.6 2 Q 15 16 17 20 21 23 23 0.3 0.3 0.3 0.8 - 5 -8 - 12 -8 - 10 - 14 - 15 3.7 2.9 1.9 3.8 ciclohexane in decanol 2.8 0.8 2.0 octane in decanol 3.1 1.1 2.0 a The accuracy of the limiting alcohol values are + 2 kJ mole'. The accuracy of the limiting hydrocarbon values are k0.5 kJ mol-l. CJ ref. (6). 81-22444 Thermodynamics of Alcohol-Hydrocarbon Systems 0 0 0 0 (I) d 0 0 0 * 4 0 0 0 2 0 0 0 v 0 0 0 *A .Pettersson, P . Saris and J. B. Rosenhoh 2445 18000 16000 d I - 8 14000 b n -.- .- @ 12000 I0000 8000 6000 4000 2000 0 0.2 0. 4 0. 6 0. 8 1.0 x( decanol) Fig. 4. The partial molar enthalpies of the components of the alcohol-benzene systems (a), the alcohol*yclohexane systems (b) and the decanol-hydrocarbon systems (c) at 298.15 K us. the mole fraction of alcohol. The symbols refer to those in fig. 1 (a), 2 (b) and 3 ( c ) respectively. way. A negative deviation thus indicates an increase in entropy which contributes favourably to the Gibbs free energy (negative AG). In order to make the comparison of the enthalpy and entropy contributions possible we included the appropriate temperature (298.15 K) in the entropy function.Fig. 5-7 present the molar excess entropy functions plotted against the mole fraction of the alcohols. It is very interesting to note that the systems are characterized by both negative (positive entropy) and positive (negative entropy) parts. The molar excess entropy function is mainly positive for the saturated hydrocarbon systems and mainly negative for the benzene solutions. The extension of the chain length of the alcohol deepens the minimum. The maximum value of ca. 0.55 kJ mol-1 is then found for the butanol-cyclohexane system, while the lowest value of -0.61 kJ mol-1 is found for the decanol-benzene system. As found for the excess Gibbs free energies, the spacing between the - TS: curves changes with the concentration. The partial molar excess entropy functions of the alcohols do not deviate much from2446 d I 3 i$ 2 h \ WE I Thermodynamics of Alcohol-Hydrocarbon Systems 0 -100 -200 -300 -400 -500 0 0.2 0.4 0.6 0.8 1.0 x( alcohol) -2000 -8000 -10000 0 0.2 0.4 0.6 0.8 1.0 x(alcoho1) Fig. 5(a) and (b). For description see opposite.A . Pettersson, P. Saris and J . B. Rosenholm 2447 2000 0 - 1000 0 0.2 0.4 0. 6 0.8 1.0 x(alcoho1) Fig. 5. (a) The molar excess entropy (expressed as - 7‘s:) of the (0) butanol-, (A) pentanol- and (m) decanol-benzene system at 298.15 K us. the mole fraction of alcohol and the partial molar excess entropies of the alcohols (b) and benzene (c). zero for alcohol mole fractions > 0.5. Below this limit the entropy function of the mid-chain alcohols departs to positive values.In the presence of benzene the changes are small and may reverse the function to the negative side [fig. 5(b)]. Conversely, the positive ‘hump’ gets narrower when benzene is exchanged for the alkanes [fig. 6(b) and 7 (b)]. In the dilute alcohol range [especially below x(alcoho1) z 0.11 the entropy function of all the alcohols falls rapidly towards very low values (high entropy). The entropy function representing the alkanes is smooth and mainly positive. The dependence on the chain length of the alcohols is largest in the x(alcoho1) = 0.6-0.9 range. For the benzene systems the negative loop is large, while the molar excess entropy is negative (positive entropy function) only in a narrow concentration range,7 x(alcoho1) > 0.7. The limiting values are given in table 1.Discussion Although the Gibbs free energy provides the ‘final’ information about the state of the system, this function is the sum of essential interactions which compensate each other, making it a relatively insensitive parameter. Therefore higher-order derivatives in e.g. temperature and pressure are engaged when investigating in detail the interactions of thermodynamical irnportance.l5* l6 At the first-derivation level we find the entropy and volume, respectively. As has been pointed out the enthalpy may be considered as a practically accessible function needed to calculate the entropy, but which does not relate to the Gibbs free energy in a truly straightforward way.16 When comparing functions of the first-derivative level one may thence expect the entropic and the volumetric properties in the first hand to be mutually comparable.Viewing the relationship between the parameters in this way, the enthalpy can be understood as the part of the total entropy sacrificed to maintain the maximal disorder of the system and which thence is compensated in the Gibbs free energy functi0n.l’2448 0 -2000 -4000 4 F h 5 -6ooo v w -8000 Thermodynamics of Alcohol-Hydrocarbon Systems I 0 0.2 0.4 0.6 0.8 1.0 x (alcohol) -10000 -12000 0 0.2 0.4 0.6 0.8 1.0 x(alcoho1) Fig. 6(a) and (b). For description see opposite.A . Pettersson, P. Saris and J . B. Rosenholm 2449 0 0.2 0.4 0.6 0.8 1.0 x(alcoho1) Fig. 6. The molar excess entropy (expressed as - TS;) of the (0) butanol-, (A) pentanol- and (0) decanokyclohexane systems at 298.15 K us.the mole fraction of alcohol and the partial molar excess entropies of the alcohols (b) and cyclohexane (c). Gibbs Free Energy The general qualitative information obtained from the concentration dependence of the Gibbs free energies is that the cumulative interactions active in the solutions are energetically unfavourable (positive GE values). The interactions which tend to oppose the favourable state obtainable by a complete mixing [Gideal = RTX x(i) In x(i) = nega- tive] may, in the first hand, be considered as being due to preferential interaction of each component with molecules of their own kind. However, the increment of the chemical potential of both the alcohol and the hydrocarbon is negative when mixed into a solution. In agreement with the findings of Benson and coworkers5? the dominant contribution from the hydrogen bonding equilibria is confined to mole fractions of alcohol < 0.2.In this concentration range the consumption of energy for the disruption of the hydrogen bonds of the alcohol associates (fig. 4) is also reflected in a very high limiting Gibbs free energy. Diluted in the same solvent we find the largest limiting Gibbs free energies and the smallest enthalpies (and entropies) for the medium-chain alcohols (table 1). These homologues seem thence to resist most successfully the dissolving effect on the associates upon dilution. This is in accordance with the findings of Treszczanowicz and Benson, who found negative deviations in the molar excess volume (enhanced hydrocarbon chain-solvent interaction) when the homologous series of the normal alcohols were a s ~ e n d e d .~ ~ ~ ~ - ~ ~ Comparing the solvents we note that benzene seems to provide an energetically more favourable environment (lowest GE) than cyclohexane or octane (table 1). When mixed in large amounts, benzene interacts readily with the alcohols, while octane seems not to interact. Indeed, somewhat surprisingly, long-chain alkanes seem to avoid mixing with equal or longer-chain alcohols. This may be the cause for the slightly enhanced association observed for the alcohols in octane.6 The situation changes significantly when one of the components is present in excess over the other. Over the mid-concentration range the Gibbs free energy of the components of the cyclohexane systems resembles those of the benzene systems, but approaches the octane systems at2450 Thermodynamics of Alcohol-Hydrocarbon Systems 300 200 100 0 + - I 0 h E -100 2 -200 \ W E I -300 -400 -50 -600 0 0.2 0.4 0.6 0.8 1.0 x(decano1) 0 -2000 4 -4000 C v -6000 c, 1 w ? -8000 - 10000 - 12000 0 0.2 0.4 0. 6 0.8 1.0 x(decano1) Fig. 7(a) and (b). For description see opposite.A . Pettersson, P . Saris and J . B. Rosenholm 245 1 150.0 irl 0 -500 z I -1000 -1500 1 ~~~ ~ 0 0.2 0.4 0.6 0.8 1.0 x( decanol) Fig. 7. The molar excess entropy (expressed as - TS:) of the (*) octane-, (0) cyclohexane- and (A) benzenedecanol systems at 298.15 K us. the mole fraction of decanol and the partial molar entropy of decanol (b) and the hydrocarbons (c). both extremes of the concentration scale.An important contribution may thus be expected from the structural compatibility on the dilution p r o ~ e s s . ~ ~ * En t h a1 p y If the partial molar enthalpy of the alcohols is considered a sensitive indicator of the hydrogen bonding equilibria the enthalpies recorded suggest that the self association is confined to the mole fraction range below 0.1 (0.2 for the benzene systems). If associates with a larger number of hydrogen bonds would form at higher concentrations of alcohols4 one would expect a more dramatic influence on the partial molar enthalpy of the alcohols in that range. Since a smooth decay is found our partial molar enthalpies do not support this view. Alternatively two or more opposing contributions erase the effect expected.One may suggest, on the basis of the steeper limiting slopes of the decanol systems, that the association is most intense in the long-chain alkane solutions (decanol-octane system).6 In agreement with the above conclusions the associatiqn seem to be considerably retarded in the benzene system (smaller initial slopes) owing to an enhanced intermolecular interaction made possible by the n-electrons. This is also evident from the limiting values (table 1) being close to the expected enthalpy for a hydrogen bond in the alkane systems, but some 20% lower for the benzene systems. Comparing the alcohols diluted in the same solvent we note that only a small difference is found, the partial molar enthalpy being largest for decanol. Exceeding the intense association range the hydrocarbon interactions seem to dominate the enthalpic properties of the system.When comparing our results with the maximal molar excess enthalpies found for binary alkane-alkane systems21 we find that the introduction of the hydroxy group, as a rule, contributes only a fraction of the total endothermal interaction energy.6 The contribution increases in the order benzene < cyclohexane < octane in accordance with the finding of an intensified alcohol association in the latter systems. According to Patterson and coworkers7 a negative contribution to2452 Thermodynamics of Alcohol-Hydrocarbon Systems the enthalpy, entropy and volume is obtained when the segments of the chain are capable of an intensified correlation of molecular order (CMO). The highest enthalpies are recorded for benzene, which indicates a strong benzene-hydroxy interaction, while decanol mixed with octane (strong CMO internally among the octane chains) gives the lowest overall, but endothermic partial molar excess enthalpies.The limiting partial molar enthalpy of the hydrocarbons is independent of the alcohol, which indicates the interaction being of similar nature. The limiting partial molar enthalpy increases in the order benzene < cyclohexane < octane. However, the order is reversed when entering the alcohol-rich concentration range [fig. 4(c)]. There thus seems to be some kind of rapid interruption of the benzene-hydroxy interaction when x(alcoho1) > 0.9. Probably all the alcohol molecules are occupied in alcohol association, giving rise to an interaction with the chains surrounding the alcohol aggregates. Entropy As discussed above, entropy should be especially suitable as an indicator for the structural state of the system.The main shortcoming of this parameter lies in the accumulating error due to the calculation procedure. For the present purpose it suffices to consider the entropy simply as a measure of the order created in the system (positive deviation of - TS”) owing to the intramolecular interaction between each of the components. The picture emerged fits very well with the conclusions drawn in the preceding sections. Consequently the benzene system exerts the highest degree of intermolecular interaction (negative entropy function). The roughly equal spacing in the mid-concentration range suggests that the origin of the entropy increase is not linearly dependent on the chain length or that some other factors also contribute to the structure of the system.The first explanation available is the above mentioned ability of benzene to interact with polar molecules such as alcohols. In the solutions there seems to be a fraction of unassociated alcohol molecules in the benzene mixtures owing to the retardation of the association process. The surprisingly similar functional dependence as compared with volume suggests a comparison can be made with the volumetric behaviour. Since a negative entropy function (positive entropy) corresponds to a positive volume, it should be connected with the chemical (disruption of hydrogen bonds) or the physical (non-specific interactions) contributions or both.5 In accordance with the conclusions drawn on the basis of both the limiting Gibbs free energy and the limiting enthalpy values, the increase in the degree of disorder created upon dilution in hydrocarbon liquids is largest for the long-chain alcohols [fig.7(b), table 11. Mixed in the same solvent the association may be considered retarded for the long-chain alcohols [fig. 5(b) and 6(b)] owing to the increased molecular compatibility of the chain with the solvent molecules. In the case of self-association enforced by the solvent [decanol-octane system, fig. 7(b)] or non-compatibility of the alcohol associates with the solvent [medium-chain alcohol-hydrocarbon, fig. 5(b) and 6(b)] the poor mixing results in a ‘relaxation effect’ shown as a maximum in the - TSE(alcohol) function.In the high-concentration range [x(alcohol) > 0.81 all the hydrocarbons seem to be involved in some new kind of interaction with the alcohol associates, producing a positive partial molar entropy function for the hydrocarbons. If the intermolecular interaction between alcohol and benzene is taken as a basis, the effect observed for x(alcoho1) > 0.9 is probably due to a lack of alcohol molecules engaged in benzene-hydroxy group interaction. Instead the alcohol molecules seem to be consumed by the energetically more favourable hydrogen-bond association. The limiting partial molar entropies are for all hydrocarbons roughly the same when dissolved in the same alcohol (table 1). Once the option of polar interaction is excluded the interaction seems to be purely apolar in nature.Then long-chain alcohol complexes mix most readily with the hydrocarbon solutes, leading to the highest degree of intermolecular mixing (least-negative limiting hydrocarbonA . Pettersson, P. Saris and J. B. Rosenholm 2453 entropies). This conclusion is in accordance with the largest limiting enthalpies and the lowest limiting Gibbs free energies found for the hydrocarbon-decanol systems [fig. 5 (c) and 6(c)]. However, as mentioned before, decanol mixes least readily with octane (fig. 7). The insensitivity of the limiting partial molar entropies to the nature of the hydrocarbon solute may be explained if assumed that the size of the apolar alcohol aggregates determines the magnitude of the interaction.Again a parallel may be found with the volumetric behaviour of hydrocarbon mixtures, for which a positive molar excess volume has been found when a low-molecular-weight alkane is dissolved in a high- molecular-weight alkane.22 Conclusions It has been shown that head-space gas chromatography may be used to obtain accurate and thermodynamically consistent activities of volatile components of alcohol- hydrocarbon mixtures. The results suggest that the mixtures can be grouped into three concentration regions with significantly different properties : first, in dilute alcohol solutions the hydrogen-bonding equilibria determine the properties of the systems. However, the influence of the apolar interaction also influenced alcohol association.Of special importance is the retarding effect of aromaticity on association equilibria. Secondly, in the mid-concentration range the hydrogen bonding seem to be of only secondary importance for the state of the system. Again the 7r-electron interaction plays a central role. The lengthening of the alcohol chain makes intermolecular mixing more probable, but the long-chain alkanes (octane) reject intermolecular mixing. Thirdly, a new situation is created when the hydrocarbons are diluted in the alcohols. In nearly neat alcohol solutions, all the free monomers seem to be consumed by alcohol association and a purely apolar interaction seems to contribute to the solution properties. The functional dependence of the entropy is, in many respects, similar to that which is found for volumetry.It is therefore suggested that these functions are on the first hand mutually comparable, while the enthalpy may be understood merely corresponding to the part of the total entropy sacrificed to counteract the thermal fluctuations to maintain the maximal disorder of the system. Although the Gibbs free energy provides the information of the equilibrium of the system, this function is frequently a relatively insensitive parameter owing to the compensation of essential interactions. This work has been supported by the Finnish Research Council for Natural Sciences. References 1 W. E. Achree Jr, Thermodynamic Properties of' Non-electrolyte Solutions (Academic Press, Orlando, 2 J. Paquette and C. Jolicoeur, J. Solution Chem., 1977, 6, 403.3 Y. DeGrandpre, J. B. Rosenholm, L. L. Lemelin and C . Jolicoeur, Solution Behavior ofSurfuctunts, ed. 4 E. Tucker and E. D. Becker, J . Phys. Chem., 1973, 77, 1783. 5 A. J. Treszczanowicz, 0. Kiyohara and G. C. Benson, J . Chem. Thermodyn., 1981, 13. 253. 6 P. Saris, J. B. Rosenholm, E. Sjoblom and U. Henriksson, J . Phys. Chem., 1986, 90, 660. 7 S. N. Bhattacharyya, M. Costas, D. Patterson and H-V. Tra, Fluid Phase Equilibria, 1985, 20, 27. 8 K. N. Marsh and C . Burfitt, J . Chem. Thermodyn., 1975, 7, 955. 9 D. M. Mohliner, L. M. Bowman, S. J. Freeland and H. Nakadomari, J . Electrochem. SOC., 1973, 120, 1658. 10 I. M. Klotz and R. M. Rosenberg, Chemical Thermodynamics: Basic Theory and Methods (W. A. Benjamin, Menlo Park, California, 3rd edn, 1972), chap.20, p. 342. 1 1 J. Gmehling and U. Onken, Vapor-Liquid Equilibrium Data Collection, (a) Aqueous-Organic Systems, vol. 1, part 1, chap. 2.3, p. XXII, (b) Organic Hydroxy Compounds, Afcohols and Phenols, Part 2b (Dechema, Frankfurt am Main, 1978). 12 E. Sjoblom and U. Henriksson, Surfuctants in Solutions, ed. K. L. Mittal and B. Lindman (Plenum Press, New York, 1984), vol. 3, p. 1867. Florida, 1984), chap. 8, p. 150. K. L. Mittal and E. J. Fendler (Plenum Press, New York, 1982), vol. 1, p. 431.2454 Thermodynamics of Alcohol-Hydrocarbon Systems 13 H. T. French and R. H. Stokes, J. Phys. Chem., 1981,85, 3347. 14 H. T. French, J. Solution Chem., 1983, 12, 869. 15 C . Jolicoeur, Methods of Biochemical Analysis, ed. D. Glick (J. Wiley, New York, 1981), vol. 27, p.171. 16 J. B. Rosenholm, Fresenius' Z. Anal. Chem., 1985, 321, 731. 17 R. Lumry, Bioenergetics and Thermodynamics: Model Systems, ed. A. Braibanti (D. l e d e l , Dordrecht, 18 A. J. Treszczanowicz and G. C. Benson, J . Chem. Thermodyn., 1977,9, 1189. 19 A. J. Treszczanowicz and G. C. Benson, J. Chem. Thermodyn., 1978, 10, 967. 20 A. J. Treszczanowicz and G. C. Benson, J. Chem. Thermodyn., 1980, 12, 173. 21 J. J. Christensen, R. W. Hanks and R. M. Izatt, Handbook of Heats of Mixing (J. Wiley, New York, 22 R. S. Hutchings and A. van Hook, J . Chem. Thermodyn., 1985, 17, 523. 1980), p. 405-423. 1982). Paper 5/1632; Received 20th September, 1985 Appendix Tables of Thermodynamic Data for the Alcohol-Hydrocarbon Systems Table A 1. C,H,OH-C,H, GZ TSZ G~(C,H,OH) TSE(C,H,OH) GE(C6H6) /J mol-' /J mol-I x(C,H,OH) /J mol-1 /J mol-' x(C6H6) /J mol-' 23.3 38.1 77.9 154.3 233.5 342.2 466.7 591 .O 800.5 917.3 1101.8 1187.3 1120.6 970.7 835.2 639.9 515.9 355.6 268.0 115.2 10.3 22.7 51.6 117.0 117.4 140.8 169.0 160.6 91.5 69.8 - 9.3 - 99.2 - 89.4 - 129.8 - 146.4 - 189.6 - 171.1 - 142.2 - 131.4 - 80.3 0.002 26 0.004 25 0.009 53 0.020 44 0.031 07 0.050 48 0.075 96 0.099 91 0.153 31 0.196 18 0.298 32 0.423 71 0.503 58 0.631 07 0.701 59 0.805 91 0.853 91 0.908 79 0.933 98 0.974 31 9 934 8 173 7 091 6 378 6 167 5 187 4 375 4 038 3 312 2 808 1 997 1 307 893 443 279 122 68 33 23 13 4 945 6 146 6 508 5 461 2 632 1372 344 -118 - 752 - 808 - 687 - 507 ~ 393 - 233 - 199 - 122 - 68 - 33 + 23 - 13 0.997 74 0.995 75 0.990 47 0.979 56 0.968 93 0.949 52 0.924 04 0.900 09 0.846 69 0.803 82 0.701 68 0.576 29 0.496 42 0.368 93 0.298 41 0.194 09 0.146 09 0.091 21 0.066 02 0.025 69 1 3 10 24 43 84 145 208 345 455 72 1 1098 1351 1871 2 142 2 787 3 129 3 564 3 732 3 983 T s 4 c 6 H 6 ) /J mol-' -1 - 10 5 36 75 154 191 244 284 278 20 1 218 48 - 22 - 467 - 769 - 1224 - 1662 - 2623 - 3A .Pettersson, P . Saris and J . B. Rosenholm Table A 2. C,H,OH-C,H12 2455 G2 TSg /J mol-I 27.7 53.1 92.9 147.9 230.0 343.1 505.6 564.6 803.0 882.9 982.2 1063.8 1098.1 1070.7 973.4 841.8 738.8 447.1 236.2 115.6 ~~ /J mol-1 ~- ~ 11.3 61.0 88.9 71.5 38.6 -51.9 - 149.3 - 147.9 -265.6 -321.5 -401.9 - 449.9 - 506.3 - 522.6 - 499.1 - 464.1 -416.3 - 282.2 - 167.7 - 90.4 x(C,H,OH) ~ - _ _ 0.002 15 0.004 60 0.009 33 0.0 16 28 0.028 45 0.049 09 0.081 75 0.098 43 0.167 75 0.203 53 0.254 87 0.325 70 0.407 81 0.503 27 0.611 89 0.719 15 0.773 66 0.890 97 0.948 07 0.976 17 ~~ G~(C,H,OH) TS~C,H,OH) E(C6H12) /J mol-l /J molP x(C,H1,) /J rno1-l - 11 043 9 606 8 409 7 672 6 706 5 578 4 543 4 183 3 052 2 647 2 165 1 628 1156 738 388 168 91 37 18 10 7 116 6 553 4 710 - 232 -2 386 -2 938 -2 543 -2 423 -1 932 -1 767 -1 525 - 1068 - 736 - 468 - 228 - 88 -31 - 37 - 18 - 10 0.997 85 0.995 40 0.990 67 0.983 72 0.971 55 0.950 91 0.918 25 0.901 57 0.832 25 0.796 47 0.745 13 0.674 30 0.592 19 0.496 73 0.388 11 0.280 85 0.226 34 0.I09 03 0.051 93 0.023 83 4 8 14 23 40 72 146 169 349 43 1 577 79 1 1057 1407 1895 2564 2953 3792 4206 4422 TSE(C6H12) /J mol-' -4 31 45 76 109 97 63 100 70 48 - 17 - 151 - 347 - 577 - 925 - 1424 - 1733 - 2280 - 2886 - 3362 G g /J mol-I TSg /J molP 20.4 37.4 73.4 129.1 179.4 276.9 375.0 469.5 63 1.4 754.3 905.2 963.0 938.5 845.1 743.4 598.1 463.9 312.7 164.7 88.4 20.0 34.1 69.2 121.7 166.4 227.3 203.3 249.8 300.5 3 14.0 290.6 196.9 136.4 98.8 - 40.4 - 119.4 - 88.0 - 56.2 - 38.4 - 32.9 Table A 3.C,H,,OH-C,H, G~(c,H,,oH) TS~C,H,,OH) x(C5Hl,0H) /J mol-l /J mol-l x(C,H,) 0.002 65 7 612 7667 0.997 35 0.004 89 7 196 7443 0.995 11 0.010 56 6 504 7 015 0.989 44 0.020 23 5 866 6053 0.979 77 0.029 97 5 395 4204 0.97003 0.050 63 4 729 2230 0.949 37 0.070 56 4 063 856 0.92494 0.100 24 3 586 493 0.89976 0.149 59 2 890 269 0.85041 0.200 22 2 441 18 0.799 78 0.299 90 1705 -145 0.700 10 0.400 04 1117 -197 0.59996 0.499 97 714 -194 0.50003 0.598 75 405 -115 0.401 25 0.700 46 218 - 138 0.299 54 0.800 56 113 -113 0.19944 0.848 45 57 -57 0.151 55 0.897 81 21 -21 0.102 19 0.949 69 9 -9 0.050 31 0.973 33 3 -3 0.026 67 GE(C6H6) /J mol-l TSF<C6H6) /J mol-' 1 2 4 10 18 39 75 122 234 33 I 562 860 1162 1500 1972 2544 2738 2873 3101 3210 - 1 -2 -4 0 41 120 174 222 305 388 477 459 467 419 187 - 144 - 258 - 363 - 591 - 11302456 Thermodynamics of Alcohol-Hydrocarbon Systems Table A 4. C,H,,0H-C6H,, GlE TSE G~(c,H,,oH) TSE(C,H,,OH) GE(C6H1'2) TSE(C6Hl'2) /J mol-1 /J mol-' x(C,H,,OH) /J mol-l /J mol-I x(C,H,,) /J mol-I /J mol-I 34.3 75.7 105.3 195.0 253.3 412.7 501.2 582.1 7 16.0 841.6 942.4 1022.3 1003.4 896.9 767.9 624.1 465.2 353.1 195.2 80.2 21.4 35.6 60.2 43.0 15.5 - 109.2 - 135.6 - 148.6 -216.0 - 298.3 - 342.4 -414.3 -428.7 - 388.2 -351.4 - 356.1 -268.5 - 206.4 - 126.3 - 60.5 0.003 03 0.007 11 0,010 46 0.021 23 0.030 23 0.059 85 0.078 58 0.101 96 0.148 57 0.198 90 0.306 30 0.399 94 0.501 95 0.603 74 0.699 53 0.794 52 0.859 54 0.898 10 0.946 21 0.981 09 10 379 8 892 8 138 7 126 6 327 4 968 4 532 3 948 3 187 2 672 1589 I 150 745 41 7 205 84 26 10 4 7 8 020 3 987 2 021 - 1 446 -2 567 -2 568 -2 412 -2 092 - 1 747 -1 592 - 989 - 782 - 505 - 257 - 125 - 84 - 26 - 10 -4 -7 0.996 97 0.992 89 0.989 54 0.978 77 0.969 77 0.940 15 0.921 42 0.898 04 0.851 43 0.801 10 0.693 70 0.600 06 0.498 05 0.396 26 0.300 47 0.205 48 0.140 46 0.101 90 0.053 79 0.018 91 3 12 20 44 63 122 157 199 284 386 659 937 1263 1627 2078 2710 3149 3369 3559 3877 -3 7 39 75 96 47 58 72 51 23 - 59 - 169 - 351 - 587 - 878 - 1406 - 1749 - 1929 - 2279 - 2837 Table A 5.C,,H,,OH-C,H, 15.8 20.5 41.4 91.4 130.0 204.2 302.2 373.0 468.1 582.0 712.6 763.8 755.8 708.0 603.5 445.3 292.3 230.4 105.7 68.7 40.4 56.3 117.9 247.4 273.8 364.8 437.6 512.5 592.5 615.2 562.9 526.0 435.3 337.7 264.5 176.4 106.5 71.0 2.1 - 13.0 0.003 42 0.004 45 0.009 09 0.020 61 0.029 97 0.049 30 0.078 22 0.102 01 0.153 98 0.198 66 0.302 84 0.393 96 0.505 81 0.586 63 0.679 09 0.777 94 0.859 53 0.890 77 0.950 95 0.968 34 4571 4551 4459 4223 4037 3675 3 197 2864 2273 1916 1330 910 547 369 160 41 17 13 2 1 11 908 11 608 10 900 8 896 6 202 4 204 2 962 2 295 1406 883 229 25 - 107 - 193 - 80 -41 - 17 - 13 -2 -1 0.996 58 0.995 55 0.990 91 0.979 39 0.970 03 0.950 70 0.921 78 0.897 99 0.846 02 0.801 34 0.697 16 0.606 04 0.494 19 0.413 37 0.320 91 0.222 06 0.140 47 0.109 23 0.049 05 0.031 66 1 1 1 4 9 24 56 90 174 25 1 444 668 968 1188 1541 1858 1972 2000 2123 2136 -1 4 19 65 90 165 223 309 409 548 707 85 1 99 1 1091 994 94 1 867 759 76 - 376A . Pettersson, P. Saris and J . B. Rosenholm 2457 Table A 6. Cl,H,,OH-C,H,, 18.4 39.5 69.0 135.6 174.9 260.7 329.3 423.4 545.3 640.9 764.8 820.4 819.6 759.1 640.2 498.6 367.7 295.5 136.5 52.1 27.5 51.9 113.3 171.2 137.0 96.9 82.3 48.3 8.7 -42.3 - 83.4 - 119.9 - 154.1 -191.1 - 199.3 -212.1 - 143.5 - 120.9 - 77.4 -35.5 0.002 19 0.004 97 0.009 52 0.021 76 0.030 14 0.051 18 0.070 81 0.102 04 0.152 22 0.203 46 0.303 50 0.402 76 0.497 43 0.601 69 0.703 31 0.789 32 0.854 09 0.886 27 0.950 70 0.981 45 8057 7013 6103 4964 452 1 3 809 3379 290 1 2361 1944 1320 958 713 429 176 83 42 39 10 1 12 942 11 386 8 896 2 395 38 - 529 -715 - 741 -681 - 568 - 360 - 334 - 345 - 253 - 106 - 83 - 42 - 39 - 10 -1 0.997 81 0.995 03 0.990 48 0.978 24 0.969 86 0.948 82 0.929 19 0.897 96 0.847 78 0.796 54 0.696 50 0.597 24 0.502 57 0.398 31 0.296 69 0.210 68 0.145 91 0.113 73 0.049 30 0.018 55 1 4 11 28 39 69 96 141 219 307 522 727 924 1257 1739 2055 2 269 2 294 2 562 281 1 - 1 -4 28 121 140 130 143 138 132 92 37 24 35 - 97 -419 - 695 - 733 - 758 - 1362 - 1883 Table A 7. C1,H,,OH-C,Hl8 TSE /J mol-' 27.2 50.3 83.1 149.9 21 1.6 328.3 446.9 541.2 684.1 807.4 93 1.2 953.4 902.2 799.2 651.7 470.2 365.8 251.6 131.4 78.5 36.9 59.7 76.7 152.7 135.1 75.4 - 33.3 - 113.2 - 150.9 - 256.5 - 330.9 - 422.4 -446.5 - 378.6 - 293.2 -282.3 -219.8 -151.8 -81.3 - 49.2 0.003 68 0.006 92 0.011 84 0.022 70 0.033 64 0.056 86 0.084 74 0.112 56 0.163 51 0.221 85 0.327 99 0.430 46 0.534 14 0.630 69 0.726 90 0.819 35 0.864 81 0.910 92 0.955 69 0.974 52 7282 6890 6479 5889 545 1 4715 3993 3336 2764 2150 1378 865 529 31 1 147 96 49 24 7 3 10 157 7 589 4 520 2 270 548 -1 595 -2 353 -2 056 -1 754 -1 350 -818 - 465 - 269 - 101 -7 - 96 - 49 - 24 -7 -3 0.996 32 0.993 08 0.988 16 0.977 30 0.966 36 0.943 14 0.915 26 0.887 44 0.836 49 0.778 15 0.672 01 0.569 54 0.465 86 0.369 31 0.273 10 0.180 65 0.135 19 0.089 08 0.044 31 0.025 48 1 2 6 16 29 63 118 186 277 424 712 1019 1329 1631 1 994 2 165 2 389 2 571 2 814 2 945 - 1 7 23 93 120 176 181 133 162 55 - 92 - 389 - 649 - 851 - 1054 - 1125 - 1309 - 1451 - 1684 - 1795