J . Chem. SOC., Faraday Trans. 1, 1984,80, 153-181 Thermodynamics of Solution of Homologous Series of Solutes in Water BY MICHAEL H. ABRAHAM Department of Chemistry, University of Surrey, Guildford, Surrey GU2 5XH Received 9th May, 1983 Values of AGF (g --+ aq) and AGF (liq -+ aq) at 298 K are documented for 14 homologous series of gaseous and liquid solutes, and corresponding enthalpies of solution listed for 7 homologous series. It is shown by a thermodynamic argument that only parameters for the process g -+ aq can be used to assess solute-water interactions and that the standard state of pure liquid solute includes a differsnt solute-solute interaction term for each solute standard state. For most of the homologous series, parameters for the process g --+ aq are linear in the number of carbon atoms in the solute; from such linear equations, methylene and group contributions are obtained.It is shown that the methylene increments to AG?(g + aq) and to AHF(g -+ aq) are not constant but vary from one homologous series to another. In a few homologous series the methylene increment is not constant, the most outstanding examples being the alkan-1-01s and n-alkanes. Above dodecan- 1-01, AGF(g -+ aq) becomes gradually more negative than expected, so that octadecan-1-01 is 16 times as soluble as calculated from results on the low alkan-1-01s. A similar, but much larger, effect is observed for the n-alkanes: n-octadecane is more soluble than expected by a factor of 5 x lo3 (the factor for n-hexatriacontane is 2 x 10'") and it is deduced that the n-alkane C,,H,,, will be as soluble in water as in the non-aqueous solvents ethanol and phenol.There are a number of concentration scales used to express the solubility of gases in liquids, and a corresponding number of sets of standard states used to define standard Gibbs energies (and standard entropies) of solution of gases in liquids. Hine and Mookerjeel in their extensive compilation used standard states of 1 mol dm-3 gas and 1 mol dm-3 in solution, as did also Cabani et aL2 in their tabulation of Gibbs energies of solution, AGP, of gases in water. Other workers have reported solubilities or AGP values in terms of the process ideal gas (1 atm) + ideal solution (unit mol fraction solute), and these are probably the most common standard states u ~ e d .~ - l ~ Other standard states that have been used are 1 mmHg for the gas and unit mol fraction solute in ~ o l u t i o n , ~ ~ - ~ ~ 1 mmHg for the gas and 1 mol dm-3 for the solute in and more recently 1 kPa for the gas and 1 mol m-3 for the solute in solution.20 Since gas solubilities, or AGP values, reported in terms of one set of standard states are normally easily converted into corresponding values on any other set of standard states, it does not usually matter which set is employed.7 In table 1 are given numerical values to convert Gibbs energies of solution of gases on various standard states to those on the standard state of ideal gas (1 atm) and ideal solution (unit mole fraction solute). Because the same conversion quantities, table 1, apply to all solutes, differences in standard Gibbs energies of solution between two solutes in a given liquid are However, note that because the solvent molecular weight is used in calculating the mole fraction solute in solution, the standard state of unit mole fraction solute cannot be used with solvents that have no well defined molecular weight, e.g.biological fluids and polymeric materials. 153154 THERMODYNAMICS OF SOLUTION IN WATER independent of these standard states. Thus for the solution of methane and ethane in water at 298 K, AGF (methane, gas) - AGP (ethane, gas) = 0.17 kcal mo1-I on any of the standard states shown in table 1. This is most important in considerations of the methylene increment to the solution of gaseous solutes in a homologous series, because this increment will also be independent of the standard states shown in table 1.Likewise, although values of AS? for gaseous solutes will differ on various standard states, differences between AS? will be independent of the standard states in table 1, as will also the entropic methylene increment to solution of gaseous solutes in a given solvent. Table 1. Effect of standard states on values of AGp(g + solution), in kcal mo1-I at 298 K standard states 6AGFa gas solvent water methanol hexane ~ ~ ~~ 1 atm unit mol fraction 0 0 0 1 atm 1 mol dm-3 2378 1896 1201 1 atm 1 mol kg-' 2380 2039 1452 1 mol dm-3 1 mol dm-3 4272 3790 3095 1 kPa 1 mol dm-3 3734 3252 2557 solvent molecular weight 18.015 32.04 86.18 solvent density 0.997 1 0.7865 0.6548 a Defined so that AG?( 1 atm + unit mole fraction) = AGF (any other standard state) plus the given correction term.However, a quite different set of standard states has been advocated by Tanford2l9 22 and has been used by several w o r k e r ~ , ~ ~ - ~ ~ especially in discussion of the methylene in- crement to solution of solutes in 25 Tanford's standard states are those of the pure liquid solute and the ideal solution (unit mole fraction solute). The relationship of these standard states to those given in table 1 may most simply be discussed with reference to that of the ideal gas (1 atm) and the ideal solution (unit mole fraction solute). For solution in a given solvent, say water, the two standard-state processes g -+ aq and liq -+ aq are related through the standard Gibbs energy of vaporisation of the pure liquid solute to the ideal gas at 1 atm: AG3g --+ aq) ideal gas at 1 atm- solute in solvent water.AGF 2 AGp(liq -+ aq) (1) pure liquid solute From eqn (1) it may be seen that AGp(g -+ aq) + AG? = AGP(1iq -+ as). (2) Similar equations may be set up in terms of enthalpy, entropy etc. Now since AGF (or AH? etc.) will differ from solute to solute, the conversion from AGP(1iq + aq) to AGP(g --+ aq) will differ numerically even for solutes as similar as n-hexane and n-heptane. Thus the standard state of pure liquid solute amounts to assigning a different standard state to each solute. This has been pointed outM. H. ABRAHAM 155 before,l2? l3 and the relationship shown in eqn (1) and (2) has been used by Butler et al.15 and subsequently by other worker~.~**-ll In spite of this, Tanford22 has argued again that the standard state of pure liquid hydrocarbon is equivalent to assigning the same standard state to the various liquid solutes concerned, for example n-hexane liquid and n-heptane liquid.Tanford22 advances a thermodynamic argument to support his views, as follows. For the solution of a small liquid n-alkane solute in a long-chain n-alkane solvent such as n-hexadecane or n-octadecane, the difference between pe for the small n-alkane in the pure liquid (itself) and pe for the small n-alkane in the long-chain n-alkane is only ca. 60calmol-1, when the small n-alkane solute and long-chain n-alkane solvent differ in chain length by some 10 carbon atoms. This amounts to only ca. 6 cal mol-l per methylene group, which is negligible.The validity, or otherwise, of Tanford’s argument can rigorously be demonstrated. Let py be the standard chemical potential of an alkane solute of carbon number rn in an alkane solvent of carbon number 1: thus p& represents the standard chemical potential of n-hexane in n-hexadecane, with mole fraction standard states, and pz represents the standard chemical potential of n-hexane in n-hexane itself. Then for the solution of liquid n-hexane solute in n-hexadecane (Raoult’s law activity coefficient = 0.87) and for the solution of liquid n-heptane solute in n-hexadecane (Raoult’s law activity coefficient = 0.91) Thus Tanford22 is quite correct in stating that numerically p& -p: or --pi amounts to ca. 60 cal mol-l.However, this value has nothing to do with the relative energy of the standard states of n-hexane in n-hexane (pfi) and of n-heptane in n-heptane (pi), which is given by the term p i - p z . The relationship of this term to the ideal-gas standard states of n-hexane and n-heptane can be obtained by considering the solution of gaseous alkanes (ideal gas, 1 atm) into solvent n-hexadecane (unit mol fraction solute). Denoting the ideal gas standard state asppat,, then for the solution of n-hexane gas into n-hexadecane (Henry’s law constant = 0.173 atm) ( 5 ) and for the solution of n-heptane gas into n-hexadecane (Henry’s law constant = 0.055 atm) ,&-&atm = RTln (0.055) = - 1720 cal mol-l. (6) @I6 -/.4!6) - @: atm -p! at,) = - 680 cal m0l-l (7) (p: - pg) - - p! = - 708 cal mol-l.(8) j.46--& = RTln (0.87) = - 84 cal mol-1 (3) = RTln (0.91) = - 56 cal mol-l. (4) & 6 - / 4 atm = RTln(0.173) = - 1040 cal mol-1 Then from eqn ( 5 ) and (6) and now combining eqn (7) with eqn (3) and (4) Thus with reference to the ideal-gas standard states, in which there exist no solute-solute interactions, the standard states of pure liquid n-hexane and pure liquid n-heptane (& -pz) differ by 708 cal rnol-l, identifiable [see eqn (l)] as being due to solute-solute interactions in the pure liquids. As I have pointed out before,l29l3 this difference is given by the ratio of the saturated vapour pressures (or more correctly, fugacities) of n-hexane and n-heptane, uiz: RTln(P7/P6) = -(AGp7-AGy), see eqn (1). To summarise, if Tanford’s standard state of pure liquid n-alkane, or more generally pure156 THERMODYNAMICS OF SOLUTION IN WATER liquid solute, is used then this will lead to the incorporation of a different solute-solute interaction term for each solute standard state.In such a case, little meaning can be attached to the variation of AGP [AGP (liq + solution)] with carbon number along a homologous series, because, defined in this way, the AGP values contain various contributions from solute-solute interactions in the pure liquid solute. A more readily interpretable quantity is AGp(g + solution) because only solute-solvent interactions now contribute. It is the purpose of this paper to set out values of AG?(g -+ aq) and AGP(1iq + aq) for solution of solutes of various homologous series in water and to show how the calculated methylene increment depends on these standard states ; where possible, similar quantities will be tabulated in terms of enthalpy and entropy.In addition, methylene increments will be analysed carefully to determine whether or not the increment is indeed constant along an homologous series, or whether, as found by Beezer et ~ 1 . ~ ~ for a series of monoalkylated resorcinol compounds, there is an alternation in the methylene increment with carbon number. There are two main methods of obtaining AGP values. First, Henry’s law constants maybeobtainedforsolutionofgaseoussolutesinwater ; thenAGP(g -+ aq) = RTln KH. If the solute vapour pressure (or fugacity) is known, AG? = -RTlnP and then through eqn (2) AGP(1iq -+ aq) may be deduced. Secondly, the solubilities of sparingly soluble solutes may be obtained. If expressed on the mole fraction scale, then AGP(1iq -+ aq) = -RTln A‘, and combination with AG? will now yield corresponding values of AG?(g -+ as).For solutes of high carbon number, it is almost impossible to obtain Henry’s law constants, and even the determination of solubilities becames difficult and subject to considerable error. For solutes of low carbon number, solubilities are much easier to obtain, but AGP(1iq -+ aq) may only be set equal to -RTln Xprovided that the secondary medium activity coefficient of the solute in the saturated solution is unity. Corresponding AH? values are again obtained by two main methods. First, variation of Henry’s law constants with temperature will yield AH?(g + aq), and then combination with AH? will give AHP(1iq + aq).Secondly, calorimetric determina- tions of AHp(1iq + aq) may be carried out and values of AHp(g -+ aq) obtained by again using the AH? values. A large number of gas and liquid solubilities have been carried out on the n-alkanes. For the series methane to n-octane there is general agreement on the AG?(g -+ aq) values,2$13* 2o and in table 2 the values are 1i~ted.l~ Vejrosta et ~ 1 . ~ ~ have recently measured Henry’s law constants, as Cwater/Oas, for the n-alkanes from n-pentane to n-nonane over a range of temperature. They summarised all their results in one equation, but I thought it useful to fit the given values of ln(Cwater/Oas) to an equation in A / T+ B + L In T for each alkane separately in order to obtain values of Caterloas and of AH* at 298.15 K.Conversion to the standard states used in this work leads to AGp(g --+ aq) values as follows$ n-pentane (6.59), n-hexane (6.78), n-heptane (7.00) and n-octane (7.21), in kcal mol-l. These are in very good agreement with those in table 2, and confirm the generally accepted values. Combination of the AGP(g + aq) values with vapour pressures27 or fugacities then leads to values of AGP(1iq + as), see also table 2. For the n-alkane series n-nonane to n-hexadecane, there are available the liquid solubilities, listed by Mackay and Shiu,20 that lead directly to AGP(1iq -+ aq) and thence t@AGp(g -+ as). A number of investigations into the solubilities of the solid n-alkanes have been reported,20 the best documented study being that of Sutton and Calder.28 From the solid mole fraction solubilities, values of t Determinations for n-nonane were carried out at 287.95 and 293.20 K only.M.H. ABRAHAM 157 Table 2. Standard Gibbs energies of solution and of vaporisation of n-alkanes, in kcal mol-l at 298 K n-alkane Platma AGPb AGp(g -+ aq)c AGp(1iq -, aq)" methane 87.3 ethane 24.07 propane 7.68 butane 2.19 pentane 0.674 hexane 0.199 heptane 6.028 x lo-, octane 1.847 x lo-, nonane 5.724~ lo-, decane 1.797 x lo-, undecane 5.645 x dodecane 1.737 x lo-* tridecane 5.226 x tetradecane 1.542 x lov5 pentadecane - hexadecane - hep t adecane - octadecane - eicosane, C,, - hexacosane, C,, - hexatriacontane, C,, - - 2.65 - 1.88 - 1.21 - 0.46 0.23 0.96 1.66 2.36 3.06 3.75 4.43 5.13 5.84 6.56 (7.26)g (7.96)Q (8.67)Q (10.77)g (1 5.0)Q (22.0)g (9.37)g 6.28 6.1 1 6.23 6.35 6.61 6.82 6.90 7.16 7.42" 7.44" 8.25" 7.72" 6.64" 5.88h 3.88h 2.19h - - - - 3.25h - 12.55h 3.61 4.23 5.02 5.89 6.84 7.78 8.56 9.52 10.48f 11.19 12.68f 12.89 13.20f 13.84f 13.25i (13.40y 12.96i (13.59y 11.7S (1 3.77Y 9.4Y (13.94y - - - a From Dreisbach,,' except for values from methane to butane which are fugacities, see J. P. Montfort and J. R. Varela H., Chem. Eng. J., 1976, 12, 1. Standard states, 1 atm gas and pure liquid hydrocarbon. Standard states, 1 atm gas and unit mole fraction solute in solution. Values from Abraham13 except where indicated. Standard states, pure liquid hy- drocarbon and unit mole fraction solute in solution. " From AGP(1iq -+ aq) and the tabulated value of AGP.f From the solubility of the liquid alkane, given in ref. (16). Q Estimated from plots of log P or AGP against carbon number. From AGp(1iq -+ aq) and the estimated value of AGP. From the solubility of the solid alkane,,* corrected using the data of A. A. Schaerer, C. J. Busso, A. E. Smith and L. B. Skinner, J. Am. Chern. SOC., 1955,77, 2017, on fusion and solid-solid transitions of n-alkanes. * Value of AGF(so1id -+ as). From the solubility of solid hexatriacontane given by E G. Baker, Science, 1959, 129, 871, corrected as in footnote (i). AGF(so1id + aq) may be calculated, and these values then corrected through the following equation to AGP(1iq + aq) values. In eqn (9), AHg is the molar enthalpy of fusion of the solute in question, Tm is the solute melting point and T is the temperature of the solubility determination (298.15 K in the present instance). If the solute undergoes a solid-solid transition between T and Tm then the second correction term in eqn (9) must also be applied; AHt is the molar enthalpy of transition and Tt is the transition temperature.For solutes that undergo two such transitions between Tand Tm, two such transition correction terms are needed.? t Note that in eqn (9) it is assumed that AH% and AH? are temperature independent over the range T, to T and to T, respectively.158 THERMODYNAMICS OF SOLUTION IN WATER In table 2 are listed AGP(1iq -+ aq) values determined through eqn (9), together with corresponding AGp(g -+ as) values obtained from AGP(1iq -+ aq) and the extrapolated values of AGP.With the exception of the value for n-undecane, which seems much too positive, there is a reasonable straight-line plot of AG?(g -+ aq) against N , the carbon number, from N = 2 to N = 12. Beyond n-dodecane, however, the AGp(g -+ aq) values become rapidly much more negative than expected. Nelson and de Ligny,14 who had available values only up to n-octadecane, attributed this phenomenon to the coiling of alkyl chains in aqueous solution, but the magnitude of the effect is far greater than previously imagined. Results are availablel33 29 for enthalpies of solution and vaporisation of n-alkanes up to n-octane, table 3, although the AH? values for n-octane are rather doubtful. The given AHg(g -+ aq) values may be compared with those I have calculated from the results of Vejrosta et aZ.,26 after a minor correction (45 cal mol-l) from the molar Table 3.Standard enthalpies and entropies of solution and of vaporisation of n-alkanes, in kcal mo1-1 and cal K-l mo1-I at 298 K methane ethane propane butane pentane hexane heptane octane nonane decane undecane dodecane - 2.3 1 3.60 5.02 6.39 7.54 8.74 9.92 11.10 12.28 13.46 14.65 - 3.30 -4.72 - 2.41 - 5.38 - 1.78 -6.21 - 1.19 - 6.5 -0.1 1 - 7.5 0.04 -8.1 0.64 - 9.5 0.42 - 32.1 14.1 - 36.3 - 22.2 16.1 - 38.9 - 22.8 18.4 - 42.1 - 23.7 20.7 - 44.0 - 23.3 22.1 - 48.0 - 25.9 23.7 - 50.3 - 26.6 25.4 - 55.9 - 30.5 a From Ducros et al.,29 except for ethane and propane from Dreisba~h.~’ Values given by From AG? and AH?, standard states 1 atm gas and From AGF and AH?, standard states pure liquid Abraham.I3 From AGF and AH?.unit mole fraction solute in solution. hydrocarbon and unit mole fraction solute in solution. to mole fraction aqueous solution standard state: n-pentane ( - 6.43), n-hexane (- 7.3 I), n-heptane (- 8.76) and n-octane (- 9.82), in kcal mol-l. When taken together with values for ethane to n-butane, table 3, these new values do not give as good a straight line as the values in table 3 on plotting against N , the solute carbon number.? I have therefore carried out all subsequent calculations with the results in table 3, but use of these new values would not affect the general conclusions reached in this work. The corresponding entropy values are in table 3, and the results of the various plots of enthalpy and entropy against carbon number (C, to C,) are in table 4.Although the solution results are not accurate enough to probe any alternation effects, they can be used to obtain the various methylene contributions. The AHF values for the n-alkanes in water show how misleading Tanford’s standard states can t Plots of AHp(g --* aq) against N have correlation coefficients of 0.9776 (new values) and 0.9946 (table 3) for ethane to n-heptane, or 0.9812 (new values) and 0.9882 (table 4) for ethane to n-octane. Values for the corresponding AHp(1iq -+ aq) plots are 0.9394 (new values) and 0.9872 (table 3) for ethane to n-heptane, or 0.9085 (new values) and 0.9586 (table 3) for ethane to n-octane.M. H. ABRAHAM I59 be. Whereas the increment to AHP(1iq -+ aq) is +0.62 kcal mol-l, it is actually -0.67 for the solution process g -+ aq.For solution of alk-l-enes in water, only the Gibbs energies are available for any extended set of solutes. There is quite good agreement on AGF values between various compilations,'. 2* 6* 2o and these values are also compatible with recent solubility meas~rements.~~ Details are in table 5, with the methylene increments given in table 4. There seems to be a slight alternation effect in AGP, although the differences (ca. 0.1 kcal mol-l) are very small. Cabani et aI.2 have surveyed results for Gibbs energies of solution of alk-l-ynes; details are in table 6. For this series of homologues there is a slight alternation effect in AGP(1iq -+ as), again very small in magnitude. The various methylene increments are in table 4.The n-alkylbenzenes have been studies by numerous sets of workers who have obtained the solubilities of the liquid solutes in order first to obtain AGP(1iq -+ as). Combination with AGP then leads to the AGp(g + aq) values often tab~lated.l-~ In table 7 are the mol fraction solubilities from a number of reviews,'? 11* 2o together with some recently determined values;30-32 in some cases recorded solubilities in mol dm-3 have been recalculated to mole fraction solubilities. In general there is reasonable agreement between the various sets. The values taken, final column table 7, are mostly based on the average values listed by Mackay and Shk2O It should be noted that the solubilities of Ben-Naim and Wilfj' are significantly larger than the average 'best' values, so that AGP values calculated from Ben-Naim and Wilf's data will be smaller than the 'best' values of AGF.This is significant when comparing values of AGF(g -+ aq)for then-alkylbenzenes, see table8, because thereisamarkeddisagreement between the values givent by Ben-Naim and Wilf3I and those calculated from the data of Tewari et aL30 Whereas the latter, as is usual for homologous series up to at least the C,, or C,, compound, increase with carbon number, the former data show a continual decrease after n-propylbenzene. The data of Tewari et al. are preferred, and in table 9 are given the various sets of Gibbs energies; the results of plots of these energies against carbon number are summarised in table 4. have obtained values of AHp(1iq -+ aq) for a number of alkylbenzenes calorimetrically, and combination with AH? values29 leads to the AHp(g -+ aq) values in table 10.Also in table 10 are the corresponding entropy values, and in table 4 are listed the regression equations for plots of all these values against carbon number. There is as good agreement as can be expected between the calorimetrically determined AH? values in table 10 and values obtained3* 3 1 9 32 from the temperature dependence of solubilities$ As well as the above results on solution of hydrocarbons, there are available also results for various other homologous series. Details of such series, in which a reasonable number of homologues have been studied, follow. Cabani et aL2 and Rytting et al.19 give values for solution of gaseous n-alkylamines from which AGp(g -+ aq) may be calculated; the two sets of data are in reasonable agreement, see table 1 I .Results are available3*- 35 for calculation of the corresponding Wadso and t Ben-Naim and WilP' list polynomials from which the Ostwald absorption coefficient may be calculated. This coefficient is then easily converted into Henry's law constant (atm/mol fraction). t Note added in proox A recent value of AGP(1iq + aq) for n-hexylbenzene (9.49 kcal mol-l) is very close to that gven in table 9 (see W. E. May, S. P. Wasik, M. M. Miller, Y. B. Tewari, J. M. Brown-Thomas and R. N. Goldberg, J . Chem. Eng. Data, 1983, 28, 197). The corresponding value for AHP(liq -+ aq) of 1.83 _+ 0.33 kcal mol-* when combined with data in table 10 leads to methylene incrementsof0.30 kcal mol-' for AHP(1iq -+ aq), -0.77 kcal mol-I for AHp(g + aq), - 1.7 cal K-I mol-I for A e ( l i q -+ aq), and -3.1 cal K-' mol-I for ASp(g -+ aq), and to Ph group contributions (see table 29) of -6.44 kcal mol-l to AHp(g aq) and - 23.0 cal K-' mol-I to A@(g -+ as).1 60 THERMODYNAMICS OF SOLUTION IN WATER Table 4.Regression equations for thermodynamic parameters of solution regression equation ra sb nc solute ranged n-alkanes AGp(g -+ aq) = 5.71 1 +(0.177+0.009) N AGp(1iq +as) = 2.399+(0.887+0.010) N AHP(g -+ aq) = -3.374-(0.673&0.035) N AHp(1iq + aq) = - 3.603 + (0.623 f 0.050) N 1@(g+ aq) = -30.51 -(2.834+0.106) N Aw(liq +as) = -20.11 -(0.883_+0.167) N AGp(g - aq) =4.895 + (0.150 5 0.024) N AGP(1iq -+ aq) = 1.424 + (0.876 & 0.028) N AGp(g -+ aq) = 3.079+(0.247_+0.010) N AGp(1iq -+ aq) = 0.129 + (0.900 0.009) N n-a1 k ylbenzenes AGp(g + aq) = 3.323 +(O.146 5 0.003) N AGp(1iq -+ aq) = 4.579+(0.809$0.010) N AHp(g -+ aq) = - 7.767 - (0.91 5 k 0.020) N AI@(liq + aq) = 0.340 + (0.070 & 0.0oO) N A@(g - aq) = -37.27-(3.500f0.116) N Aw(1iq -+ aq) = - 14.53-(2.300f0.058) N AGp(g + aq) = -0.539+(0.144+0.002) N AGp(liq -+ aq) = - 1.998 + (0.799_+ 0.004) N AHP(g - aq) = - 1 1.278 - (0.725 k 0.032) N AHP(1iq -+ aq) = - 7.102 + (0.368 k 0.095) N A@(g -+ aq) = - 36.12 - (2.890 k 0.125) N A@(liq -+ aq) = - 17.08 - (1.460 f 0.088) N AGP(g + aq) = -0.380 + (0.229 0.008) N alk- 1 -enes alk- 1 -ynes n-alk ylamines alkan-Zones 0.9927 0.9997 0.9946 0.9872 0.9972 0.9354 0.05 1 0.054 0.147 0.2 10 0.445 0.698 ethane to n-octane ethane to n-heptane 0.9420 0.9975 0.126 0.148 7 7 prop- 1 -ene to non- 1 -ene 0.9962 0.9998 0.05 1 0.047 7 7 prop- 1 -yne to non- 1 -yne 0.9992 0.9997 0.0 12 0.042 0.029 0.0oO 0.163 0.082 toluene to n-hexylbenzene toluene to n-propylbenzene 0.9993 0.9999 0.9970 0.990 1 0.9972 0.9946 0.013 0.020 0.103 0.095 0.394 0.278 ethylamine to n-octylamine ethylamine to n-hexylamine 0.9965 0.05 I 8 butan-2-one to undecan- 2-one AGP(1iq -+ aq) = - 1.610+(0.848f0.009) N AHp(g +as) = -7.547-(0.818f0.028) N 0.9997 0.998 1 0.057 0.111 8 5 butan-2-one to nonan- 2-one AHP(1iq -+ aq) = - 3.479 +(0.210 k 0.027) N A@(g -+ aq) = -23.82-(3.561 k0.128) N A@(liq + aq) = -5.89-(2.215k0.074) N 1-chloroalkanes AGp(g + aq) = 3.390+(0.163+0.019) N 0.9755 0.998 1 0.9983 0.105 0.492 0.286 5 5 5 0.9745 0.078 6 1-chloroethane to l-chloro- heptane AGP(1iq -+ aq) = 1.730+(0.870_+0.021) N 1 -bromoalkanes AGp(g --+ aq) = 3.070+(0.219+0.009) N AGp(1iq -+ aq) = I .975 + (0.920 k 0.009) N AGp(g -+ aq) = 3.163+(0.200+0.015) N 1 -iodoalkanes 0.089 0.9988 6 0.9953 0.050 7 1-bromoethane to l-bromo- octane 0.9998 0.047 7 0.9946 0.055 4 1 -iodoethane to 1 -iodo- heptane AGP(1iq -+ aq) = 2.832+(0.876+0.014) N 0.9997 0.053 4M. H.ABRAHAM 161 Table 4. (con?.) alkan- 1-01s AGp(g -+ aq) = - 1.094 + (0.163 f 0.005) N AGP(1iq + aq) = - 0.928 + (0.822 k 0.004) N b@(g + aq) = - 1 1.245 - (0.851 f 0.021) N AHp(g -, aq) = - 11.245-(0.851 k0.021) N AhHp(1iq + aq) = -3.347+(0.297f0.013) N A@(g -+ aq) = -34.07-(3.390f0.083) N ASP(liq -+ aq) = -8.17-(1.750*0.038) N methyl alkanoates AGp(g + aq) = 0.575+(0.226f0.017) N AGp(1iq -+ aq) = -0.01 5 f (0.855 k 0.020) N AHp(g -+ aq) = - 8.203 -(0.825 k0.003) N AHP(1iq -+as) = -2.570+(0.165f0.009) N A@(g + aq) = - 30.00 - (3.400 f 0.173) N A@(liq -+ aq) = - 9.20 - (2.150 f 0.260) N n-alkyl acetates AGp(g -+ aq) = 1.046 + (0.144 f 0.003) N AGP(liq -+ aq) = 1.032 + (0.768 f 0.014) N ethyl alkanoates AGp(g + aq) = 1.294+(0.099f0.019) N AGP(1iq +as) = 1.317+(0.688f0.018) N dGp(g + aq) = 1.239+(0.186f0.019) N n-alkyl propanoates ACP(1iq -+ aq) = 2.08 + (0.680 0.052) N AHP(Mg -+ aq)= 10.27-(1.01 f0.37) N alkanoic acids AHp(1iq -+ aq) = - 1.391 +(0.262+0.015) N 0.9960 0.046 0.9999 0.031 0.9991 0.066 0.9991 0.066 0.9970 0.042 0.9991 0.263 0.9993 0.120 0.9825 0.134 0.9984 0.154 0.004 0.012 0.245 0.367 0.9994 0.008 0.9997 0.031 0.8943 0.145 0.9977 0.137 0.040 0.112 0.8894 0.82 0.9968 0.033 9 9 5 5 5 5 5 propan- l-ol to dodecan- l-ol propan- l-ol to heptan- l-ol 8 methyl propanoate to 8 3 methyl propanoate to 3 3 3 methyl pentanoate methyl pentanoate 4 ethyl acetate to n-pentyl- 4 acetate 9 ethyl acetate to ethyl 9 decanoate 3 ethyl propanoate to 3 n-pentyl propanoate 4 butanoic acid to heptanoic 4 acidf a Correlation coefficient.Standard deviation. Number of solutes. Range of homologous solutes covered. If methyl decanoate is excluded, slope = (0.200&0.012), t = 0.991 1 and s = 0.075 (n = 7). f If the smoothed AH9 values are used to calculate AHp(g-+aq), the resulting equation is AHp(g + aq) = - 11.24-(0.814+0.016) N , with r = 0.9996 and s = 0.036.enthalpy and entropy of solution, see table 12. The regression equations for various plots against carbon number are in table 4. There is no sign of any alternation effect in the n-alkylamine series of results. The solution of alkanones and alkanals in water may be complicated by formation of the corresponding gem-diols ; equilibrium constants for such hydrate formation are 1 x for propanone and 1.06 for ethana1.36 The latter value is so large that observed solution parameters for alkanals cannot be used without correction for hydrate formation, but the equilibrium constants for alkanones seem small enough for hydrate formation to be disregarded. Buttery et aZ.37 have determined Henry’s law constants for a series of n-alkylmethylketones (alkan-2-ones) from which AGp(g -+ as) values may be obtained.Combination with vapour pressures38 (or AGP values) enables AGp(liq -+ aq) to be calculated. For the less soluble ketones, AGP(1iq -+ aq)may also be162 THERMODYNAMICS OF SOLUTION IN WATER Table 5. Standard Gibbs energies of solution and of vaporisation of alk-1-enes, at 298 Ka alk- 1 -ene P/atmb AG? AGp(g -+ aq) AGg(1iq -+ aq) ethene prop- 1 -ene but- 1 -ene pent-1-ene hex- 1 -ene hept- 1 -ene oct- 1 -ene non- 1 -ene 59.91 11.29 2.92 0.854 0.246 7.41 x 10+ 2.29 x 7.02 x 10-3 - 2.42 - 1.44 - 0.63 0.09 0.83 1.54 2.24 2.94 5.55 5.59 5.65 5.94 5.85 5.93 6.19 6.33 2.93 3.85 5.02 6.03 6.6P 7.47d 8.43d 9.27d a Standard states and units as in table 2. Data from ref. (1) and (6) unless shown otherwise. Ref. (27), except for the value for ethene from ref.(20). Average of values in ref. (1) and (30). Ref. (30). Table 6. Standard Gibbs energies of solution and of vaporisation of alk-1-ynes, at 298 K" alkyne P/atmb AGP AG?(g -+ aq) AGP(1iq + aq) ethyne prop- 1 -yne but- 1 -yne pent- 1 -yne hex- 1 -yne hept- 1 -yne oct- 1 -yne non- 1 -yne 48.52 5.51 1.86 0.568 0.179 6.91 x 1.79 x 8.24 x 10-3 - 2.30 - 1.01 -0.37 0.34 1.02 1.58 2.38 2.84 4.26 3.79 4.1 1 4.29 4.56 4.87 4.98 5.32 1.96 2.78 3.74 4.63 (4.85)c 5.58 (5.21)c 6.45 7.36 8.16 a Standard states and units as in table 2. Data from Cabani et aL2 unless shown otherwise. Ref. (20) and (27). Ref. (30). Table 7. Mole fraction solubilities of liquid n-alkylbenzenes, at 298 K ref. 1 31 11 20 32 30 values n-alkylbenzene (1975) (1980) (1981) (1981)a (1982) (1982) taken benzene ( x 4.14 4.21 4.03 4.12 (8) 3.73 - 4.12 toluene ( x 1.02 1.21 1.06 1.05 (7) 1.03 1.13 1.05 ethylbenzene ( x lo+) 2.61 3.61 2.69 2.85 (6) 2.87 3.18 2.85 n-propylbenzene ( x lop6) 8.26 - 8.28 - 7.64 7.84 8.00 n-butylbenzene ( x lo+) - - 1.64 1.94 (4) - 1.86 1.94 n-pentylbenzene ( x lo-') - - - - - 4.68 4.68 n-hexylbenzene ( x lo-') - - - - - 1.13 1.13 a Average values given, the number of investigations covered is in parentheses.determined directly from solubility measurements of the liquids,30* 39 there being good agreement between the two sets of values, see table 13. There is a suggestion of an alternation effect in AGp(liq--+aq), but such an effect must be very small. The regression equations yielding methylene increments are in table 4.Della Gatta et aL40 have determined AH? and AHP(1iq + aq) values for the alkan-2-ones. Their enthalpiesM. H. ABRAHAM 163 Table 8. Comparison of tabulated AGp(g -+ aq) values for n-alkylbenzenes, in kcal mol-l at 298 K ref: 3 1 31 2 from tables n-alkylbenzene (1 972) (1 975)" (1 980)" (198 1)" 7 and 9b benzene 3.40 toluene 3.39 e thy1 benzene 3.48 n-propylbenzene - n-butylbenzene - n-pentylbenzene - n-hex ylbenzene - n- hep t yl benzene - n-oc t yl benzene - 3.39 3.51 3.66 3.74 3.88 3.37 3.35 3.47 3.50 3.42 3.09 2.53 1.91 1.37 3.39 3.39 3.48 3.48 3.74 3.61 3.88 3.75 - 3.91 - 4.04 4.2 1 - a After conversion to standard states of 1 atm gas and unit mol fraction solution. Using the mole fraction solubilities in the final column of table 7 and the solute vapour pressures in table 9.Table 9. Standard Gibbs energies of solution and of vaporisation of n-alkylbenzenes, at 298 Ka P/atmb AG: AG?(g + aq)" AG?(liq + as)" n-a1 ky benzene benzene 0.1252 1.23 3.39 4.62 toluene 3.742 x 1.95 3.48 5.43 ethylbenzene 1.259 x 2.59 3.61 6.20 n-prop ylbenzene 4.524 x 3.20 3.75 6.95 n-pen t yl benzene 4.316 x 4.59 4.04 8.63 n- bu t y 1 benzene 1.428 x 10-3 3.88 3.91 7.79 n-hexylbenzene 1.383 x 5.26 4.21 9.47 a Standard states and units as in table 2. Ref. (27). Table 10. Standard enthalpies and entropies of solution and of vaporisation of n-alkylbenzenes, at 298 K" From tables 7 and 8. AH? AH? A@ A* n-alkylbenzene AHFb (g -, (liq + aq)d A* (g + aq) (liq -, aq) benzene 8.09 -7.59 0.50 23.0 -36.8 -13.8 toluene 9.08 - 8.67 0.41 23.9 -40.7 -16.8 ethylbenzene 10.10 - 9.62 0.48 25.2 -44.4 -19.2 n-propylbenzene 11.05 - 10.50 0.55 26.3 -47.7 -21.4 a Units and standard states as in table 3.Determined calorimetrically. 33 Ref. (29). From AH: and AHF(liq + aq). of vaporisation are not quite the same as those listed by Ducros et aZ.,35 but in table 14 are given all the relevant results of Della Gatta et aL40 for consistency, with the methylene increments in table 4. The aqueous solubilities of a number of liquid 1-halogenoalkanes are known, see table 15, and lead directly to AGP(1iq -+ as). Combination with values of AG? gives164 THERMODYNAMICS OF SOLUTION IN WATER Table 11. Standard Gibbs energies of solution and of vaporisation of n-alkylamines, at 298 K a n-alk ylamine P/atmb AGP AG?(liq -+ aq)d me thy lamine ethylamine n-propylamine n-butylamine n-pentylamine n-hexylamine n-hep tylamine n-octylamine 3.527 - 0.75 1.398 - 0.20 0.405 1 0.54 0.1367 1.18 4.54 x 10-2 1.83 1.50 x 2.49 5.20 x 10-3 3.12 1.76 x 10-3 3.76 - 0.29' - 0.23' -0.12' 0.03" (-0.02)' 0.18" (0.18)' 0.32" (0.24)' 0.4P 0.62" - 1.04 - 0.43 0.42 1.21 2.01 2.81 3.60 4.38 a Standard states and units as in table 2.Ref. (19) and (27). ' Ref. (2). From the previous two columns. Ref. (19). Table 12. Standard enthalpies and entropies of solution and of vaporisation of n-alkylamines, at 298 Ka AH? AH? A* A* n-alkylamine AH? (g -+ aq) (liq --+ aq) A,!@ (g --+ aq) (liq -+ aq) methylamine 5.80 - 10.82 -5.02 22.0 ..: 35.3 - 13.3 ethylamine 6.36 - 12.83 -6.47 22.0 -42.3 - 20.3 n-butylamine 8.53 -14.11 -5.58 24.7 -47.4 - 22.7 n-pentylamine 9.58 - 14.85 -5.27 26.0 - 50.4 - 24.4 n-hexylamine 10.78 - 15.72 -4.94 27.8 - 53.8 - 26.0 n-propylamine 7.49 - 13.38 -5.89 23.3 -44.5 -21.2 a Standard states and units as in table 3.Results from ref. (34) and (35). Table 13. Standard Gibbs energies of solution and of vaporisation of alkan-2-ones, at 298 Ka alkan-2-one P/atmb AGP AG?(g -+ aq)" AG?(liq -+ aq)d propanone but an-2-one pentan-2-one hexan-2-one heptan-2-one octan-Zone nonan-2-one decan-2-one undecan-2-one 0.304 0.71 0.1 19 1.26 4.66 x 1.82 1.53 x 2.48 5.07 x 10-3 3.13 1.78 x 10-3 3.75 - (4.34)f - (4.96)5 8.42 x 10-5 5.56 0.46 0.56 0.75 0.98 1.23 1.39 1.78 1.928 2.1 1 1.17 1.82 2.57 (2.61)" 3.46 (3.44)e 4.36 (4.32)e 5.14 (5.18)e 6.12 (5.90)" 6.88e 7.67 a Standard states and units as in table 2.From Henry's law constants in ref. (37). Ref. (38) except for undecan-2-one [ref. (37)]. Calculated from solubilities of the liquid alkan-2-0nes.~~. 39 f Estimated from a plot of AG? against carbon number (butan-2-one to undecan-Zone). g From AG?(liq --+ aq) and AGP. From the previous two columns.M. H. ABRAHAM 165 Table 14. Standard enthalpies of solution and of vaporisation of alkan-2-0~, at 298 Ka AH$' AH? A* A* alkan-2-one AH? (g 3 aq) (liq -B aq) A* (g + aq) (liq + aq) ~ ~~ propanone 7.29 -9.72 -2.43 22.0 - 34.1 - 12.1 butan-2-one 8.35 - 10.91 -2.56 23.8 - 38.5 - 14.7 pentan-2-one 9.20 -11.64 -2.44 24.8 -41.6 - 16.8 hexan-2-one 10.12 - 12.38 -2.26 25.6 -44.8 - 19.2 heptan-2-one 1 1.02 -13.16 -2.14 26.5 -48.3 -21.8 nonan-Zone 13.51b - 15.01' - 1.Y 30.7 - 56.3 - 25.6 a Units and standard states as in table 3; all results from Della Gatta et aL40 (in enthalpies) except for nonan-2-one.Ref. (35). From AH? and AHP(1iq --+ aq). R. Bury, M. Lucas and P. Barberi, J. Chim. Phys.. 1978, 75, 575. Table 15. Mole fraction solubilities of 1-halogenoalkanes, at 298 K 1-halogenoalkane ref: 1 39 30 taken values 1 -chloropropane 1 -chlorobutane 1 -chloropentane 1 -chloroheptane bromoethane 1 -bromopropane 1 -bromobutane 1 -bromopentane 1 -bromohexane 1 -brornoheptane 1-bromo-octane iodomethane iodoe t hane 1 -iodopropane 1 -iodobutane 1-iodoheptane 6.26 x 1.31 x 10-4 3.36 x 10-5 5.37 x 10-4 1.30 x 10-4 1.50 x 10-3 3.60 x 10-4 7.89 x 10-5 1.59 x 10-3 3.34 x 10-4 7.78 x 10-5 1.81 x 10-3 4.54 x 10-4 1.14 x 10-4 2.07 x 10-5 - 1.81 x 10-3 4.54 x 10-4 9.27 x 10-5 1.98 x 10-5 - 1.70 x 10-4 - 1.82 x - 1.14 x 10-4 1.51 x 10-5 1.56 x 10-7 2.82 x 10+ 6.70 x - 2.80 x 10-7 - 5.82 x 10-4 1.31 x lo-* 3.36 x 1.82 x lo+ 1.55 x 10-3 3.47 x 10-4 7.84 x 10-5 1.51 x 10-5 6.70 x 10-7 1.81 x 10-3 4.54 x 10-4 1.03 x 10-4 2.02 x 10-5 2.80 x 10-7 2.82 x 1.56 x lov7 AGp(g-+aq) as shown in table 16; the methylene increments are listed in table 4.Unfortunately there are too few AH? values2 to determine methylene contributions. The alkan-1-01s form a particularly important series of solutes. They have been studied a number of times, and the values of AGp(g ---* aq) have been used by Beezer and Hunter25 as an example of the alternation effect; that is, the alternation or oscillation of methylene increments along an homologous series.Beezer and Hunter25 used the old data of Butler et a[.,14-17 but there have been many subsequent investigations and it seemed essential to set out the best available values to date. Solubilities of the higher alcohols have been determined not only by Butler et al.14-17 but also by Amidon et U Z . , ~ Tewari et al. 30 and Kinoshita et aL41 The AGP(1iq as) values calculated directly from mole fraction solubilities are in table 17, together with values from Raoult's law activity coefficients given by Pierotti et ~ 1 . ~ ~ In order to convert these AGP (liq -+ aq) values into AGp(g -+ aq) it is necessary to know the166 THERMODYNAMICS OF SOLUTION IN WATER Table 16. Standard Gibbs energies of solution and of vaporisation of 1-halogenoalkanes, at 198 K" 1-halogenoalkane P/atmb AGg AGp(g + aq)" AG?(liq + aq)d chloromethane chloroethane 1 -chloropropane 1 -chlorobutane 1 -chloropentane 1 -chlorohexane 1 -chloroheptane 1-chloro-octane bromomethane bromoe t hane 1 -bromopropane 1 -bromobutane 1 -broniopentane 1 -bromohexane 1 -bromoheptane 1-bromo-octane iodomethane iodoethane 1 -iodopropane 1 -iodobutane 1 -iodopentane 1 -iodohexane 1 -iodoheptane I-iodo-octane 5.672 1.577 0.454 0.135 4.09 x 1.27 x 3.99 x 2.148 0.617 0.182 5.43 x 10-2 1.66 x 1.25 x 10-3 - 1.03 -0.27 0.47 1.19 1.89 2.59 3.27 3.96 - 0.45 0.29 1.01 I .73 2.43 3.72e 3.64g 3.94 4.1 1 (4.05)h 4.21 (4.26)h (4. 27)h 4.56 - 3.46e 3.54 3.71 3.87 4.18 5.13 x 1.61 x 5.00 x 0.533 0.179 5.67 x 1.82 x 0-3 3.12 4.4s 0-3 3.81 4.61 0-4 4.50 4.79 0.37 3.31 1.02 3.54 0 - 2 1.70 3.74 0-2 2.37 4.03 - 5.78 x 3.05 1.84 x I 0-3 3.73 - 5.92 x 10--4 4.40 4.54 1.84 x lo-* 5.10 __ 2.69f 3.37f 4.4 1 5.30 6.10 6.86f 7.83 - 3.01f 3.83 4.72 5.60 6.58 7.57 8.42 9.29 3.74-f 4.56 5.44 6.40 - 8.94 - a Standard states and units as in table 2.Ref. (27). Obtained from AGF(1iq + aq) and From the solubilities given in table 15 except where shown. D. N. Clew and E. A. Moelwyn-Hughes, Discuss. Faraday Soc., 1953, 15, 150. f From From Henry's law constants, D. T. Leighton Jr AGF except where shown. AGg(g + aq) and AGP. and J. M. Calo, J . Cheni. Eng. Data, 1981, 26, 382. ' Ref. ( I ) and (2). Table 17. Values of AGF(liq + aq) from mole fraction solubilities of alcohols, at 298 K ref: 14 42 8 41 30 values alcohol (1933) (1959) (1974) (1958) (1982) taken pen tan- 1 -01 3.19 3.04 3.19 3.19 3.57 3.19 hexan- 1-01 4.03 4.03 4.06 4.26 4.03 heptan- l-ol 4.85 - 4.85 4.88 5.03 4.85 5.58 octan- 1-01 5.58 5.5 1 5.58 5.69 nonan- l-ol - _.6.47 6.49 6.65 6.48 decan- 1-01 - 7.26 7.42 7.33 7.34 undecan- 1-01 - - - - - - 8.93 dodecan- l-ol - - 8.71 (8.93)" - - - - - a Given in ref. (46).M. H. ABRAHAM 167 vapour pressures of the alcohols at 298 K. These are quite well established for the alkan-1-01s up to h e p t a n - l - ~ l , l * ~ ~ but those for the higher alkan-1-01s are not so reliable. There have been several sets of determinations or evaluations of vapour pressures of a l k a n - l - ~ l s , ~ ~ - ~ ~ but only in the study by Davies and K ~ b e t t ~ ~ were temperatures close to room temperatures used.In table 18 are listed AG? values derived from the vapour pressures given by Rytting et aZ.19 and by Davies and K ~ b e t t . ~ ~ In other cases, the required AGP values have been obtained by interpolation of the (good) straight line plot of AGP against carbon number. For the lower alkanols, the solubility method is not appropriate, but Henry’s law constants have been obtained by several w o r k e r ~ . l ~ - ~ ~ ? l9 These are all in reasonable agreement and table 18 presents AGp(g --+ aq) values for the C, to C, alkan-1-01s derived from results of Rytting et a1.19 Table 18. Standard Gibbs energies of solution and of vaporisation of alkan-1-ols, at 298 Ka alkan- l-ol P/atmb AG? AGF(g --* aq)“ AGF(liq -+ aq)d methanol ethanol propan- 1-01 butan- 1-01 pentan- 1-01 hexan- l-ol heptan- 1-01 octan- l-ol nonan- 1-01 decan- 1-01 undecan- 1-01 dodecan- 1 -01 tridecan- 1-01 tetradecan- l-ol pentadecan- l-ol hexadecan- 1-01 octadecan- 1-01 0.1 672e 0.0776 0.0264 2.85 x 8.92 x 10-3 9.47 x 10-9 1.07 x 10-4i 1.20 x 10-5” - - 1.1 1 x 10-6” - 1.36 x 10-7“ - 1.57 x 1.06 1.51 2.15 2.80 3.47 4.13 4.799 5.42 6.099 6.7 I 7.40s 8.12 8.719 9.37 10.029 10.65 12.00s -0.83 - 0.73 -0.58 - 0.45 -0.30 -0.14 0.06h 0.18j 0.39h 0.63h 0.81h 0.54l 0.53h 0.27l 0.211 - - 0.23 0.78 1.57 2.35 3.17 (3.19)f 3.99 (4.03)f 4.89 5.60 (5.58)f 6.48f 7.34f 8.9Y - 9.91l (10.34)m 10.5P (1 1.03p 10.92l (1 1.93)m 12.21l (13.84)m a Standard states and units as in table 2.From ref. (19) and (43) except where shown.From AGF and AGp(g --* aq) except where shown. Ref. (45). From the mole fraction solubiIities in table 17. 9 Estimated from a plot of AGF against carbon number. From AG? and AGp(1iq -+ aq). G. Geiseler, J. Fruwert and R. Huetting, Chem. Ber., 1966. 99, 1594 [see ref. (45)]. j From a direct determination3? of Henry’s law constant. From the solubility of the solid Value of AGF(so1id -+ aq). From a corrected value of the solubility given in ref. (8). From Henry’s law constantslg except where shown. Ref. (43). corrected through eqn (9) and eqn (lo), see text. The solubilities of the solid alkanols, tetradecan-1-01, pentadecan- 1-01 and hexadecan- 1-01, have been determined by Amidon et aZ.,* who corrected the observed solubilities to the hypothetical solubilities of the liquid alkanols using literature values for enthalpies of fusion of the alkanols.More recently, Yalkowsky and V a l ~ a n i ~ ~ listed molar solubilities of the alkanol-1-01s as averages of literature values but gave no literature references. The listed46 values for tetradecan- 1-01 and pentadecan- 1-01 are the same as those given before (log S = -5.84 and -6.35, respectively),? but new t S is the solubility in mol dmP3.168 THERMODYNAMICS OF SOLUTION IN WATER values for hexadecan-1-01 (log S = 7.00) and octadecan-1-01 (log S = -8.40) were given. After recalculation to the mol fraction scale, these values lead directly to AGp(so1id --+ aq), and application of eqn (9) affords the required values of AGP(1iq + as). Unfortunately the various solid-solid transitions of these alkanols are not well documented and the only correction that can be applied is that of an ‘overall’ AHg value that includes any transition AH? values.For the alkanols tetradecan-1-01, hexadecan-1-01 and octadecan-1-01 such a correction has been made using the AHg and T, values given by Davies and K ~ b e t t . ~ ~ Another procedure is to calculate AG?(g + aq) through the equation AGP(g --+ aq) = AGP(so1id --+ aq) - AGgbl (10) where AGgbl is the standard Gibbs energy of sublimation of the solid at the experimental temperature, T. This method, whilst theoretically impeccable in that no solid-solid transitions need be considered, is subject to possibly large errors in AGg?,,, obtained as AGgbl = - R T h Psubl, where Psubl is the sublimation vapour pressure at temperature T, in atm.Davies and K ~ b e t t ~ ~ recorded &,l for the even alkan-1-01s and so it is possible to compare AGP(g --+ aq) obtained via eqn (10) with values obtained through eqn (9) together with eqn (2). These are, respectively, in kcal mol-1 : tetradecan-1-ol(O.51 and 0.57), hexadecan-l-ol(0.29,0.25) and octadecan-1-ol(O.41, 0.01). Considering that the first set of figures includes AGgbl, and the second set in- cludes not only the correction via eqn (9) but also an extrapolated value of AG?, agreement between the two sets of values is remarkably good. Table 18 gives AGP(g + aq) as average values of the two sets for the three even alkan-1-01s studied, and the value given by Amidon et aZ.* for pentadecan-1-01. Plots of AGP(g + aq) or AGp(1iq --+ aq) against N are reasonably linear for N = 3 to N = 12, but beyond dodecan-1-01 the AGP values become more negative than expected, so that, as for the n-alkanes, the very-long-chain alkan- 1-01s are more soluble in water than expected.This effect, possibly due to coiling of the alkyl chains,8 although large, is not of the same magnitude as for the n-alkanes. Thus n-octadecane is more stable in solution by 5.0 kcal mol-l, corresponding to an increased solubility by a factor of 4800, but octadecan-1-01 is more stable in solution by 1.65 kcal mol-l, corresponding to an increased solubility by a factor of only 16. Inspection of the results in table 18 for the C, to C,, alkanols indicates that any alternation effect must be within experimental error. In table 19 are set out three series of values for AGP(g + aq), the original ones of Butler et aI.,l7 the more recent values of Amidon et aL9 and those from table 18.The slight alternation effect observed by Beezer and Hunter2, in the results of Butler et al. is not found at all with the results on the C , to C, alkanols from table 18. Enthalpies of solution of the alkanols have also been studied by several sets of w o r k e r ~ . ~ ~ - ~ ~ The usual method is to obtain AHp(1iq -+ aq) by direct calorimetry and to combine this with AH? to yield AHP(g --+ as). Fortunately, AH? values are well known,29 and there is good agreement between at least four sets of calorimetrically determined AHP(1iq + aq) values for the C , to C , a l k a n - l - ~ l s ~ ~ - ~ ~ and three sets of AH? values for pentan-1 For hexan- l-ol and heptan- l-ol, Hill and White53 have obtained AHp(liq --+ aq) both by calorimetry and by the temperature variation of solubility, and from a graph given by Hill and White53 a value of - 0.76 kcal mol-1 for AHp(liq + aq) for octan-1-01 may be deduced.has obtained a value of AHp(1iq --+ aq) from the temperature variation of the solubility of dodecan- 1-01 but unfortunately gives no numerical data: from an expanded reproduction of a graphM. H. ABRAHAM 169 Table 19. Examination of the alternation effect in AGp(g --+ as) for alkan- 1 -01s’ at 298.1 5 K alkan-1-01 Butler et a1.l’ Amidon et aL9 this work methanol ethanol propan- l-ol - 0.57 butan- l-ol - 0.44 pentan-1-01 -0.21 I hexan- l-ol heptan- 1-01 octan- l-ol 0.17 nonan- 1-01 decan- l-ol - 0.10 0.17 0.13 0.23 0.12 0.12 0.14 0.72 0.21 0.13 0.22 0.21 -0.28 0.33 0.38 0.26 -0-83 1 -0.73 \ I -0.45 \ -OS8 1 0.63 0.10 0.15 0.13 0.15 0.16 0.20 0.12 0.21 0.24 in Benjamin’s paper, a value of 2.60 kcal mol-l was estimated.? The AHp(g -+ aq) and AHP(1iq + as) values are set out in table 20.Benjamin4, showed that in a plot of AHp(liq + aq) against carbon number, points for the first three or four alkanols did not fall on the more-or-less straight line from butan-1-01 to dodecan-1-01. An equivalent graph constructed by Hill and White, however, is clearly a continuous curve with no straight section at all. However, from the numerical data in table 20, it seems that for the C, to C , alkan-1-01s it is possible to construct a reasonable straight line.It is rather unfortunate that the main outlying point, for dodecan-1-01, is derived from Benjamin’s graph and not from results of any rigorously presented experiment. On the assumption that the C , to C , alkan-1-01 points do lie on a straight line, the methylene increments listed in table 4 have been calculated. The solubilities of a very large number of esters have been determined,l. 2 y 3 0 7 39 but there are only four series of these compounds for which a reasonable number of homologues have been studied. Buttery et aZ.37 determined Henry’s law constants for a series of methyl alkanoates, leading to AGp(g --+ as), and combination with AGP values obtained from several ~ o u r c e s ~ ~ ~ 54* 55 leads to AGP(1iq + as). The latter are in reasonable agreement with values derived from sol~bilities~~ of the liquid esters.In addition, Tewari et al.,O have recorded solubilities of the higher esters, methyl nonanoate and methyl decanoate, leading to the various AG? values as set out in table 21. Kieckbusch and King56 have determined Henry’s law constants for several n-alkyl acetates, from which the various AGP values may be obtained, see table 22. There t Note ihat numerical values of AHP(1iq + aq) from Benjamin4’ or from Hill and White53 are often quoted, but Benjamin gives no numerical values at all, and Hill and White numerical values for only hexan- 1-01 and heptan- 1-01.170 THERMODYNAMICS OF SOLUTION IN WATER Table 20. Standard enthalpies and entropies of solution and of vaporisation of alkan- 1 -ols, at 298 Ka A€€?- AH?- A*- Ah?- alkan- 1-01 AH$'b (g --+ aq)" (liq --* aqId A* (g --+ aq) (liq -+ aq) methanol ethanol propan- 1-01 butan-1 -01 pentan- l-ol hexan- 1-01 heptan- l-ol octan-1-01 nonan- l-ol decan- 1-01 undecan- 1-01 dodecan- 1-01 8.95 10.10 11.35 12.51 13.61 14.75 15.97 16.96 18.37 19.48 20.688 21.98 - 10.69 - 12.53 - 13.77 - 14.73 - 15.46 - 16.30 - 17.24 - 17.72 - 1.74 - 2.43 - 2.42 - 2.22 - 1.85 - 1.55" - 1.27" - 0.76f - - 19.38 - 2.60h 26.5 28.8 30.8 32.6 34.0 35.6 37.5 38.7 41.2 42.8 44.5 46.5 - 33.1 - 39.6 -44.2 - 47.9 - 50.8 - 54.2 - 58.0 - 60.0 - - 6.6 - 10.8 - 13.4 - 15.3 - 16.8 - 18.6 - 20.5 -21.3 - - 67.0 - 20.5 a Standard states and units as in table 3. Average values from ref. (49)-(52), unless shown otherwise. Ref. (29). From AH$' and AH?(liq --* as).Average of values in ref. (53) obtained by calorimetry and temperature variation of solubility. f Taken from a graph given in ref. (53). 8 Interpolated value from a plot of AH$' against carbon number. Taken from a graph given in ref. (47). Table 21. Standard Gibbs energies of solution and of vaporisation of methyl alkanoates, at 298 Ka methyl alkanoate P/atmb AG? AG?(g -+ aq)' AGP(1iq -+ aq)d methyl formate methyl acetate methyl propanoate methyl butanoate me thy1 pent anoate methyl hexanoate methyl heptanoate methyl octanoate methyl nonanoate methyl decanoate 0.822 0.2845 0.1136 4.24 x - 4.29 x 10-3 5.25 x 10-4 - 6.44 x 10-5 0.12 0.74 1.29 1.87 2.54-f 3.15 3.82f 4.47 5.08f 5.72 1.49 1.10 1.34 1.44 1.70 1.78 2.23 2.588 3.059 - 1.61 1.84 (1.67)e 2.63 (2.51)" 3.31 (3.44)e 4.24 4.93 6.70 - (7.66)h (8.77)h a Standard states and units as in table 2. From ref. (I), (46), (54) and (55). Ref. (37), From AG$' and AG?(g -+ aq) f Estimated from a plot of AG$' From solubilities of the liquid except for methyl formate, ref. (2), from Henry's law constants. except where shown. against carbon numbers. From solubilities of liquid From AG$' and AG?(liq + as). is reasonable agreement between the indirectly determined AGP(1iq -+ aq) values and those calculated from solubilities of the liquid esters.'* 30- 57 For a rather long series of ethyl alkanoates, on the other hand, it is the liquid ester solubilitiesl9 39 that lead to a prime set of AG?(liq -+ as) values. There are only a limited number of AG? values available,lY 4 5 9 58 but it is possible to obtain the remaining valuesM.H. ABRAHAM 171 Table 22. Standard Gibbs energies of solution and of vaporisation of n-alkyl acetates, at 298 Ka n-alkyl acetate P/atmb AGF AGF(g + aq)" AGP(1iq --* aq)d methyl acetate 0.2845 0.74 1.16 1.90 (1.67)" - (1.59)g n-propyl acetate 4.438 x 1.85 1.48 3.33 (3.28)" (3.33)s (3.30)s n-butyl acetate 1.45 x lop2 2.51 1.63 4.14 (4.25)" (4.07)f (4.13)g n-pentyl acetate 5.39 x 10-3 3.09 1.76 4.85 (4.92)" - (4.90)g ethyl acetate 0.1244 1.23 1.33 2.56 (2.43)" (2.57)s - a Standard states and units as in table 2. Ref. (1) and (55). From directly determined From AGF and AGp(g + aq); values in parentheses are from Henry's law constants.56 solubilities of the liquid esters. Ref. (1). f Ref. (30).9 Ref. (57). "able 23. Standard Gibbs energies of solution and of vaporisation of ethyl alkanoates, at 298 Ka ethyl alkanoate P/atmb AGV AGg(g -, aq)" AGP(1iq + aq)d ethyl formate ethyl acetate ethyl propanoate ethyl butanoate ethyl pentanoate ethyl hexanoate e thy1 hep tanoa te ethyl octanoate ethyl nonanoate ethyl decanoate 0.3218 0.67 0.1244 1.23 4.89 x 1.79 1.98 x 2.32 6.32 x 10-3 3.00 8.95 x 10-4 4.16 - 3.568 -_ 4.74s - 5.339 - 5.929 1.70 1.33" 1.59 1.77 1.77 2.03 1.95 2.26 2.23 2.04 2.27 2.56" (2.57)f 3.38 (3.51)s 4.09 4.77 5.59 6.1 1 7.00 7.56 7.96 a Standard states and units as in table 2. Ref. (l), (46) and (58). From AGF and From solubilities of the liquid esters'. 39 except where Estimated from plots of AG$? against carbon number. AGp(1iq --* aq) except where shown.shown. From table 22. f Ref. (30). from plots of AGF against carbon number, see table 23. A much shorter series of n-alkyl propanoates can also be constructed, see table 24. In all four series of esters, the methylene increments are not as regular as in most of the other series, but there seems to be no unusual effects in AGp(g -+ as) or in AGp(liq + as). There are a few esters for which values of AHp(liq + as) have been determined calorimetrically, and in table 25 are given results of Della Gatta et aL40 for a series of methyl alkanoates. The only other homologous series for which enthalpy data is available is that of the n-alkyl acetates, but values of AHF(1iq -+ as) given by Richon and Viallard59 and by Cross and McTigueGo are not in good agreement, viz, respectively, methyl acetate (- 2.11, - 1.70), ethyl acetate (- 2.35, - 2.09), propyl acetate (-, - 1.90) and butyl acetate (- 2.24, - 1.87), all in kcal mol-1 at 298.15.f.There have been several investigations into the solution of alkanoic acids in water,48* 6 4 9 65 but there are considerable difficulties in interpretation of results due to t The value for propyl acetate is at 297.05 K. Note also other values for methyl acetate ( - 1.87 kcal mol-I) (table 25), and ethyl acetate ( - 2.23,61 -2.346* and - 2.3663 kcal mol-l).172 THERMODYNAMICS OF SOLUTION IN WATER Table 24. Standard Gibbs energies of solution and of vaporisation of n-alkyl propanoates, at 298 Ka n-alkyl propanoate P/atmb AG? AGF(g -+ aq) AG?(liq + aq) methyl propanoate 0.1136 1.29 1 .34c 2.63c ethyl propanoate 4.89 x 1.79 1 .59d 3.38d n-propyl propanoate 1.79 x 10+ 2.38 1 .83e 4.21f n-butyl propanoate 5.55 x 10-3 3.08 - - n-pentyl propanoate 3.87 x 10-3 3.29 2.1 6e 5.49 a Standard states and units as in table 2.From AGF and AG?(liq + aq). f Ref. (1). Ref. (l), (46) and (58). Table 21. Table 23. Table 25. Standard enthalpies and entropies of solution and of vaporisation of methyl alkanoates, at 298 Ka AH?- AH?- A@- A*- methyl alkanoate AH? (g -+ aq) (liq + aq) A* (g + aq) (liq + aq) methyl acetate 7.57 -9.44 -1.87 22.9 - 35.3 - 12.4 methyl propanoate 8.61 - 10.68 -2.07 24.5 - 40.3 - 15.8 methyl butanoate 9.58 -11.50 -1.92 25.9 - 43.4 - 17.5 methyl pentanoate 10.59 -12.33 -1.74 27.0 - 47.1 - 20.1 a Standard states and units as in table 3. All data on enthalpies from ref.(40). Table 26. Enthalpies of solution and of vaporisation of alkanoic acids, at 298 Ka AH? AH?(g+Wb alkanoic acid Id IIe If 11s AHg(1iq + as)" methanoic acid ethanoic acid propanoic acid butanoic acid pentanoic acid hexanoic acid heptanoic acid octanoic acid 11.1 12.3 13.1 13.9 14.9 17.5 17.2 19.8 10.93 12.00 13.08 14.15 15.23 16.30 17.38 18.45 -11.3 - 12.6 - 13.5 - 14.2 - 15.0 - 17.3 - 16.8 - 19.1 - 11.09 - 12.28 - 13.45 - 14.50 - 15.32 - 16.08 - 16.96 - 17.75 -0.16 - 0.28 - 0.37 -0.35 - 0.09 0.22 0.42 0.70h a Standard states and units as in table 3; all values refer to the monomeric alkanoic acids. From AH$? and AHF(1iq + aq). Ref. (48) and (65). Observed values from ref. (65) and (67), corrected where necessary to vaporisation to monomeric acid.Smoothed values from a plot of AH? against carbon number, table 27. f From AHg(1) and AH?(liq + as). g From AHF(I1) and AHP(1iq + as). Estimated value.M. H. ABRAHAM 173 dimerisation of the acids in the vapour phases5-s7 and possibly also in aqueous The latter is not so much of a problem, and AHP(1iq -+ aq) values are known for all the n-alkanoic acids up to heptanoic 65 Dimerisation in the vapour phase, however, is extensive especially for the lower acids (acetic acid for example is 90% associate6 at 298 K)ss, but Konicek and Wadsos5 have corrected observed AHv values to vaporisation from the liquid to the gaseous monomer, and de Kruif and Oonks7 have obtained the required AH? values for the homologues pentanoic to octanoic acid. In table 26 are set out the various enthalpies of solution of the pure liquid and the monomeric gaseous acids.There are unfortunately not enough data on AGP valuess4 to construct a reasonable series of homologues. Inspection of table 26 shows that, as in the case of the alkan-1-ols, the AHP(1iq -+ aq) values for the lower homologues are more positive than expected. It is not so easy to discern such a trend in the AHP(g -+ aq) values because the observed AH? values are subject to considerable random error. However, de Kruif et aLs8 have determined AH? values for a large number of the higher n-alkanoic acids. A plot of AH? against N is linear from N = 1 to N = 15, and if smoothed values of AH? are obtained from such a plot, the resulting AHp(g + aq) values show exactly the same trend as do the AHp(1iq -+ aq) values, see table 26.Wadso et aZ.69 have obtained values of AH?, AHp(liq + aq) and AHp(g --* aq) for two series of difunctional compounds, ROCH,CH,OH and ROCH,CH,OMc (where R = methyl, ethyl, n-propyl and n-butyl), but neither series is extensive enough to ascertain if the methylene increments are constant or not. However, in a related series of RO(CH,CH,),H (where R = H, ethyl, n-butyl, n-hexyl, n-octyl, n-decyl and n-dodecyl) the methylene increment in AHP(1iq + aq) is definitely not constant but varies in quite a similar manner to AHP(liq -+ aq) for the alkan-1-01s. The solubiluty of a similarly extensive series of n-alkyl p-aminobenzoates has been determined by Yalkowsky and Valvani ;46 for the homologues methyl to n-dodecyl (except the n-decyl and n-undecyl compounds) the methylene increment for solution of the solid esters is constant at 0.82 kcal mol-l, a value quite comparable to those of AGP(1iq + aq) for the various series in table 4.DISCUSSION THERMODYNAMICS OF VAPORISATION The parameters for vaporisation in the various homologous series are quite linear with respect to carbon number, N . Regression equations for AG?, AH? and A* against N are collected in table 27; the correlation coefficients and standard deviations indicate that these simple equations are good enough for the estimation of vaporisation parameters within any homologous series. Indeed, if a datum point deviates signifi- cantly from the regression equation, it is almost certainly due to experimental error.7 The slopes of these regression equations differ from series to series because of the different solute-solute interactions in the pure liquid state, so that it is not possible to construct a generalised equation in, say, AG? that will cover all the homologous series.Because AG? and AH? are both linear in N , it follows that AH? is linearly related to AGP in any given series. This is the condition for the so-called compensation phenomenon to a ~ p l y , ~ ' ~ 72 and wherever reasonable sets of AH? and AGP values are available, there is found an excellent linear relationship. The slopes of the regression t Except for the first member of the homologous series, where the vaporisation parameters do often deviate from the given regression equations.174 THERMODYNAMICS OF SOLUTION IN WATER Table 27.Regression equations for thermodynamic parameters of vaporisation regression equation ra n-alkanes AG? = - 3.2802 + (0.7027 & 0.001 5) N AH? = 0.06424-(1.2247 k0.0125) N A* = 11.221 +(1.7502&0.0373) N alk- 1 -enes AG? = -3.4768+(0.7146&0.0026) N AH? = 0.1832+(1.1861 k0.0066) N AS$' = 12.276+(1.5812f0.0183) N alk- 1 -ynes AG? = -2.9281 +(0.6504&0.0185) N AH? = 2.2355 + (0.891 7 k 0.0387) N AS? = 17.319+(0.8094&0.1268) N n-alkylbenzenes AG? = 1.2576+(0.6601 kO.0058) N AH? = 7.6490+(1.1263f0.0201) N AS? = 21.437 + (1.5636 & 0.0720) N n-alkylamines AGF = - 1.4759 + (0.6595 & 0.0074) N AH? = 4.1222+(1.1091 k0.0139) N AS? = 18.776+(1.5080&0.0591) N alkan-2-ones AGF = - 1.2321 +(0.6192&0.0043) N AH? = 3.7771 +(1.0790+0.0292) N AS? = 16.801 +(1.5423+0.1034) N 1 -chloroalkanes AG? = - 1.6469 + (0.7036 k 0.0042) N AH? = 3.2815+(1.1768f0.0051) N AS? = 16.530 + (1.5868 k 0.03 1 1) N 1 -bromoalkanes AG? = - 1.0968+(0.7019~0.0030) N AH? = 4.0949 + (1.I837 & 0.0059) N AS? = 17.413+(1.6161 k0.0297) N 1 -iodoalkanes AGF = -0.3377 + (0.6783 & 0.0009) N AH? = 5.1604+(1.1465+0.0115) N AS? = 18.440+(1.5703f0.0374) N alkan- 1-01s AG$' = 0.1912+(0.6552f0.0019) N AH? = 7.6911+(1.1863+0.0067) N AS? = 25.155+(1.7813+_0.0213) N 1 .oooo 0.9995 0.9980 1 .oooo 0.9999 0.9997 0.9984 0.9962 0.9542 0.9998 0.9990 0.9937 0.9997 0.9997 0.9969 0.9999 0.9978 0.9868 0.9999 1 .oooo 0.9990 1 .oooo 0.9999 0.9992 1 .oooo 0.9997 0.9986 1 .0000 0.9998 0.9985 sb nc solute ranged 0.020 0.130 0.391 0.0 14 0.035 0.097 0.078 0.162 0.530 0.037 0.130 0.466 0.03 1 0.058 0.247 0.028 0.189 0.670 0.022 0.027 0.165 0.0 16 0.03 I 0.157 0.004 0.061 0.198 0.027 0.098 0.310 13 ethane to n-tetradecane 11 ethane to n-dodecanee 1 1 7 but-1-ene to dec-1-end 7 7 6 but- 1 -yne to non- 1 -yne 6 6 8 ethylbenzene to n-nonyl- 8 8 benzend 6 ethylamine to n-heptyl- 6 6 amine 8 butan-2-one to undecan- 8 8 2-ones 7 1-chloroethane to 1 -chlorooctanee 7 7 7 1-bromoethane to 1 -bromooctanee 7 7 7 1-iodoethane to 1-iodo- 7 7 octanee 12 ethanol to hexadecan- 12 12 1 -olhM.H. ABRAHAM Table 27. (cont.) 175 methyl alkanoates AGV = -0.65 17 + (0.6374 & 0.0045) N 0.9999 AH? = 5.4534 + (1.0347 k 0.0071) N A S = 20.447 + (1.3324 & 0.0251) N 0.9999 0.9993 n-alkyl acetates AG? = -0.01 39 + (0.6242 & 0.0099) N 0.9998 AG? = 6.5050+(0.9750+0.0116) N 0.9999 AS? = 21.864 + (1.1765 k 0.0293) N 0.9994 ethyl alkanoates AG? = 0.0282+(0.5888 kO.0110) N 0.9995 n-alkyl propanoates AG? = 0.7776 + (0.5294 k 0.0424) N 0.9905 n-alkanoic acids AH? = 9.8538 + (1.0747 & 0.01 22) N 0.9994 0.026 0.042 0.146 0.022 0.026 0.065 0.042 0.134 0.201 6 methyl propanoate to 6 6 methyl decanoatei 4 ethyl acetate to n-pentyl 4 4 aceta teb 5 ethyl acetate to ethyl heptanoa te 5 methyl propanoate to n-pentyl propanoate 11 methanoic acid to penta- decanoic acidi a Correlation coefficient.Standard deviation, defined as (b(obs.) -y(calc.)12/(n - 2)}:. All values for the solutes taken from Additional AH? values from ref. (27). f Additional Additional Additional AH: values from R.Fuchs and L. A. Peacock, Can. Number of solutes used in the regression equation. previous tables, unless shown otherwise. AG? and AH? values from ref. (27). AH? values from ref. (29). J. Chem., 1980, 58, 2796. j Additional AH? values from ref. (68). Additional AH? values from ref. (35). equations differ from one homologous series to another, and therefore there is no common compensation temperature, p, amongst these series. Furthermore the standard deviations in AH? from plots of AH? zgainst AG? are usually rather larger than the standard deviations from plots of AH? against N , so that for the prediction of new AH? values, the latter plots are generally to be preferred. THERMODYNAMICS OF SOLUTION For nearly all the homologous series, there are found excellent linear plots of AGP or AH? against N , as summarised in table 4.Before considering the important deviations from such linearity, it seemed first useful to discuss the information that can be derived from the linear regression equations in table 4. The slopes of the regression equations represent the contribution of a methylene group to the particular process considered; thus for solution of the n-alkanes from ethane to n-octane, the methylene contribution to AGP(g -+ aq) is 0.178 kcal mol-l, and to AGP(1iq --+ aq) is 0.887 kcal mol-l. As shown in the introduction, the difference between these two quantities is due to solute-solute interactions in the pure liquid, and in order to concentrate only on solute-solvent interactions it is the term AGp(g -+ aq) that must be considered.This is even more evident for enthalpies of solution, because for most of the homologous series listed in table 4 AH?(g -+ aq) is negative but AH?(liq --+ aq) is positive. Of course, the regression equations in AGP(1iq -+ aq) or in AHP(liq -+ aq)176 THERMODYNAMICS OF SOLUTION IN WATER can be used to correlate and to predict values just as well as the corresponding equations for the process g -+ aq, the standard deviations between calculated and observed values being about the same for the liq -+ aq regression equations and the g -+ aq equations, see table 4.f It follows from the very good linear regression of AGP and AH? with N , that if a liq -+ aq regression equation is linear in N then so will be the respective g -, aq regression equation and vice versa.Which process will lead to the best fit, in terms of the standard deviation, depends to a large extent on the nature of the experimental observations. Thus if AGp(g -+ aq) is determined directly through Henry’s law constants, the fit of the AGp(g -+ aq) regression equation will be better than the indirectly determined AGp(liq -+ aq) regression, as is the case for the methyl alkanoates and n-alkyl acetates (see table 4). If, on the other hand, it is the AGP(1iq --* aq) values that have been directly determined through solubilities of the liquid solutes, then the fit of the AGp(liq -+ aq) regression equation will be better than that of the indirectly determined AGp(g -+ aq) regression, see for example the ethyl alkanoate regressions in table 4.There are available enough results on extended homologous series to test the possibility of alternation effects on the methylene contributions, as outlined for alkan-1-ols, see table 19. In any given series, methylene contributions will fluctuate around a mean value merely through experimental error, and it is to be expected that such fluctuations will lead to alternation effects purely on a statistical basis. Thus for a series of say, six consecutive methylene contributions, three of which are higher than the average (H) and three of which are lower than the average (L), the alternation sequences HLHLHL or LHLHLH will occur by chance in about one case out of ten, and ‘partial’ sequences such as LHLHHL in one case out of three. In my view, all the alternation effects shown in the various homologous sequences studied in this work can be regarded as arising through random experimental error.This in no way contradicts the observation of Beezer and of alternation effects in a bifunctional homologous series, for partition between water and octan- 1-01. In order to probe solute-water interactions, it is necessary to deal only with parameters for the g -+ aq process. Wolfenden and Lewis4 first reported on methylene contributions to AGp(g -+ aq) for a series of homologous compounds. Although the contribution did vary somewhat from one series to another, Wolfenden and Lewis regarded this variation as being within experimental error,$ and calculated an overall methylene contribution of 0.150 kcal mol-l. From the more extensive data given in table 4 and summarised in table 28, it seems that the variation in methylene contribution is outside experimental error, ranging from 0.099 f 0.019 (ethyl alkan- oates) or 0.146 k 0.003 (n-alkyl benzenes) up to 0.229 k 0.008 (alkan-2-ones) or 0.247+0.010 (alk-1-ynes), in Gibbs energy.There is less information on the en- thalpic methylene increment, see tables 4 and 29, but there is substantial variation in the contribution to AHp(g -+ aq), viz. from - 0.673 f 0.035 (n-alkanes) to -0.915f0.02 (n-alkyl benzenes). A number of schemes for the estimation of AGp(g -+ aq) or AHp(g -+ aq) have been constructed on the basis of constant group contributions,lP 2 v 74 and variation of methylene contribution from one series to another might seem to negate such schemes.However, unless long-chain homologues t The correlation coefficients for the regression equations in ACP(1iq + aq) are nearly always better than the coefficients for equations in AGp(g -+ aq), but this merely reflects the larger values of the slopes in the AGP(1iq -+ aq) regression equations. For comparison purposes, the standard deviation is a better ‘goodness-of-fit ’ parameter than the correlation constant, at least in the present case. The extreme limits were 0.137 +_ 0.094 kcal mol-I for n-alkanes and 0.179 +_ 0.078 kcal mol-’ for n-alkyl acetates .M. H. ABRAHAM 177 Table 28. Methylene and group contributions to AG? values for homologous series, in kcal mol-1 at 298 K CH, incrementa group contribution* AG?(g -+ aq) AG?(liq -+ aq) group nc AG?(g+aq) series n-alkanes alk- 1 -enes alk- 1 -ynes n-alkylbenzenes n-alkylamines alkan-2-ones 1 -chloroalkanes 1 -bromoalkanes 1 -iodoalkanes alkan- 1-01s methyl alkanoates n-alkyl acetates ethyl alkanoates n-alkyl propanoates 0.178 0.150 0.247 0.146 0.144 0.229 0.163 0.219 0.200 0.163 0.226 0.144 0.099 0.186 0.887 0.876 0.900 0.809 0.799 0.848 0.870 0.920 0.876 0.822 0.855 0.768 0.688 0.680 CH3 C6H5 NH2 CH,=CH CHEC CH,CO c1 Br I HO MeO. CO CH,CO, EtO.CO CH,CH,CO, 7 7 7 6 7 8 6 7 4 9 8 4 9 3 3.03 k0.02 2.40 f. 0.1 1 0.79 k 0.05 0.44 f 0.01 - 3.42 f 0.01 - 2.72 f. 0.05 0.52 f 0.07 0.26 _+ 0.05 0.33 f 0.04 - 3.96 f. 0.04 - 2.00f 0.12 - 1.84+0.01 -1.54k0.14 - 1.61 & 0.03 a Taken from the regression equations in table 4. Calculated on the basis of a constant Number of members of the homologous series used methyl contribution of 3.03 kcal mol-I.to obtain the given group contribution. Table 29. Methylene and group contributions to AH? and A@ values for homologous series, in kcal mol-, or cal K-I mo1-I at 298 K CH, incrementa group contributionb series AHg(g -, aq) AH?(liq + aq) group nc AHg(g-+aq) n-alkanes -0.673 0.623 n-alk ylbenzenes -0.915 0.070 n-alk ylamines - 0.725 0.368 alkan-2-ones -0.818 0.210 alkan- 1-01s - 0.85 1 0.297 methyl alkanoates - 0.825 0.165 n-alkanoic acids -0.814 0.262 A@& -+ as) A W i q -+ aq) CH3 C6H5 NH2 CH,CO HO Me0 . CO H0,C group n - 2.36 f 0.07 - 6.32 k 0.02 - 9.64 _+ 0.09 - 7.64 0.10 - 9.74 f 0.06 - 7.49 0.01 - 10.51 f0.03 A*(g -+ 4 ) n-alkanes - 2.83 - 0.88 CH3 6 -18.1k0.2 n-alk ylbenzenes - 3.50 - 2.30 C6H5 3 -22.7k0.1 n-alk ylamines -2.89 - 1.46 NH2 5 -20.9k0.3 alkan-2-ones - 3.56 - 2.21 CH,CO 5 -16.4f0.4 alkan-1 -01s - 3.39 - 1.75 HO 5 -19.4kO.2 methyl alkanoates - 3.40 -2.15 Me0 .CO 3 -18.7k0.2 a Taken from the regression equations in table 4. Calculated on the basis of a constant methyl contribution of - 2.36 kcal mol-l to AHF(g + aq) and of - 18.1 cal K-I to A@(g + aq). Number of members of homologous series used to obtain the given group contribution.178 THERMODYNAMICS OF SOLUTION IN WATER are considered, any error due to the assumption of a constant methylene increment is probably within the claimed accuracy of the schemes put f0rward.f. The great advantage of the postulate of the constancy of group contributions is that it enables quantitative measures of group-water interactions to be calculated. In the present work it is clearly not logical to regard the methylene contributions as constant, but if the methyl contribution to solution of the gaseous n-alkanes is taken as constant, then other group contributions may be obtained.$ Group contribution values obtained in this way are in tables 28 and 29; because the basis for the calculation is not the same as in the schemes previously reported,l! 2, 73 the numerical values of the group contributions are not the same.However, in all the group or atomic contribution schemes, hydrophilic groups such as NH,-, HO-, RC0,- etc. all make negative contributions to AGP(g -+ aq) as expected. What is remarkable about the results in table 29 is that both hydrophobic groups (CH,, C6H5) and hydrophilic groups (CH,CO,NH,,OH) are transferred from the gas phase to aqueous solutions exo- thermally.Gianni et aZ.73 have suggested that there is a clear separation between AH? for hydrophobic and hydrophilic groups, but the results in table 29 do not bear this out: compare for example values for the C6H5 group and the NH, group. For the homologous series (table 4) for which both AGP(g -+ aq) and AHP(g -+ aq) values are available, there are good linear correlations between these two quantities, demonstrating the existence of the compensation effect. As for the corresponding vaporisation parameters, the slopes of the plots of AH? against AGP vary from one series to another, so that no general conclusion can be drawn about the mechanism of the solution process.ANOMALOUS SOLUTION EFFECTS In a number of the homologous series, linearity of AGF or AH? with respect to carbon number, N , is not completely observed. For the alkan- 1 -ols, there is a deviation from linearity at low carbon number both in AGP and in AH? as has been pointed out b e f ~ r e , ~ ~ ? ~ ~ and for the alkanoic acids there is also a similar deviation in AH?; unfortunately there is not enough information to determine AGP values for an extended series of alkanoic acids. The origin of these effects is not clear, but may be due to incorporation of the small, hydrophilic solutes into the general water structure. More important are deviations as N becomes very large. Tanford22 has discussed this effect in connection with the related transfer of alkanoic acids from heptane to water and concludes that AGP (heptane + aq) is linear with N up to a carbon number of at least 22.In the present work, results on AGF values for two series of compounds, the alkan-1-01s and the n-alkanes, indicate that linearity with N is not maintained for values of N above ca. 12. The effect in the alkan- 1-01 series is not so large ; octadecan- 1-01 is 16 times as soluble as expected, from the linear regressions in table 4, but should the effect continue above octadecan- 1-01, the deviation factor will become progressively larger. For the g -+ aq transfer, the methylene increment from tetradecan-1-01 to octadecan-1-01 is -0.1 kcal mol-l, each extra methylene group now increasing the alkanol solubility.If the enhanced solubility is due to coiling of the long alkyl chains, with methylene-methylene interactions replacing methylene-water interactions, the methylene increment when coiling takes place might be expected to be intermediate between the methylene-water contribution in the lower alkan-1-01s (+ 0.16 kcal t In the scheme of Hine and Mookerjee', the standard deviation between calculated and observed AGp(g + as) is 0.16 kcal mol-I, in the scheme of Cabani et al.,* it is 0.17 kcal mol-I for AGp(g + aq) and 0.40 kcal mol-I for AHF(g + aq), and in the differentiated atom scheme of Gianni et uI.,'~ it is 0.55 and 0.76 kcal mol-I, respectively. $ Note that all gas-to-water standard-state effects are included in the methyl contribution.2+ l3M.H. ABRAHAM 179 mol-l) and the methylene-methylene contribution for solution of n-alkyl chains in n-alkanes. The methylene increment to AGP for solution of gaseous n-alkane in solvent n-hexadecane is -0.74 kcal mol-l* l3 and so a net value of -0.1 kcal mol-l for the higher alkan- 1-01s is not unreasonable. The deviations for the solution of the n-alkanes in water above about n-dodecane are very much larger in magnitude, the C,, compound, n-octadecane, being 4.9 x lo3 times as soluble as expected (cf. the factor of only 16 for octadecan-1-01). For the n-alkanes between n-hexadecane and n-hexatriacontane, there is a good correlation of AGP(g -+ aq) with N , the slope being - 0.92 kcal mol-l. This methylene contribution is even more negative than that for solution of n-alkanes in n-hexadecane, so that it is easier to introduce a methylene group into a hydrocarbon-like volume surrounded by water (i.e.the coiled n-alkane) than it is into pure hydrocarbon.7 It is possible to compare the solution of n-alkanes in water with solution in non-aqueous solvents. Pierotti et al.42 have recorded activity coefficients for n-alkanes up to eicosane (C,,) in ethanol and up to triacontane (C3,,) in phenol, from which AGF (g + solvent) values may be obtained using the AGF values in table 2; for the g+ethanol transfer, additional AGp(g + solvent) values are a~ai1able.l~ With both solvents the AGp(g -+ Table 30. Comparison of the mol fraction solubility of n-alkanes in water and in ethanol and phenol, at 298 K AGp(g + solvent) solubility factora alkane waterb ethanolc phenold ethanol/water phenol/water methane ethane propane butane pentane hexane heptane octane nonane decane undecane dodecane tetradecane hexadecane octadecane eicosane, C,, hexacosane, c 2 6 triacontane, C3, hexatriacontane, '36 - 6.28 3.95 6.1 1 2.98 6.23 2.33 6.35 1.65 6.6 1 1.15 6.82 0.52 6.90 -0.13 7.16 - 0.66 7.42 - 1.25" 7.44 - 1.77 7.66f - 2.44e 7.72 - 3.03" 6.64 - 4.22e 5.88 - 5.39 3.88 - 6.60" 2.19 - 7.80 - 3.25 - 1 1.35e - 13.73" 12.55 - 17.30" - 3.26" 2.63e 2.00" 1.37 0.66 0.07 - 0.52" - 1.15" - 1.71 - 2.40 - 3.03 - 4.29e - 5.47 - 6.80" - 8.01 - 1 1.83" - 14.42 - 18.12" 5.1 x lo1 2.0 x 102 7.2 x lo2 2.8 x 103 1.0 x 104 4.1 x 104 1.4 x 105 5.4 x 105 2.5 x 107 7.6 x 107 9.1 x 107 4.8 x 107 2.1 x 107 3.0 x 103 2.3 x lo6 5.6 x lo6 1.8 x lo8 8.6 x lo5 - 1.2 x 102 4.4 x 102 1.5 x 103 6.9 x 103 3.3 x 104 1.0 x 105 4.3 x 105 2.4x 107 7.6 x 107 6.7 x 107 3.0 x 107 1.2 x 104 1.9 x lo6 5.1 x lo6 1.0 x 108 2.1 x 108 1.9 x lo6 - a Mole fraction solubility of gas (or liquid) in ethanol or phenol/mole fraction solubility of gas (or liquid in water).From table 2. Ref. (1 3) and (42). Ref. (42). Estimated from linear plots of AGF against carbon number. f This is the value calculated from the regression in table 4. The observed value, 8.25 kcal mol-I, (table 2) seems much to high. t An alternative possibility to the coiling of long alkyl chains is the formation of micelles in aqueous solution. However, the solubilities of the solid n-alkanes at 298 K seem far too small for micellar formation, for example 6 x mol dmP3 (eicosane) or 4 x loP9 mol dmP3 (hexacosane). 7 FAR 1180 THERMODYNAMICS OF SOLUTION IN WATER solvent) values are accurately linear with N and hence other values for the n-alkanes may be estimated with reasonable certainty up to triacontane, and probably well beyond.The various g + solvent transfer values are collected in table 30 and are then combined to yield solubility factors that represent the enhanced solubility of alkanes in ethanol or phenol over the solubility in water.7 For both solvent/water systems, the solubility factors steadily increase from methane onwards, level off at about n-hexadecane and then steadily decrease due to the more negative AGp(g + aq) values. Judging from results on the C , to C , n-alkanes, both sets of solubility factors lead to the conclusion that n-hexacosane and n-hexatriacontane are more soluble in water than expected by factors of no less than 1.3 x 1Olo and 2.0 x 1Ol8, respectively.Furthermore, if the trend in solubility from the C,, compound onward is continued beyond n-hexatriacontane, it may be deduced that the C,, n-alkane will be as soluble in water as in the non-aqueous solvents ethanol and phenol. Certainly these predictions depend on results of the solubility of n-alkanes in water from but few investigations, and further experimental work would be most desirable, not only on the long-chain n-alkanes but also on other homologous series. I am grateful to Dr A. R. Beezer for communicating results prior to publication, and to a referee for valuable suggestions which have greatly benefitted the paper.J. Hine and P. K. Mookerjee, J. Org. Chem., 1975,40, 292. S . Cabani, P. Gianni, V. Mollica and L. Lepori, J. 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