3478
DANIELE. MARTIREAND PETER RIEDL
dency for molecules with high inductive power to show a slightly smaller shift than those with a lower inductive power. A possible reason for this lack of a high correlation is that the value of the Taft inductive factor, u*, might not be valid when the molecule in question is adsorbed on the solid surface of silica gel. It might, therefore, be difficult to treat the adsorption of these compounds on silica gel in a more quantitative manner
until more exact measures of inductive effects are known. Davydov, et a1.,16have already shown that the shift in the hydroxyl frequency does not correspond with the dipole moment of the adsorbed molecule, and it, therefore, appears that a detailed consideration of the structure and electronic arrangement within a moIecule will be needed in order to predict the specific interaction of molecules on silica gel.
A Thermodynamic Study of Hydrogen Bonding by Means of
Gas-Liquid Chromatography by Daniel E. Martire and Peter Riedl Chemistry Department, Georgetown Uniuersity, Washington, D. C. 80007 (Received April 8, 1968)
A gas-liquid partition chromatographic method is proposed for the thermodynamic study of hydrogen-bond formation. It is applicable to low molecular weight hydrogen donors (the solute component) and high molecular weight electron donors (the liquid-phase or solvent component) with no active hydrogens. A procedure is described for evaluating the nonhydrogen-bonding interactions between the hydrogen donor and the electron donor. It involves the use of a nonpolar alkane “reference” solvent that has the same molecular polarizability, size, and shape as the electron donor and requires the measurement of solute specific retention volumes in both solvents. The advantages of the glpc method are: (a) the simplicity, speed, and accuracy with which a large number of systems can be investigated, (b) the wide available range of easily controllable temperatures, (c) the possibility of studying volatile, impure, or scarce hydrogen donors, (d) the ability to work at a single solution concentration (pure electron donor and infinite dilution of hydrogen donor), and (e) the assurance that only 1:1 complexes are being formed. In this investigation eight alcohols are studied in di-n-octyl ether and di-n-octyl ketone; n-heptadecane is the reference solvent. Equilibrium constants, enthalpies, and entropies of hydrogen-bond formation are obtained; the results are within the ranges normally found for OH---0 bonds. It is concluded that glpc should be useful for the systematic study of variations in the equilibrium constant with progressive structural changes in the hydrogen donor or the electron donor. This technique compares favorably with the common spectroscopic ones and is, in fact, complementary.
Introduction It is now well established that gas-liquid chromatography is an effective and advantageous method for studying the thermodynamics of nonelectrolytic solutions. Most of the work to date has been on systems involving the interactions of nonpolar or slightly polar molecules, where dispersion forces play the predominant role. Purnell’ has pointed out that glpc also offers many advantages for the study of specific interactions and for the measurement of association constants. However, despite increasing evidence that glpc should be competitive with conventional methods, only a few thermodynamic studies have been performed on systems where complex formation is possible. Accordingly, the aim of the present work was to investigate the feasibility of glpc for the determination of equilibThe Journal of Physical Chemistry
rium constants, enthalpies, and entropies of hydrogen bonding. The existence of a definite complex species in systems capable of hydrogen-bond formation between a hydrogen donor and an electron donor is well established by spectroscopic evidence. The common methods used for studying hydrogen bonding in solution are ir, uv, and nmr spectroscopy. However, the efficacy of these techniques is reduced by various experimental difficulties. Furthermore, the reliability of the measurements is far from satisfactory, and the discrepancies among
(1) J. H. Purnell, “Gas Chromatography, 1966,” A. B. Littlewood, Ed., Elsevier Publishing Co., Amsterdam, 1967, p 3. (2) G. C. Pimentel and A. L. McClellan, “The Hydrogen Bond,” W. H. Freeman and Co., San Francisco, Calif., 1960.
A
THERI\IODYK;.A;1IIC S T U D Y O F
HYDROGEN BONDING BY GLPC
values obtained by different methods and investigators are often considerable.2 One of the main problems encountered with these spectroscopic inethods is the self-association of the hydrogen donor, which can be appreciable even at the lowest concentrations used. The resulting simultaneous equilibria give rise to considerable problems in interpreting the measurements. I n addititm, the current literature gives no clear indication at out the nature of the species formed in self-association. These difficulties do not arise in the proposed glpc method, since infinite dilution of the hydrogen donor (the solute component) is easily attained. Furthermore, the solute can be impure, volatile, and scarce. Another advantage of glpc is that concentrations need not be varied, thus eliminating the bother of preparing solutions and the need to employ “inert” diluting solvents. Numerous solutes can readily be studied in the electron donor which is used here in the pure state as the stationary liquid phase (hereafter referred to as the solvent). One of the drawbacks of the proposed glpc method is the need to utilize a reference solvent for evaluating the nonhydrogen-bonding contributions to solute retention in the electron-donor solvent. Other limitations are determined by the general characteristics of glpc, e.g., the nonequilibrium effects (such as adsorption on the solid support) that may influence solute retention. Finally, it must be established generally that stability or association constants measured by glpc are true values and not special “dynamic” values. The considerable success of glpc in the general field of activity coefficient measurements gives great initial confidence. While glpc has often been used for qualitative investigations on hydrogen bonding, there have been only two attempts at determining the thermodynamic quantities of complex formation. Russian workers3 have investigated the hydrogen bonding of 1-alkynes with various electron-donor solvents. The weakness in their approach was the rather arbitrary choice of the reference ~ o l v e n t . ~The activity coefficient and hence the specific retention volume of the solute is determined by all kinds of :interactions with the solvent and also by statistical effects due to molecular size differences. Therefore, one cannot expect t o elucidate the hydrogenbonding contribution unless all other contributions t o the deviations from ideality are the same for the electrondonor solvent and the nonpolar reference solvent. This gave rise t o the difficulty in estimating the enthalpy change for the complex formation from the experimental heat of solution and to the impossibility of determining the equilibrium constant. It also indicated the necessity for a more careful choice of the reference solvent. Quite a different approach was presented by Littlewood and Will~rnott,~ who studied alcohols and various electron donors as solutes and mixtures of 1-dodecanol
3479
in squalane as the solvent. It was found that, due t o its terminal hydroxyl. group, 1-dodecanol associated very strongly to form polymer chains. As a result, a mathematical treatment of the experimental data, involving the solution of simultaneous equilibria, was necessary. Although their data can be interpreted reasonably well by the suggested treatment, the large self-association of the solvent complicates the system unnecessarily and obscures the results. It is significant that no effect of the structural changes of the solute alcohols on the equilibrium constants and enthalpies could be found. Furthermore, the inherent simplicity of glpc is lost by the use of several columns with different additive concentrations.
Method The first step in the process of evaluating the feasibility of a new experimental approach should be the accurate study of simple, well-defined systems. These results should then be compared, if possible, with those obtained using a more established method. Accordingly, in this initial study we restricted the systems to hydrogen-donor solutes with single active hydrogens and to electron-donor solvents with no active hydrogens (to avoid solvent self-association). Furthermore, to minimize the effect of dipole-dipole interactions between the solvent molecules, we chose molecules with the proton-accepting group in the center of a long paraffin chain. Therefore, we could validly assume that only 1: 1 complexes between the solvent and solute were possible. Following the approach of Langer, et ~ l . one , ~ can derive the following expression for the specific retention volume, Vg0,of a solute which forms a 1: 1 complex with the liquid phase (the solvent)
where yz’ is the apparent (experimentally measured) solute activity coefficient, y2 is the actual activity coefficient of uncomplexed solute molecules, and x is the fraction of solute complexed. The complex is assumed to have negligible vapor pressure. To determine x and from this the equilibrium constant for hydrogen-bond formation, one first has t o evaluate the activity coefficient of uncomplexed solute molecules. This problem corresponds to finding the partition coefficient of the uncomplexed solute between the liquid and gas phase, as pointed out by Purnell (reactions of his class Biz). Since an exact determination (3) A. V. Iogansen, G. A. Kurkchi, and 0. V. Levina, “Gas Chromatography, 1966,” A. B. Littlewood, Ed., Elsevier Publishing Co., Amsterdam, 1967, p 35. (4) J. Novak, J . Chromatogr., 28, 391 (1967). ( 5 ) A. B. Littlewood and F. W. Willmott, A n d Chem., 38, 1031 (1966). (6) S. H. Langer, C. Zahn, and G. Pantazoplos, J . Chromatogr., 3, 164 (1960). Volume 78, Number 10 October 1968
3480
DANIEL E. MARTIRE AND PETER RIEDL
is not possible, an approximate method has to be devised. The rationale for a proposed L‘comparative” approach to the problem will now be considered. The purpose of the ensuing analysis is to obtain an approximate cxpression for the activity coefficient ratio of a nonpolar solute in a particular solvent pair (reference, electron donor). The result will indicate that it is reasonable to assume that this ratio is equivalent to the activity coefficient ratio of the uncomplexed hydrogen-donor solute in the same solvent pair. As discussed by MartireI7the activity coefficient of a nonpolar solute at infinite dilution in a high molecular weight nonpolar or slightly polar solvent is given to a good approximation by the expression
where T is the ratio of molar volumes of solvent and solute and x is the interaction parameter. Furthermore, the following sum can be written for x
x
+
(3) where Xh and xs are, respectively, the enthalpy and entropy contributions to the interaction parameters. Huggins8j9 has shown that, for negligible orientational effects, xs l/x, where z is the number of nearestneighbor lattice sites. Since this term is small and since we are working with ratios of activity coefficients, the xs contribution may be neglected in further treatment. We can now write eq 2 in the form R 2 E
S2E
RT
R
In y 2 m = - - - -L
=
Xh
Xh
Xs
f
(In
+ 6 In 5r+1
where RZE and SZE are the solute partial molar excess enthalpy and entropy, respectively. Since the potential energy change accompanying the formation of a solution is the major part of the heat of mixing, we have the approximation
(7)
If we neglect the small induction forces, then the solute and solvent can interact only by London’o dispersion forces, according t o the approximate expression
where a and v are, respectively, the polarizabilities and frequencies of the electronic vibrators and a is the distance between molecular centers. I n general, the polarizabilities differ much more widely than the frequencies, and a will not vary much for solutions involving different solvents of the same molar volume and shape with a given solute. Therefore, for two solvents with the same polarizability, eq 7 reduces to T2a e [zNofllal/zRT _b -L- ,[+Nonibl/ZRT (9) -72
This implies that for any nonpolar solute in two different solvents of the same size, shape, and polarizability, the activity coefficient ratio depends primarily on the pairwise potential energies between solvent molecules and is essentially independent of the solute. Furthermore, this suggests that the ratio of the activity coefficients of the uncomplexed hydrogen donor in the solvent pair should also be given by eq 9. This last approximation is valid if all solute-solvent orientational effects are contained in the complexation term and if the dipole-induced dipole interactions between the uncomplexed hydrogen donor and the solvent are negligible. Thus if one experimentally determines the ratio of the activity coefficients of alkane solutes in the electron donor and the reference solvent, this ratio should be constant for all solutes which interact predominantly by dispersion forces with both solvents and should be approximately the same as the activity coefficient ratio of the uncompkexed hydrogen-donor solute in the same solvent pair. The equilibrium constant, K , of the hydrogen-bonded complex can be related to the term 1 - x in eq 1
h!t where No is Avogadro’s number, A e is the molecular interchange energy, and ell, €22, and €12 are, respectively, the solvent-solvent, solute-solute, and solvent-solute pairwise potential energies of interaction. Consider a pair of solvents, a (the reference) and b (the electron donor), with identical molar volumes. The ratio of the activity coefficients of a nonpolar solute in the two solvents, if x is assumed to be the same for both solutions, is then given by
Since
=
€22,this reduces to
The Journal of Physical Chemistry
+D
K = - -~ -M MUD
MD
-
D
CMD C M ~ D
(10)
(11)
and, since the solvent activity is not changed by the complex formation
(7) D. E. Martire, “Gas Chromatography, 1966,” A. B. Littlewood, Ed,, Elsevier Publishing Co., Amsterdam, 1967, p 21. (8) M. L. Huggins, Ann, N. Y. Acad. Sei., 43, 1 (1942). (9) M. L. Huggins, J . Amer. Chem. Soc., 86, 3535 (1964). (10) F. London, 2.Phys., 63, 245 (1930).
A THERMODYNAMIC STUDY OF HYDROGEN BONDIKG BY GLPC where an%, aD,arid alllD are the activities of the hydrogen donor (Ill),the electron donor (D), and the complex (RID). The activities of M and MD are taken equal to their concentrations because the solution is infinitely dilute. This is consistent with the spectroscopic convention. Later, in order to obtain K, a calculation will be made for the activity of the electron donor. To continue CMD
X S E
cni
+
CMD
(13)
The combination of eq 12 and 13 yields
--
-K’+l
1-x
(14)
3481
of course, under the assumptions made for the choice of the reference solvent. Experimental Section On the basis of the considerations discussed in the preceding sections, di-n-octyl ether and di-n-octyl ketone were chosen as the electron-donor solvents and n-heptadecane was chosen as the reference solvent. Their polarizabilities and molar volumes are given in Table I. The polarizabilities were calculated from electronic bond polarizations given by LeFevre and Steel.ll Table I : Polarizabilities and Molar Volumes of Solvents.
which, when coimbined with eq 1, gives
lo*&ao
n-Heptadecane Di-n-octyl ether Di-n-octyl ketone
If one now defines four different specific retention volumes
(hydrogen-donor solute in reference nonpolar solvent)
314 303 314
lJ1Q
Ref
317.4 308.3 313.1
C
b d
a a. is the polarizability in ml/molecule and v10 is the molar volume in ml/mol at 50’; the molar volumes were calculated using the densities from the given references. ’F. D. Rossini, K. S. Pitaer, R. L. Arnett, R. M. Braun, and G. C. Pimentel, Ed., “Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds,” Carnegie Press, Pittsburgh, Pa., 1953, p 288. A. I. Vogel, J. Chem. Soc., 618 (1948). L. Ruzicka and G. Giacomello, Helv. Chim. Acta, 20, 554 (1937).
(hydrogen-donor solute in electron-donor solvent)
(nonpolar solute in reference nonpolar solvent) 273R 5zbfi20Mb (nonpolar solute in electron-donor solvent) pg0b =
and assumes, as previously explained, that
Ea- %a b -
Y2
-b
72
then
This means tha,t one can determine K’ by measuring only the specific retention volumes of hydrogen donor in the electron-donor and reference solvent and by making a simple correction for differences in the activity coefficients of uncomplexed solute in these two solvents. For this correction the ratio of the specific retention volumes of nonpolar alkane solutes in the same two solvents is mea,sured. The correction factor will include the differlent energies required for breaking solvent-solvent interactions (eq 9) and will also correct for small differences in size effects. This is only valid,
The hydrogen-donor solutes selected for the study were alcohols and secondary amines. One of the major problems in measuring their retention times was the tailing of peaks due to solute adsorption on the solid support (particularly with the reference solvent). Various support materials were examined t o find one which was sufficiently inert but yet could easily be coated with a high loading of the liquid phase. Teflon was excluded primarily because of the latter consideration; there were also technical difficulties in preparing the packing, and the column efficiencies were poor. The following supports were then examined in detail : (a) Johns-Manville Chromosorb-W, acid washed, DRlCS treated, 60-80 mesh; (b) Johns-Manville Chromosorb-W, acid washed, DMCS treated, 80-100 mesh, high performance; (c) Johns-Manville Chromosorb-W, 60-80 mesh, treated with DMCS in toluene, according t o the procedure given by Holmes and Stack,12 and also the support was refluxed for several hours with a solution of DJICS in toluene; (d) Bioglass 2500 (from Bio Rad), a porous glass bead support; (e) Bioglass 2500 treated with HMDS in the vapor phase according to the procedure recommended by the (11) R. J. W. LeFevre and K. D. Steel, Chem. Ind. (London), 670 (1961). (12) W. L. Holmes and E. Stack, Biochem. Biophys. Acta, 56, 163 (1962). Volume 7,9?Number 10 October 1968
DANIELE. MARTIRE AND PETERRIEDL
3482 manufacturer; (f) Bioglass 2500 treated with a mixture of DIICS and TAICS in toluene. Each of these supports was coated with 10 wt yo n-heptadecane; l-propanol and diethylamine were chosen as test solutes at 30". It was found that all supports gave tailing of the peaks, but the least tailing (and best efficiency) was obtained with support b, which consequently was chosen for the experiments. I n order to obtain meaningful retention volumes for the alcohols and amines, the effect of sample size on retention time and peak asymmetry was then examined. The following behavior was observed with l-propanol as the solute. (a) The initial retention time of the peaks remained constant over a wide range of sample sizes down to about 0.2 pl; with still smaller sample sizes, it increased with decreasing sample size. (b) The retention time of the peak maximum decreased with decreasing sample size, reached a minimum, and then increased again as the initial retention time increased. The same effects were observed with diethylamine, except that the increase in the initial retention time began at larger sample sizes (about 1 pl). According to the asymmetry definition of Dal Nogare and Juvet,13 the peaks showed negative asymmetry (retardation of peak maximum) at large sample sizes, which gradually changed t o positive asymmetry (tailing) a t small sample sizes. For all sample sizes, the front edge of the peak rose very sharply from the base line. With large sample sizes, the constancy of the initial retention time with decreasing sample size indicates that the active sites of the support are being saturated by the first molecules of the peak as it advances through the column. This is because the rapid increase in solute concentration at the peak front (as indicated by the sharp leading edge) is sufficient to produce a complete saturation of all active sites. Thus the support appears inert to all the molecules that follow. With small sample sizes, the saturation of active sites is incomplete, tailing becomes evident, and the whole peak is shifted toward longer retention times. The other observed effect, i.e., the retardation of the peak maximum with increasing sample size, is due to the nonlinearity of the absorption isotherm. Consequently, the following procedure was adopted for obtaining meaningful peak retention times that were independent of support and sample-size effects: (a) the initial and peak retention times were measured and plotted against the sample size and (b) it was assumed that the peak maximum retention time was independent of support effects as long as the initial retention time remained constant; therefore, (c) the peak maximum retention time of those peaks which had constant initial retention time was extrapolated to zero sample size. The specific retention volumes obtained by this method were found to be independent Of the liquid loading. The same Vg0values were obtained for four The Journal of Physical Chemistry
systems (l-propanol and diethylamine, each in n-heptadecane and di-n-octyl ether, respectively) with both 10 and 15% loadings. This also indicated that solute adsorption as the gas-liquid interface14was negligible. The other salient features of the experimental procedure may now be considered. Each of the liquid phases employed had a minimum purity of 99.0%, as determined by high-temperature glpc. The n-heptadecane and di-n-octyl ether (from Humphrey) did not require further purification. The di-n-octyl ketone (from K & E() was recrystallized in methanol until the reported freezing point (49") was attained. The column packings were prepared in a rotary vacuum dryer using an appropriate solvent for the liquid phase. A 10% loading was used for di-n-octyl ether and nheptadecane (lower temperatures) ; a 15% loading was used for di-n-octyl ketone and n-heptadecane (higher temperatures). A combustion method was devised to determine the exact liquid-phase percentage. Simply, a sample of the packing (approximately 1 g) was weighed before and after the burning off of the organic liquid phase. This method was found to be simpler and more reproducibie than the common Soxhlet extraction method. A dual-column glpc apparatus was employed. The columns were made from 6 ft of 0.25 in. 0.d. copper tubing and then were coiled. They were installed in a thermostated water bath where the temperature could be maintained to 10.05". The liquid solute samples were introduced through a Carle injection port (set at about 140") with a 10-pl Hamilton syringe. The inlet pressure of the carrier gas (helium) was regulated with a Negretti-Zambra precision pressure regulator, Model R/182, and was measured to within ik0.05 psi with a calibrated Series 1400 U. S. test gauge (range 0-30 psig). The outlet pressure (atmospheric) was determined from a barometric reading. The flow rates (which ranged from 15 to 220 ml/min) were measured with a soap-film meter and were chosen to give convenient elution times and reasonable column efficiency. A Perkin-Elmer hot-wire thermal conductivity detector operating at about 200" and a Sargent l-mV recorder, Model SR, were used.
Results The specific retention volumes of the solutes in the various solvents were calculated from the experimental data using the well-known equation of Littlewood, et ~ 1 . ~ The 6 results are given in Tables II-IV. Some high-temperature values were deleted for methanol and ethanol because the measured retention times were too short and irreproducible. (13) S.Dal Nogare and R. 9. Juvet, "Gas-Liquid Chromatography," Interscience Publishers, New York, N. Y., 1962, p 168. (14) D. E.Martire, Anal. Chem., 38, 244 (1966). (15) A. B. Littlewood, C. S. G. Phillips and D. T. Price, J . Chem. sot., 1480 (1955).
A THERMODYNA.MIC STUDY OF HYDROGEN BONDING BY GLPC
3483
Table I1 : Specific Retention Volumes in n-Heptadecane
n-Pentane Isopentane n-Hexane 2-Methylpentane 3-Methylpentane 2,2-Dimethylbutane 2'3-Dimethylbutane n-Heptane 3-Methylhexane 2'4-Dimethylpentane Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol sec-Butanol t-Butanol Diethylamine Methyl-n-propylamine Methylisopropylaniine Methyl-n-butylamine Di-n-prop ylamine Diisopropylamine
173.6 125.2 575.6 396.4 460.4 260.9 372.5 1860 1375 811.2 9.17 34.50 126.9 69.15 437.2 290.1 251.2 111.7 287.2 355.3 225.8
133.4 97.21 418.3 293.4 343.2 198.3 279.4 1303 975.2 583.6 8.53 28.21 95.46 52.64 317.0 215.8 188.0 88.53 215.3 263.5 169.6 827.8 1911 655.3
95.24 71.23 286.7 204.8 236.2 141.9 195.0 831.9 634.4 391.0 6.85 19.95 69.09 38.77 210.2 150.7 132.2 63.90 149.2 179.8 119.3 542.1 1178 433 * 3
Table I11 : Specific Retention Volumes in Di-n-octyl Ether
vk?
7
Solute
22.5'
n-Pentane Isopen tane n-Hexane 2-Met hylpentane 3-Methylpentane 2'2-Dimethylbutane 2,3-Dirnethylbutanie n-Heptane 3-Methylhexane 2,4-Dimethylpentane Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol sec-Butanol &Butanol Diethylamine Methyl-wpropylamine Methylisoprop ylamine Methyl-n-but ylamine Di-n-propylamine Diisopropylamine
30'
yz" =
1.704 X lo7 MlP,OV,O
40.28 31.91 102.4 77.73 88.20 57.65 75.76 255.1 205.1 135.7
31.38 25.08 75.83 58.59 66.20 44.43 57.53 179.9 147.0 99.49
12.87 39.10 23.87 109.8 78.88 71.29 36.64
9.99 30.24 18.55 82.14 60.58 54.35 28.07
23.38 14.71 60.73 45.63 41.00 22.63
Table IV : Specific Retention Volumes in Di-n-octyl Ketone
50'
67.31 52.14 191.4 139.9 160.1 98.61 133.8 514.7 401.9 254.8 24.32 49.86 152.3 76.23 438.4 312.0 220.3 99.26 123.3 152.3 99.95 418.8 846.1 315.6
The solute activity coefficients at infinite dilution were calculated from the expression'o
( ~ 2 ~ )
52.52 40.94 140.5 104.9 119.7 75.95 101.5 366.0 290.1 187.9
7
40'
175.5 132.8 93.38 127.1 97.26 69.98 576.4 412.6 279.0 398.7 290.6 200.5 338.7 230.4 462.9 261.2 195.9 136.5 372.9 276.4 189.7 1863 1278 800.7 1376 962.3 614.3 812.5 580.5 382.4 68.37 50.60 34.43 174.4 122.0 72.85 607.3 397.7 242.5 277.1 184.7 113.2 2082 1341 712.0 1395 910.2 508.5 908.0 606.3 345.9 343,2 242.0 147.2 265.1 177.6 328.4 219.1 209.1 144.1 1030 643.7 2286 1379 754.9 480.6
-
69.54 53.08 197.1 144.6 165.5 102.3 138.9 539.4 419.7 266.2 6.37 16.27 50.57 29.89 154.8 107.7 95.05 48.82 107.8 128.6 85.06 359.5 756.5 292.6
vgo
Solute
%-Pentane Isopentane *Hexane 2-Methylpentane 3-Methylpentane 2,2-Dimethylbutane 2'3-Dimethylbutane n-Heptane 3-Methylhexane 2,4-Dimethylpentane lllethanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol sec-Butanol &Butanol
50'
55.91 42.92 155.0 113.8 130.6 81.19 111.7 414.7 326.3 208.7 43.19 87.06 251.0 130.7 746.1 517.7 360.1 173.1
60'
70'
800
42.23 32.70 25,78 33.06 26.01 20.71 81.86 61.50 111.0 83.06 62.42 47.69 95.06 71.24 54.09 60.81 46.72 36.23 81.09 61.14 47.09 282.5 199.0 142.8 225.5 162.2 117.7 148.4 108.5 80.68 60.36 165.3 88.00 450.8 323.6 236.4 115.6
43.37 114.8 81.27 63.25 45.60 298.3 199.0 216.8 148.1 162.4 113.6 81.23 58.82
where MI is the solvent molecular weight and p,O is the pure solute vapor pressure, in millimeters, at the column temperature. The vapor pressures at various temperatures were calculated by means of the Antoine equation, using the constants from Dreisbach's compilation. Since no Antoine constants were available for the alcohols, their vapor pressures were obtained (16) D. E. Martire, "Gas Chromatography," L. Fowler, Ed., Academic Press, New York, N. Y . , 1963,p 33.
Volume 72,Number 10 October 1968
3484
DANIEL E. MARTIREAND PETER RIEDL
Table V : Activity Coefficients in n-Heptadecane
Solute
----
n-Pentane Isopentane n-Hexane 2-Methylpentane 3-Methylpentane 2,2-Dimethylbutane 2,3-Dimethylbutane %-Heptane 3-Methylhexane 2,4-Dimethylpent ane Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol sec-Butanol t-Butanol Diethylamine Di-n-propylamine
---
Ygm
I _
22.5’
30’
40’
50’
0.875 0,899 0,909 0.937 0.901 0.938 0.897 0.945 0.944 0.995 70.4 41.7 32.7 27.1 27.5 25.5 19.3 17.7 1.15
0.864 0.891 0.905 0.931 0.886 0.927 0.887 0.931 0.933 0,990 51.9 32.0 26.9 22.8 22.4 20.4 15.6 14.1 1.12 1.17
0.858 0.877 0.885 0,910 0.875 0.907 0.876 0.921 0.922 0.973 39.7 26.4 20.4 17.3 17.4 15.4 11.9 10.8 1.08 1.15
0.853 0.869 0.887 0.904 0 873 0.904 0.870 0.928 0.926 0.971 27.4 19.7 16.1 13.4 12.9 11.9 9.31 8.31 1.03 1.11
Table VI : Activity Coefficients in Di-n-octyl Ether
I
70‘
60‘
0.839 0.848 0.880 0.896 0 865 0.895 0 863 0.921 0.916 0.961 I
I
15.1 12.3 10.3 10.3 9.43 7.31 6.78
13.1 9.80 8.40 8.23 7.43 5.90 5.64
0.820 0.830 0.874 0.885 0.829 0.878 0.851 0.921 0.912 0.951
8.06 6.96 6.88 6.20 4.98 4.61
Table VI1 : Activity Coefficients in Di-n-octyl Ketone yam
p--
Solute
22.50
30‘
40°
50‘
*Pentane Isopentane n-Hexane 2-Methylpentane 3-Melhylpentane 2,PDimethylbutane 2,3-Dimethylbutane n-Heptane 3-Methylhexane 2,4-Dimethylpentane Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol sec-Butanol &Butanol Diethylamine Di-n-propylamine
0.858 0.878 0,900 0.924 0.889 0.929 0.889 0.936 0.936 0,985 9.38 8.19 6.77 6.71 5.72 5.25 5.30 5.70
0.861 0.883 0,910 0.933 0.891 0.931 0,890 0,942 0.938 0.987 8.68 7.33 6.40 6.44 5.24 4.80 4.81 5.10 0,899 0.974
0.868 0.886 0.902 0.922 0.890 0.935 0.893 0.949 0.944 0.987 7.84 7.16 5.77 5.88 5.09 4.52 4.52 4.67 0,900 0.970
0.875 0.877 0.906 0.927 0.895 0.930 0.896 0.964 0.959 1.007 7.12 6.36 5.29 5.21 4.50 4.08 3.98 4.06 0.894 0.987
from other source^.^^^^^ Vapor pressure data were available for only two of the secondary amines. The activity coefficients are listed in Tables V-VII. These values have not been corrected for the nonideality of the vapor phase,16because only the relative magnitudes will be considered in the discussion of results. Furthermore, knowledge of absolute activity coefficients is not necessary for the computations which follow. In order to determine the equilibrium constant (K’) of the complex, the ratios of the specific retention volumes of all the solutes in the electron-donor and in The Journal of Physical Chemistry
800
0.829 0.836 0 875 0.889 0.859 0.884 0.855 0,915 0,909 0.951
Solute
n-Pentane Isopentane %-Hexane 2-Methylpentane 3-Methylpentane 2,2-Dimethylbutane 2,3-Dimethylbutane *Heptane 3-Methylhexane 2,4-Dimethylpentane Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol sec-Butanol &Butanol
1 _
--.
50’
60’
70’
800
1.003 1.015 1.066 1.086 1.045 1.076 1.022 1.140 1.125 1.171 3.82 3.47 3.06 2.90 2.52 2.34 2.32 2.22
0.986 0.993 1.053 1.070 1.029 1.056 1.020 1.128 1.113 1.150
0.965 0.969 1.034 1.047 1.006 1.031 1.002 1,108 1.087 1.125
0.943 0.950 1.020 1.028 0.990 1.016 0.982 1 096 1.077 1,109
3.04 2.76 2.64 2.38 2.17 2.08 2.03
2.84 2.44 2.33 2.16 1.96 1.86 1.84
2.19 2.12 1.98 1.81 1.70 1.68
the reference solvent were calculated. As discussed previously, the correction fact’or V2b/V2’ is a measure of the deviation from unity of the ratio of the activity coefficients of the uncomplexed hydrogen-donor solute. This correction factor was determined by taking an average value for all the alkanes being studied. (17) R. R. Dreisbach, “Physical Properties of Chemical Compounds,” Advances in Chemistry Series, No. 15, American Chemical Society, Washington, D. C., 1955; R. R. Dreisbach, Advances in Chemistry Series, No. 29, American Chemical Society, Washington, D. C., 1961. (18) J. Timmermans, “Physico-Chemical Constants of Pure Organic Compounds,” Elsevier Publishing Co., New York, N. Y., 1950. (19) Landolt-Bornstein, “Zahlenwerte und Funktionen,” Vol. 2, 6th ed, Springer-Verlag, Berlin, 1960, Part 2A.
3485
A THERXODYNAMIC STUDY OF HYDROGEN BONDING BY GLPC Table VI11 : Average Values of
vgob/
vp
Solvent pair
22.50
30"
40'
Di-n-o ctyl ethern-heptadecane Di-n-octyl Iketonen-heptad'ecane
1.005
0.990
0.973
Table IX : Equilibrium Constants ( K ' ) in Di-n-octyl Ether ~
K'-----..
Solute
22.5'
30'
40'
50'
Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol see-Butanol &Butanol
6.41 4.03 3.77 2.99 3.74 3.79 2.59 2.05
4.99 3.36 3.21 2.55 3.27 3.27 2.26 1.76
4.17 2.75 2.61 2.00 2.48 2.46 1.69 1.36
2.96 2.17 2.12 1.64 1.93 2.01 1.40 1.10
Table X : Equilibrium Constants ( K ' ) in Di-n-octyl Ketone
-- -_--
Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol see-Butanol &Butanol
50'
7.58 5.77 5.28 4.53 5.10 5.09 3.80 3.49
60'
0,793
4.91 4.33 3.65 4.18 4.17 3.19 2.98
0,802
0.813
Since the specific retention volume ratios for the amines showed only small variations with temperature, their thermodynamic complexation values were not determined. Also, AH' was not calculated for methanol and ethanol in di-n-octyl ketone because of the insufficient number of reliable data points. I n order t o calculate the equilibrium constants ( K ) from eq 12, one first has t o determine the activity (uD) of the pure electron donor, where UD = YDcD. Then the enthalpy ( A H ) and entropy ( A S ) change for the complex formation can be calculated from the temperature dependence of K . The required concentrations of the pure electron donors can be obtained from the known densities20s21 at the various temperatures. The activity coefficients (YD) must be estimated. In spectroscopic studies, where the electron donor is diluted in an inert solvent, the convention used is that YD 4 1 as CD --t 0. For consistency, the same convention is employed here. This necessitates the estimation of the activity coefficient of the electron donor in its pure state. Consider a hypothetical solution of the electron donor (b) in the reference solvent (a). It can be validly assumed that the activity coefficient of the reference solvent obeys a simple Van Laar expression In
800
700
800
0,965
K'
Solute
ioo
60'
0.790
As expected (see eq 9), it was virtually independent of the solute molecule. The standard deviation from the average value given in Table VI11 is about 1% in each case. The equilibrium constants ( K ' ) were calculated through eq 17. The enthalpy changes ( A H ' ) for the complex formation were then obtained, using a leastsquares fit, from the slopes of log K' vs. reciprocal temperature plots. The results are given in Tables IXXI.
,
50'
ya,= &b2
with the usual convention that ya 1 as zb 0, where Utilizing the Gibbs-Duhem equation and the convention that Y b += 1 as x b 0, one obtains for the electron-donor component
z is the mole fraction.
4.41 3.74 3.25 3.49 3.46 2.73 2.60
3.28 2.81 3.03 3.00 2.41 2.20
-
(19)
In
Yb =
p(za2 - 1)
(20)
For the solutions being considered, it is apparent that /3 is determined primarily by the interchange energy,
i.e. ~~
~~
Table XI: Enthalpy Changes (AH')of Hydrogen-Bond Formation A H ' , koal/mol -7 Di-n-ootyl ether Di-n-ootyl ketone
7
Solute
Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-But an01 sec-Butanol t-Butanol
-5.12 -4.22 -3.97 -4.21 -4.66 -4.51 -4.40 -4.40
i 0.48 f 0.14
k 0.06 f 0.09 i 0.30 zt 0.23 2c 0.28 i 0.28
-3.79 -3.73 -4.20 -4.27 -3.67 -3.65
0.19 0.29 0.14 0.14 + 0.13 f 0.13 f f f f
Furthermore, since the molecules have approximately the same polarizability and size and since the pairwise interaction energy, €ab, is determined mainly by dispersion forces, then €ab = eaa and
(20) A. I. Vogel, J. Chem. Soc., 618 (1948). L. Ruzicka and G. Giaoomello, Helo. Chim. Acta, 20, 554 (1937).
(21)
Volume 72, Number 10 October 1968
3486
DANIELE. MARTIREAND PETER RIEDL
Table XI1 : Estimated Activity Coefficients of Pure Electron Donors YD
Electron donor
22.5'
30'
40°
Di-n-octyl ether Di-n-octyl ketone
1.012
0,997
0.981
This means that for the pure electron donor eq 20) Yb = ,-P
(2, =
0 in
e[aNo(~aa-tbb)l/2RT
which, when compared with eq 9, indicates that Yb
.
=
a*
Tzb
where j z a / ~ a b is the activity coefficient ratio of an alkane solute in the reference (a) and the electron donor (b). Furthermore, from eq 18 and 24
50'
60'
0.973 0.836
Table XIII:
0.838
70'
800
0.849
0.857
Equilibrium Constants ( K ) in Di-n-octyl Ether
--K ,l./mol
c
Solute
Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol sec-Butanol &Butanol
1
22.5'
30'
40'
50'
1.91 1.20 1.12 0.890 1.11 1.13 0.771 0.610
1.52 1.02 0.976 0.776 0.994 0.994 0.687 0.535
1.30 0.857 0.814 0 623 0.773 0.767 0 I527 0,424
0.938 0.688 0.672 0 I520 0.612 0.637 0,444 0.349
I
Table XIV : Equilibrium Constants ( K ) in Di-n-octyl Ketone
Since the values for Vgob/VgOa have been already tabulated, Y b can be readily determined. However, the Yb determined from eq 25 is based on the mole fraction convention ( Y b 4 1 as q,+ 0), while the desired Yb is based on the concentration convention (Yb 3 1 as cb -+ 0). Denbigh's approachz2can be used to obtain thi: relationship between the activity coefficients of the two conventions at concentrations other than infinite dilution. It can be shown that the electron-donor activity coefficient based on the concentration convention is given by eq 25 only if the components of the solution have the same molar volume. Such is the case for the systems in question. Therefore, the activity coefficients of the pure electron donors (rD) were calculated through eq 25 using the known molecular weight ratios and the average of the specific retention volume ratios for nonpolar alkane solutes in the reference and electron donor (from Table VIII). The computed values can be found in Table XII. The noticeable negative deviations from ideality for the di-n-octyl ketone is an indication that ebb > eaa (See eq 23). Most likely, this is due to the fact that dipoledipole interactions between the ketone molecules contribute to its over-all interaction energy. Finally, one can now calculate K, AH, and AS. The results are given in Tables XIII-XVI. The standard deviations of AH and A S were calculated from the deviations of the single experimental points from the best straight line values. The inaccuracy of the term K' 1 is estimated to be about 5%, if the retention volumes Vgoband Vgoaare measured to 2% and the correction factor Vgob/ Vgoais measured t o 1%.
+
The Journal of Physical Chemistry
,-Solute
Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol sec-Butanol &Butanol
K , l./mol
50'
2.84 2.16 1.98 1.70 1.91 1.91 1.42 1.31
-----
60Q
70'
800
1.85 1.63 1.37 1.57 1.57 1.20
1.65 1.41 1.22 1.31 1.30 1.03 0.978
1.23 1.05 1.13 1.12 0.900 0.822
1.12
Table XV : Enthalpy and Entropy Changes for Hydrogen-Bond Formation in Di-n-octyl Ether Solute
Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol sec-Butanol &Butanol
A H , kcal/mol
-4.69 -3.79 -3.32 -3.77 -4.21 -4.08 -3.96 -3.93
I 0.50
f 0.16 i 0.10 zk 0.10 i 0.32 f 0.22 f 0.27 zt 0.15
AS, eu
-14.6 -12.5 -11.7 -13.0 -14.0 -13.6 -13.9 -14.3
f 1.7 jz 0 . 5 f 0.3 zt 0 . 3 jz 1 . 0 f 0.7 f 0.9 f 0.5
Discussion An examination of the equilibrium constant ( K ) results reveals certain well-defined trends: (a) with both electron donors, K decreases with increasing carbon number of the alcohol; (b) with both electron donors, K decreases in going from the primary to the tertiary alcohol of the same carbon number; and (c) for a given (22) K. Denbigh, "The Principles of Chemical Equilibrium," 2nd ed, Cambridge Gniversity Press, Cambridge, 1966, p 276.
A
THERMODYNAMIC
STUDY OF HYDROGEN BONDING BY GLPC
Table XVI : Enthalpy and Entropy Changes for Hydrogen-Bond Formation in Di-n-octyl Ketone Solute
1-Propanol 2-Propanol 1-Butanol %Butanol sec-Butanol &Butanol
A H , koal/mol
-3.57 -3.54 -3.98 -4.06 -3.45 -3.47
f 0.15 i 0.27 f 0.10 zk 0.10 & 0.05 f 0.16
AS, eu
-9.7 -9.9 -11.0 -11.3 -10.0 -10.2
f f f f f f
0.5 0.8 0.3 0.3 0.2 0.5
alcohol, K is greater with the ketone than with the ether. The first two trends are readily explainable by the well-established inductive and steric effects of the alcohol alkyl groups, and the last trend is explainable by the greater accessibility of the keto group to the alcohols. The results for the enthalpy and entropy changes cannot be as easily explained. With a given electron donor the differences between the alcohols are small and somewhat obscured by experimental inaccuracy. The AH and AS values, however, are within the ranges normally found for OH---0 bonds.2 Closer examination of the A S values for a given electron donor seems t o indicate that two counteracting effects are taking place. On the one hand, there is the parallelism between AH and A S noted by Pimentel and nlcClellan.2 A more negative AH value means stronger bonding and therefore a higher steric requirement for the complex, resulting in a more negative A S value. On the other hand, there is the greater steric hindrance for the approach of tertiary and secondary alcohols to the electron donor compared with primary alcohols, also resulting in a more negative contribution t o AS. Comparison of the AH values for the same alcohol with the ether and the ketone reveals that the ketone values are somewhat smaller. This may appear surprising if one considers the larger dipole moment of the ketone, and the electrostatic model of hydrogen bonding. However, it has been shown2 that no correlation exists between the hydrogen-bond strength and the dipole moment, of the base. The explanation for this lies in the deficiency of the electrostatic model, which emphasizes only the ionic contribution and neglects the covalent Contribution to hydrogen bonding. The near equality of the AH values in the two electron donors also indicates that the more negative free energy change for the alcohol-ketone complex formation is primarily due t o a less negative value of AS. This is reasonable because the keto group is much more accessible to an approaching allcohol molecule than the ether group. The major aim of this work was to explore the feasibility of glpc for the thermodynamic study of hydrogen bonding in solution. It is felt that the main advantage of the proposed method lies in the simplicity, speed, and accuracy with which a large number of systems can be
3487
investigated over a wide range of easily controllable temperatures. Glpc should prove useful for the systematic study of (a) the variation in K with progressive structural changes in the hydrogen donor and (b) the variation in K with electron-donor type, for a given series of hydrogen donors. The relative K values should be quite accurate, since any small systematic errors should be the same for all solutes. In addition, the range of equilibrium constants that can be determined is limited only by the accuracy with which V,O can be measured. An examination of recent article^^^-^^ on spectroscopic investigations of hydrogen bonding indicates that the glpc method has a comparable precision for the determination of K and AH. None of these methods (glpc included) seems to offer a distinct advantage for studying small variations in AH with progressive structural changes in the hydrogen donor. The experimental inaccuracy in AH often obscures the results in spectroscopy as well.23s26With respect t o this, perhaps more definitive calorimetric work is needed.28 In the spectroscopic methods one normally invest]igates a dilute solution of both the electron donor and hydrogen donor in an inert solvent. One might inquire whether it is necessary, desirable, and feasible to do the same in glpc, i e . , employ a stationary liquid phase where the electron donor is an additive of known low concentration in an inert solvent. In general, this is not feasible because the additional solute retardation due to complexing usually is too small t o enable accurate measurements. Even with the pure electron donor as the liquid phase, the complexing contribution t o retention is sometimes too small t o produce accurate K values and/or accurate AH values (as was the case for the secondary amine solutes). If one must study an electron donor that undergoes appreciable self-association, one has no choice but to dilute it, in order t o obtain meaningful results. Then one would have to combine the proposed method with the experimental approach of Littlewood and W i l l m ~ t ti.e., , ~ dissolve the electron donor in an inert solvent with the same polarizability and molar volume, make measurements at various electron-donor concentrations, and extrapolate the results t o infinite dilution. However, when possible, it is desirable t o use the electron donor in the pure state. Then, since there is no danger of solute selfassociation and since only 1: 1 complexes are formed, the specific retention volumes of many different solutes (23) E. D. Becker, Spectrochim. Acta, 17, 436 (1961). (24) L. J. Bellamy, G. Eglinton, and J. F. Morman, J . Chem. Soc., 4762 (1961). (26) B. B. Bhowmik and S. Basu, Trans. Faraday Soc., 59, 813 (1963). (26) T. J. V. Findlay and A. D. Kidman, Austral. J . Chem., 18, 521 (1965). (27) I. Motoyama and C. H. Jarboe, J . Phys. Chem., 71,2723 (1967). (28) T. D. Epley and R. S. Drago, J . Amer. Chem. SOC.,89, 5770 (1967). Volume 72. Number 10 October 1968
3488 can be readily determined without the necessity of using a series of concentrations. The major questionable points in the proposed approach are: (a) the validity of the various assumptions concerning the attainment of meaningful specific retention volumes (and activity coefficients) from the experiment and (b) the validity of the various assumptions concerning the pure electron donor and the equality of nonhydrogen-bonding interactions in the electron donor and the reference. It is possible to establish that glpc does not give special "dynamic" values and that support and samplesize effects have been correctly accounted for. A few of the alcohol solutes can be studied in bulk samples of both the electron donor and the reference, under welldefined static equilibrium conditions. A McBain balance apparatusz9 can be used to obtain yzmb: yz"' ratios for the alcohol solutes, which may then be compared with the glpc values. Also, a comparison can be made between the glpc values for K and AH with those obtained from, say, an nmr study on identical systems, i.e., using our reference solvent as the inert solvent. The glpc results (K' and AH') have been converted into general quantities (K and A H ) for this
The Journal of Physical Chemistry
DANIELE. MARTIRE AND PETERRIEDL purpose. Thus one should not find that glpc and nmr results fit into different self-consistent schemes of data.30 It is expected that the proposed glpc method can be utilized to study low molecular weight alcohols and primary and secondary amines as hydrogen donors and simple high molecular weight ketones, ethers, esters, tertiary amines, and tertiary amides as electron donors. It would also be of interest to investigate low molecular weight electron donors (e.g., acetone, diethyl ketone, etc.) by employing volatile-solvent glpc technique^.^^,^^ However, it is felt that liquid surface effectsl4~32and vapor phase imperfection effects31 would make the data interpretation extremely difficult and could possibly obscure the results.
Acknow1t:dgrnent. This work was supported through a research grant from the U. S. Army Edgewood Arsenal, Maryland. (29) D. E. Martire, R. L. Peosok, and J. €1. Purnell, Trans. Faraday SOC.,61, 2497 (1965). (30) A. B. Littlewood and F. W. Willmott, ibid., 62, 3287 (1966). (31) P. E. Barker and A. K. Hilmi, J . Gas Chromatogr., 5, 119 (1967). (32) B. L. Karger and A. Hartkopf, Anal. Chem., 40, 215 (1968).
