( 2 7 ) Phelps, A. V.,Brown, S. C., Phys. Rev. 86, 102 (1952). (28) Phelps, A . V.,Molnar, J. P., Ibid., 89, 1202 (1953). (‘29) Phelps, A. V., Ibacl., 117, 619 (1960). 130) Platzman. R. L.. Jesse. W. P.. ‘ .Irgonne Sational Laboratory, Quartcrly R e p t . S o . 4944,(Sovember, 1952). (:31) Pompeo, D. J , Otvos, J. LT. (to Shell Development Co.), U. S. Patent 2,641,710(1953).
(32) Reed, R. I., “Ion Production by Electron Impact,” Academic Press, Yew York, 1962.
(33) Shahin, >I. XI., Lipsky, S. R., A ~ A I CHEM. ,. 35, 1562 (1963). ( 3 4 ) Sharpe, J., “Nuclear Radiation Detectors,” p. 25, Methuens, London, 1955. (35) Stern, O., Volmer, M.,Physik. 2. 20, 183 (1919). (36) Townsend, J. S., “Elertrons in Gases,” Hutchinsons, London, 1947. (37) Weissler, G . L., “Fourth International Conf. on Ionization Phenomena in Gases 1959,” K. Robert Nilsson, ed., p. 159, North Holland Publishing Co., Amsterdam, 1960.
(38) Wheatcroft, E. L. E., “Gaseous Electrical Conductors.” D. 142. Clarendon Pres?, Oxford, 1938. ( 3 9 ) Ynrnane, 11,J Phys. Suc. J a p u n 15, 1076 (1960).
RECEIVEDfor review March 26, 1964 Accepted May 18, 1964. Prevented a t 2nd International Symposium on Advances in Gas Chromatography, University of Houston, Houston, Texas, March 23-26 1964. These studies \Teere sripported in part by grants from the National Institutes of Health.
Specific Retentions of Monofunctional Organic Solutes in Monofunctional Hexa decyl Derivatives ANTHONY 6. LITTLEWOOD School o f Chemistry, The University, Newcastle upon Jyne I , England
b In an attempt to classify the various factors determining the specific retention volumes of solutes in different stationary liquids, the specific retention volumes of various simple monofunctional organic solutes were measured in various monofunctional hexadecyl derivatives-e.g., hexadecane, l -hexadecene, 1 -hexadecanol-used as stationary liquids. Heats and entropies of solution were calculated from results measured at different temperatures. In solvents which cannot form hydrogen bonds, retentions of solutes also not capable of forming hydrogen bonds can be correlated with the dipole moments and polarizabilities of solute and solvent in a manner not possible with solvents containing larger atomic proportions of polar groups. If either solute or solvent can form a hydrogen bond, the solute i s retained longer. If both solute and solvent can form hydrogen bonds, the solute i s retained much longer. The behavior of solutes in hexadecyl derivatives i s compared with their behavior in two solvents containing larger proportions of polar groups, polyethylene glycol 400 and tris( 2-cyanethoxy)propane. paper, (Is),we discussed the effect of polar groups in the molecules of stationary liquids (solvents) on the specific and relative retentions of solutes. One conclusion was that one parameter such as “polarity” is insufficient to decribe the way in which solutes of all classes are retained; qome further parameters were proposed, but no complete scheme of tlchcription of common stationary liquids could be found, and the clearest observations from the results previously I)uhli.hcd (24) were t,hat specific and rclatire rctentions of different solutes
I
N A PREVIOUS
varied from solvent to solvent in a complex manner. I n an attempt to remove some of the complexities, we have studied the specific retention volumes of a series of simple monofunctional organic solutes in a series of 1-hexadecyl derivatives differing only in the end group. Hesadecyl derivatives were chosen because they were easily available and because most did not either freeze or evaporate in the temperature range we could study most easily. We find that we may draw two kinds of deduction from our results. On the one hand, we deduce relations involving large changes of retention-e.g. of the order of 10070-between different classes of solute and between different solvents. These can be correlated with the dipole moments and polarizabilities of solvent and solute molecules and with the formation of hydrogen bonds between them. On the other hand, we have also observed a number of regularities in specific retention volumes and quantities derived from them involving comparativcly small changes in retention-e.g., of the order of 10%not many times larger than the estimated experimental error. We are only certain of such regularities because there are enough results for them t,o be observable in many individual cases. An example is the deduction roncerning tJhe entropy of solution of wlutes in n-hesadecane referred to lwlow. For practical gas chromatography, the relations involving the major changes in retention are the more significant, but the other relations help one to obtain a proper picture of the mechanics of dilute (effectively, infinitely dilute) solutions of vapors in solvents composed largely of methylene groups. We have previously \vritt.cn (15) that we have failed to find quantitative
relations between specific retention volumes and the molecular parameters of solute and solvent when considering retention> in solvents of more complex molecular itructure than are considered here. We think that, in hesadecyl derivatives, the major changes in retention from solute to solute and from solvent to solvent are produced by the specific electrical interactions mentioned above, afid that the minor changes result from complicated minor interactions a t present not adequately understood. We suppose, that in the more complicated solvents, the kindi of interactions which form minor perturbations on the main interactions in heyadecyl derivatives acquire a major role, and thus obscure the comparatively simple effects of the electrical interactions. EXPERIMENTAL
Hexadecyl derivatives were obtained from British Drug Houses and were of reagent grade, except for palmitonit ri le, which was prepared as follows. Palmitoy1 chloride (B.D.H.) was poured into concentrated aqueous ammonia solution, and the resulting palmitic amide was filtered and dried-m.p. = 100” C. (pub. 106’ C.). This was melted in a flask, and dry ammonia was passed in to convert any palmitic acid to amide. Thionyl chloride was then added. and the mixture was refluxed for 8 hours, after which excess thionyl chloride was distilled off, and the product, palmitonitrile, was distilled a t atmospheric pressure, b.p. 316-320’ C. The product was pale yellow, m.p. 30’ C. (pub. 31’ C.), and gave no carbonyl band in its infrared spectrum. Column packings were made by the slurry method ( I , I S ) , using 100- to 120mesh Celite as supliort. Columns wore about 150 em. long, 0.6-mm. i d . , and gave peaks corresponding to a column with 2,000 to 3,000 theoretical I h t e s , VOL. 3 6 , NO. 8, JULY 1964
1441
l l
1442
ANALYTICAL CHEMISTRY
thus enabling retention times to be m e a s u r d to *0.257,. On columns containing n-hesadecane, 1-hesadecene, and (to a much lesser extent) halohesadecanes, some polar solutes gave peaks with diffuse rear profiles. Such columns were therefore treated rvith dimethyldichlorosilane and trimethylchlorosilane by injecting samples of the liquids as if they were solutes. Sometimes the first sample was not eluted. If so, a further sample was injected, and in all cases, the second sample was eluted normally. I t was never necessary to use more than about 5 mg. of silanes. hfter this treatment, peaks of ordinarily polar solutes became symmetrical, but peaks due to alkanols remained somewhat unsymmetrical, and for this reason, the figures for alkanols on the above solvents given in Table I are less reliable than those for the other compounds. Though the use of chlorosilanes produced a great change in the shape of the peaks of polar solutes, the change produced in the retention volume was not more than 1070, even for alkanols. The temperature of columns was controlled to *0.05' C. in a water thermostat. Sitrogen was used as carrier gas, and a katharometer as detector. Samples were usually 0.25 to 1.0 pl. This quantity was small enough that small variations in size had no effect on retentions. The flow of carrier gas was controlled by a diaphragm valve and varied by not more than 1 % ; any such changes during a run were noted and considered in calculating specific retention volumes. Flow was measured in a thermostated capillary flowmeter calibrated by direct measurement with a soap bubble in a buret. I n repeated determinations of the same specific retention volume, variations were usually less than 0.5 cu. cm./ gram or I%, whichever limit &-asgreater. PRESENTATION OF RESULTS
Specific retention volumes were determined a t 40.0°, 50.0', and 60.0' C., except for 1-hexadecanol (m.p.l 49' C.), for which 60.0", 70.0°, and 80.0' C. were used. Free energies, heats, and entropies of solution were calculated from them. Table I cont'ains I', values at two temperatures, and the heat of solution from which to calculate sllecific retention volumes a t other temlleratures. Also attached to Table I are th(. values of the constants necessary to calculate the 0thc.r thermodynamic quantities that are described below. The frre energy of solution, AG, of a solute in a solvent is related with the partition coefficient Concn. of solute in solution a = ~ ~ _ _ - _ _ _ _ (1) Concn. of solute in vapor tly thc equation A(: = RT In a
=
AH - T A S
(2)
mhhcxrc AH and A S a r r the heat and the cntropv of wlution of the solute in the wlvcnt. FIom thiq
d In
CY
dT
-
AH
(3)
RT2
The aboi e thermodl naniic functionare the change< in the \ d u e $ of G, H , and S for the yolute n hich occur 1% hen a mole of iolute m o l e \ from a qtandard state in a solution 1iha.e at column temperature to a standard state a t the same temperature and concentration in the gas phabe a-sumed perfect I n thi5 way, AG, A H j and A S are all positive R'e alio absume linear iiotherm-, so that the Ialues of AG, AI[. and A S do not change on dilution of the iolute. This a\suniption is justified if chromatographic peak5 are hymn~etrical I n gai chromatographic practice, it i b more convenient to use T', rather than a as a basii for calculation. Free energies, heats, and entropies of iolution obtained from Ti, rather than a can be defined a5 follov b AG'
=
RT In V, = AH'
=
TAS'
(4)
I n this case, the standard state of the gas phase is a t 0" C. rather than a t the column temperature. The relations between the two forms of thermodynamic functions are:
AS'
AG'
=
AG - R T l n -
AH'
=
AH
=
AS
+ RT
Y'CP
273.16
(6)
- RT2q
(7)
Tc + R - RTq + R In 273.16 P
~
(8) where p is the specific gravity of the solvent a t column temperature T,, and is the thermal coefficient of expansion of the solvent. In Table I, we list AH' rather than AH for convenience, since the former quantity enables one more easily to celculate specific retentions a t temperatures not listed. I n the discussion which follows, we use AG, A H : and AS, since these are more fundamental. Both AH and AH' are functions of temperature, and even though the connection between them contains a temperature-dependent, term, neither is appreciably less temperature dependent than the other. In practice, d A H ; d T is about 5 cal.:nioleldegree, and so that this variation should not complicate our discussion, specific retention volumes have been measured over the comparatively narrow range of 20" C. In this range, any variation in AH is no greatrr than the eslwrimental error and can be neglccted. Also, over so narro\v a range, the additive terms of Equations 7 and 8 may be considered constant. Assuming a relative error of not great,er than *lye in 1', values,
measurements of AH over a range of 20" C. will have an error of ap1.257,. K i t h A H =7 proximatellkcal., mole, this gives limits of mean error of + O . l k c d j i n o l e . Such an error places some rrstrictions on interpreting resulti, since the total range of AH values of the systems studied is only from about 5 to 9 kcal./mole. I n discussing the results, we bear in mind that values of AH derived from measurement of small specific retention volumes carry greater error than valurs derived from larger ones. Similarly, the mean error in entropies is about +0.3 cal. /mole/ "C., increasing rapidly for solutes with small specific retention volumes. The observed consistency of relations involving entropies suggests, however, that the error is usually smaller than this.
*
RETENTIONS IN HEXADECANE
Retentions of some solutes in hesadecane are given by Kwantes and Rijnders (12). Specific retention volumes, V,, have been calculated from these, some requiring extrapolation on plots of log V , us. 1!T made from results a t other temperatures, and are compared with the present data in Table 11. Retentions from Table I of nonpolar solutes are on average about 2% less than those given by Kwantes and Rijnders, but otherwise they agree well. The values for polar solutes are considerably greater in Table I than as determined by Kwantes and Rijnders. These authors used a completely inert support for their measurements on polar solutes, and this suggests that the technique described above for inactivating the support is imperfect, as indeed has been suggested by Perrett and Purnell (18). However, our conclusions about the effects of electrical interactionh all involve comparison of retentions in other hexadecyl derivatives with those in n-hexadecane, and any spuricus effects due to adsorption on the support for each solvent appear to cancel each other.
Table 11. Specific Retention Volumes of Solutes in n-Hexadecane
Solute n-Pentane
Temp., Vo, Vo, C. Table I ( 1 2 ) 40 60
105 56 4
105 58 5
40 60 40 60 60 60 60 40
164 82 3 224 153 3 208 260 408 48 3
1.56
85 231 157 221 267 413 3:)
40 40 40
1.57 5 171 111
135 164 74
2,2-1 Xmethyl-
butane
2-Methylpentane %-Hexane Benzene Cyclohexane n-Heptane Propionaldehyde Methyl ethyl ketone Ethyl acetate 1-Propanol
VOL. 36, NO. 8, JULY 1964
1443
2 9
-
60.C 1.6
"
30
Y).C
4o.C
31
Y
I/TilO'
Figure 1 . Plots of log V , against 1 / T for solutes in n-hexadecane
I n Table 111, retentions in n-hexadecane from Table I are compared with retentions in squalane; the figures for squalanr have been checked where possible agaiiist figures given by Kwantes and Rijnder- ( I d ) and they agree well. Specific retention volumes are greater in n-hexadecane than in squalane. The specific gravity of squalane is 5% greater than that of n-hexadecane, and thus a-values rather than V , values may be compared merely by subtracting 5 from the qecond place of decimals of the figures in columns 4 and 5 of Table 111. I t is apparent that a-values are also greater in n-hesadecane. The ratio of specific retention volumes in the two alkane solvents differs significantly from solute to solute; for example, the relative retention of chloroform and 3-methylpentane is virtually unity in squalane, but the pair is easily
Table 111.
Specific Retention Volumes of Solutes in Squalane, and Ratio of Specific Retention Volumes of Same Solutes in n-Hexadecnne to These
Solute n-Pentane 2-Methylpentane 3-hlethylpentane n-Hexane 2,3-Ihmethylpentane n-Heptane Cyclohexane Benzene hfethyl ethyl ketone Eth3 1 formate Ethvl acetate Ethvl bromide Eth? 1 iodide nichloromethane Chloroform Carbon tetrachloride
1444
separated in n-hesadecane with a relative retention of about 1.2. I t is apparent that the variation in the figures of the last two columns of Table I11 cannot be attributed to experimental error since there is a definite correlation between entries at 40' C. and entries a t 60" C. S o r can the variation in the figures be correlated with possible oxidation of one or other of the alkane solvents, for in this case, polar solutes would give different entries than nonpolar solutes, and no such correlation can be seen, It is noticeable, however, that the ratio of the retention in n-hesadecane to that in squalane is smallest for compact molecules the liquids of which are dense--e.g., chloroform, dichloromethane-and is largest for the least compact molecules the liquids of which have the smallest density-e.$., the n-alkanes. The ratio is also just significantly smaller for branched alkanes than for n-alkanes. It is often assumed that different alkane solvents used in gas chromatography behave similarly toward all solutes, and indeed, this rule is approximately true, since the variations between different alkanes are almost certainly always small. Knight (10) and Janak and Komers (9) have given evidence that different alkane solvents show slight differences of behavior, and the data of Table I11 amplifies this evidence. The fact that n-hesadecane differs slightly from other alkane solvents requires that, in trying to isolate the effect of electrical interactions in retentions of solutes in polar hesadecyl derivatives, these retentions must be compared with those in n-hexadecane and not with those in any other alkane solvent. In Figure 1, log V , for solutes in n-hexadecane is plotted against 1/T for solutes of all chemical classes; to
Specific retentions in squalane 40" C. 60" C. 81 6 44 1 88 180 20 1 102 117 239 316 155 304 457 219 359 175 129 5 67 7 53 2 28 9 149 5 77 1 44 3 229 118 70 8 40 5 103 2 203 185 379
ANALYTICAL CHEMISTRY
VJn-hexadecane) V,( squalane) 40.0' C. 60.0° 1 29 1 28 1 25 1 30 1 29 1 28 1 31 1 31 1 22 1 23 1 34 1 18 1 19 1 18 1 19 1 22 1 23 1 37 1 27 1 25 1 09 1 13
1 05 1 05 1 18
1 15
1 1 1 1
16
06 06
19
avoid too confusing a diagram, not all the lines corresponding to the solutes of Table I have been drawn. The main characteri.tic is the slightly fan-shaped pattern of lines, in which the slope generally increases as specific retention volumes increase. On a small scale diagram such as Figure 1, close lines usually appear almost parallel, as for example with benzene and carbon tetrachloride. Other cases, howevere.g., n-propylchloride and 2-methylbutene-2-show that heats of solution are not esactly parallel function3 of specific retention volumes. K e have used the fact that, to a gross appro\imation. AH = AG in reference ( 1 5 ) . The finer details of the relations between heat of solution, free energy of solution, entropy of solution, and molecular structure are better displayed on a plot of AS against AG, as in Figure 2. The significance of the po5itions of the points is shown by the fact that points for members of homologous series are collinear on parallel Iineq. The first observation from this figure is that the polarity of the .elute molecules has no marked effect on the entropy of solution. Thus, the points for the cyanides, nitroethane, ethyl acetate, ethyl formate, dipropyl ether, are all close to the region occupied by the nonpolar alkanes. This is consistent with the observation already made ( 1 5 ) that a solute's dipole moment has no effect in determining its solubility in a nonpolar solvent. The second observation is that the scatter of points in Figure 2 is determined more than anything else by the molecular shape. The points for the hydrocarbons are probably more reliable than most of the others. I t is seen that the points for singly branched alkanes lie below the line for the n-alkanes, and the points for doubly branched alkanes lie lower still, suggesting that molecular compactness is accompanied by a small entropy of solution. This suggestion is reinforced by the points for benzene and cyclohesane. I t is apparent also that the points for the halogenates, the molecules of which have greater density than those of compounds just containing C, H, 5 , or 0, appear well on the low entropy side of Figure 2. These observations concerning the relative magnitudes of the free energy of solution and the entropy of solution are of practical importance, since, if for two solutes .l and B , which at a given temperature have a relative retention very close to unity, AGA A S A ~ AGB/ASB,then since (by hypothesis) G a = G B 1 it follow that AHaSAH~. This condition implieb lines m hich, if drawn in Figure 1, are close but. nonparallel, and hence a change in temperature will change the relative retention. By attention to the signs, the temperature may be changed so that the relative
Table IV. Ratio of Retentions in 1 Chlorohexadecane to Those in 1 Bromohexadecane
Rat':, 40
E1 0 FCI
2.4
2.6
2.8
3.0
3.2
3.4
3.6
AG
3.8 4.0 oical/mole)
Figure 2. Entropy of solution as function ot free energy of solution for solutes in n-hexadecane at 60" C. line connects points for n-alkanes
retention diverges from unity. The implication of the points on Figure 2 is that if two solutes of different polarity but without any great, difference in shape happen to "overlapJ1on n-hesadecane, then no change in temperature will resolve the overlap, but, if they differ in shape or size, then they may well be resolved a t a different temperature. Since the general trend among solutes is for heats, entropies, and free energies to increase in a roughly parallel manner, we may regard a line running from bobtom left to top right, (S'CVNE) of a figure such as Figure 2 as the norm, and scatter from this line at' right angles to it-Le., SE-KW scatter-measures the estent to which relative retentions change with temperature. This is of practical importance in discussing methods of expressing relative retention data in a form which, it is hoped, is as nearly as possible independent of temperature--e.g., the retention index of Kovats ( 1 2 ) or the Rg values of Evans and Smith (3). One may easily argue that if the retention indices of a set of solutes are to be independent of temperature, their points on a AG-AS plot must lie on a straight line including the points for n-alkanes. Figure 2 and the other such figures in this paper show t,hat this is not true. EFFECT O F
POLARITY A N D
POLARIZABILITY
The figures of Table I show that the retentions of alkane solutes are greater in n-hesadecane than in other hesadecyl derivatives, but the retentions of solutes containing groups with large dipole momenth-e.g., the cyanides-are greater in hesadecyl derivatives other than n-heuadecane. Because of this, arid alio because dipolar interactions are known to affect .iolubilities, we seek relations between specific retention volume:: and dipolar and induced dipolar interactions. Hesadecane, the only
nonpolar solvent, is conveniently taken as a reference solvent, and the above general observation suggests that the retention of a polar solute in a polar hesadecyl derivative differs from its retention in n-hesadecane because of two principal opposing factors: (a) its retention is less than that in n-hesadecane in the same way that the retention of an alkane is less, and for the same reasons; (b) its retention is greater than that in n-hesadecane because of dipolar attraction between the polar groups of solvent and solute. Whereas the electrical interactions of factor ( b ) are well known and calculable, the mechanisms responsible for factor ( a ) , though in general they may be related with the internal pressure of the solvent, are complicated in detail, and probably depend on detailed geometrical factors not easily calculable. We wish therefore to make factor ( a ) beyond the bounds of the present discussion. R e now consider specific retention volumes of solutes in l-chlorohexadecane and 1-bromohesadecane, the dipole moments of which are virtually identical. Their polarizabilities differ, but we show later that, except for alkanols, this difference is unlikely to produce any major difference in the electrical interactions with polar or polarizable solutes. We assume, therefore, the electrical interactions of a particular polar solute are identical in each solvent. I n Table IV are given the rat,ios of the specific retention volumes a t 40' and a t 80" C. of solutes in 1-chlorohesadecane to those in 1-bromohesadecane. I t is seen that all solutes are bett'er rehined in l-chlorohexadecane, and, except for alkanols which are considered later, the ratio of the specific retention volumes of each solute in each solvent is constant within the experimental crror. Since there are enough results that the siniilarit,y of the
Solute zso-Pentane n-Pentane 2,2-I>imethylbutane 2-Methylpentane 3-Methylpentane n-Hexane 2,4-Dimethylpentarie 3-Methylhexane n-Heptane 1-Pentene 2-Methylbutene-2 1-Hexene 1-Heptene Cyclohexane Benzene Diethyl ether Ui-n-propyl ether Ethanol n-Propanol n-Butanol Methyl formate Ethyl formate Ethyl acetate Methyl ethyl ketone Propionaldehyde n-Butyraldehyde n-Propyl chloride Ethyl bromide n-Propyl bromide sec-Butyl bromide n-Butyl bromide Ethyl iodide Ethyl cyanide n-Propyl cyanide Sitroethane Dichloromethane Chloroform Carbon tetrachloride
c.
1.28 1.26 1.29 1.28 1.27 1.28 1 . 'L3 1.28 1.28 1.24 1.23 1.25 1.25 1.21 1.22 1.29 1.31 1.07 1.12 1.11 1.15 1.22 1.25 1.21 1.20 1.24 1.25 1.23 1.17 1.23 1.23 1.17 1.21 1.23 1.27 1.20 1.20 1.22
Ratio,
APprox. error
ex60" pected (i) 1.24 0.03 1.26 0 . 0 3 1.27 0 02 1.26 0.02 1 . 2 6 0.02 1 25 0 . 0 2 1.22 0 . 0 2 1.26 0 01 1.26 0.01 1.23 0.03 1.24 0 03 1 . 2 3 0.02 1.23 0.01 1 . 2 1 0.01 1.20 0 . 0 1 1.28 0.03 1.27 0 . 0 1
c.
1.14 1.12 1.13 1.27 1.23 1 25 1.21 1.20 1 17 1.22 1.22 1.20 1 22 1.20 1.18 1.18 1.23 1.22 1.20 1.18 1,18
0 02 0.02 0.01 0.04 0.03 0.02 0.02
0.03 0.02 0.02 0.03 0.02 0.02 0.01 0.02 0.02 0.01 0 01 0 03 0.02 0.01
figures cannot be a coincidence, the table also indicates the general reliability of the figures in Table I and the validity of the estimated limits of error. We now argue: all ret'entionh i n 1-bromohexadecane are different from those in 1-chlorohexadecane, Thewfore, the mechanisms that cause wtcntions in solvents containing dipolcs t o be less than those in n-hexadecmie [factor (a) above] act to different degrees in l-chlorohexadecane and 1bromohexadecane. Sinre the ratio of the retent,ions of a polar solute in t w h solvent is the same as that of a noiil)olar solute for which solute-advent dilmlar interactions are absent, the existwctr of dipolar interactions [fartor ( b ) ] rlor,< not influenre the mechanisms (mausing retentions t,o be smaller in polar s d v c n t i [factor ( a ) ] . Also, among diffeimt polar solutes, the electrical interaction. VOL. 36, NO. 8, JULY 1964
1445
between them and either solvent have different values. Since in spite of this, the ratios of the retentions in each solvent remain the same, then the mechanisms causing retentions in polar solvents to be smaller [factor ( a ) ] do not influence the dipolar interactions [fact,or ( b ) ] . Thus, neither factor influences the other, and the two are independent. We shall assume that factors ( a ) and (6) are also independent, with other hexadecyl derivatives. Given this, the effect of factor ( a ) can be eliminated from the specific retention volumes of polar solutes in polar solvents by multiplying the specific retention volume by the ratio of the retention of an alkane in n-hexadecane to the retention of the same alkane in the polar solvent,. The quantity which remains differs from the retention of the polar solute in n-hexadecane merely because of factor (6). Factor ( a ) is shown by
~~~~
Table V.
Table IT' tc be multiplicative rather than additive, and we show below that it is convenient to express factor ( b ) by a multiplicative quantity. We can therefore define two quantities, T ( ~ and ) n b ) , both greater than unity, as follows: r(,) =
V ,(alkane in hexadecane) V,(alkane in polar hexadecyl (9) derivative)
and
r(b)
=
x
7-C.)
V,(polar solute in polar hexadecyl derivative) Vo(polar solute in n-hexadecane) (10)
Defined in this way, the ratio of the retention of a polar solute in a polar solvent to its retention in n-hexadecane is m,),'~,,); each r corresponds to each of the factors ( a ) and ( b ) above, and
~
Excess Specific Retention Volumes, Log f ( b ) , Caused by Dipolar Interaction and Dipole Moments of Solute and Solvent Groups Logu T l h i \",
Solute 2,2-Dimethylbutane 2-Methylpentane 3-Methylpentane 2,4-Dimethylpentane 3-Methylhexane n-Heptane 1-Pentene 2-Methylbutene-2 1-Hexene 1-Heptene Cyclohexane Diethyl ether Di-n-propyl ether n-Propyl chloride Ethyl bromide n-Propyl bromide sec-Butvl bromide n-Rut1.r bromide Ethyl iodide LIethyl ethyl ketone Propionaldehyde Butyraldehyde Sitroethane Ethyl cyanide n-Propyl cyanide Ben7.ene Carbon tetrachloride Chloroform Ilichloromethane
Solute 1-Chlorodipole 1-HexahexaPalmitomoment decenea decaneb nitrile0 ( a ) DIPOLE-DIPOLE INTERACTIONS 0.02 -0 01 0.00 0.00 0.00 0 00 0.02 0 00 0.01 0.02 0.04 0 00 0.00 0 00 0.00 -0.01 0.00 0 01 0.10 0.04 0 4 0 00 0.04 0.10 0 4 0 00 0.04 0.08 0 4 0 00 0.04 0.07 0 4 0 01 0.05 0.03 0 0 -0 00 0.07 0.19 1 15 -0 01 0.14 0.06 1 30 0 01 0.16 0.34 2 05 0 04 0.17 0.37 2 0 0 04 0 17 0 35 2 2 0 03 0.31 0.16 0 03 2 0 0.31 2 1 0 04 0.16 0.17 0.34 0 04 1 9 0.26 0.58 2 8 0 03 0.250 0.57 2 7 0 05 0.24 0.53 27 0 04 0.38 0.70 3 54 0 07 0.86 4 0 0 05 0.38 0.40 0.88 4 0 0 09 ( b ) INDUCED INTERACTIONS 0.34 0 03 0 17 nn n 02 0 08 0.18 0.52 0 06 0 18 i 02 0.55 1 57 0 07 0 22 0.0
0.00, solvent dipole moment 0.4 D. 0.110, solvent dipole moment 2.0 D. log T ( " ) = 0.200, solvent dipole moment 4.0 D. log r i b , (1-chlorohexadecane) d.4 = log ~ ( h (1-hexadecene) )
0
6
log log
eB
1446
=
T ( ~ ,=
log T : h ) (palmitonitrile) log T ( b , (l-chlorohexadecane)
ANALYTICAL CHEMISTRY
B-
Ad ... ... ...
, . .
...
... ... ...
, . .
I
.
.
...
... ... ...
2.5 2.5
, . .
2.0
... , . .
... 6.0
4.0 4.2 5.7 5 3 4.0 4.2 8.7 5.0 6.0
5.5 7.6 4.4 5.6 4.0 3.0 3.0
1.8 1.6 2.7 2.3 2.1 2.2 2.1
1.9 1.9 2.0 2.2
2.3 2.2 1.8 2.3 2.2
2.0 2.2 2.9 2.5
their mutual opposition is shown by the fact that they appear as a ratio. The electrical interactions which can be dissociated from the other factors determining retention by the above technique can be summarized by an equation giving t,he energy of interactions, e, of two polarizable dipoles (22):
Here, the dipoles of moments p1 and p2 and polarizabilities al and a2 (assumed spherical and homogeneous) are separated by a distance r . If subscript 1 is used for the solvent, and subscript 2 for the solute, the three terms of Equation 11 correspond respectively to : (a) interactions between dipoles in the solutes and dipoles in the solvents. We consider that, with hexadecyl derivatives as solvents, the polar groups are sufficiently dilute in the pervading mat'rix of methylene groups that there are a t least some dipoles p1 not involved in quadrupoles with their fellows, so that the arrival of a dipole p2 from the vapor phase does not necessarily require the dissociation of two dipoles p l . Hence there is no term in -p14 in Equation 11. ( 6 ) int'eractions between dipoles of the solute molecules and polarizable groups in the solvent. In a comparison with n-hexadecane, the relevant quantity is the difference between the polarizability of the characteristic group of the solvent and that of the methyl group of hexadecane which it replaces. (c) interactions between dipoles of the solvent molecules and polarizable groups in the solutes. Here, the relevant quantity is the difference between the polarizability of the characteristic group of the solute and that of the methyl group which it replaces, Dipole-Dipole Interactions. We show in the next section that, if the solutes are molecules principally composed of methyl or methylene groups and contain one polar bond only, the first term of Equation 11 is much greater t,han the latter two, which can, to the present level of accuracy, be ignored. With such solutes, we seek a relation between the dipole moments of solute and solvent and the quantit.y T(*). Since the quantity E has the units of energy, the relation between dipole moments and retention is simpler in terms of ,log r ( b ) than in terms of T ( ~ ) itself. In Table S'a, therefore, log T ( ~ is ) given for all solutes in which we expect large deviations due to large polarizability or hydrogen bonding to be absent; these include all the solvents except hexadecanol, and of the solutes, all except benzene, the esters, the chlorinated methsnes, and the alkanols. In Table V, the experimental mean error of values of log ? ( b ) is estimated to
first term of Equation 11, since the ) the dipole relation between log T ( ~ and moments must be complex. Figures 4 and 5 display the relation of entropy of solution to free energy of solution in 1-chlorohesadecane and in palmitonitrile in a similar manner to that used for solute- in hesadecane in Figure 2 . The mort notable feature of the figures is their general similarity to Figure 2 . Even though dipole-dipole interactions produce very large changes in the retentions of polar solutes when compared to n-hesadecane, the entropies of solution of polar solutes still remain close to those of nonpolar solutes of siriiilar retention. Thus, the effect of the polar group in the solvent is t o produce in polar solutes almost parallel increases both in the free energy of solution and in the heat of solution. Pople (21) has shown that the excess free energy, AG,,, the excess heat of solution, AH,,, and the escess entropy of solution, AS,,, resulting from simple dipolar attraction uncomplicated by other steric factors are related by
0 2
0 :
0 0
I
2
1
SOLUTE DlPOLT M o P I T
(D)
Figure 3. Log r(b) at 60" c. as function of solute dipole moment tor solutes in 1 -hexadecene, 1 -chlorohexadecane, and palmitonitrile T c Points for solutes a n d value o f log r(b) of which is attributed solely to dipole-dipole interaction; 1 -hexadecene, 1 -chlorohexadecone, and palmitonitrile, respectively 0 Points for solutes the value o f log r(b) o f which is attributed to induced dipolar interaction b Paints for esters in palmitonitrile 4 Points for alkanols in 1 -chlorohexadecane c- Points for alkanols in palmitonitrile
be approximately 0.01 for solutes which give symmetrical peaks both in the polar solvents and in n-hexadecane, but may be 0.02 or 0.03 for solutes which give asymmetrical peaks in either solvent; this is the case with the more polar solutes in n-hesadecane. The quantity r(al is the average value obtained from the figures for n-pentane, n-hesane, and n-heptane; the possibility of any errors in the figures for the specific retentions of these has been eliminated by confirming rcctilinearity of their points on plots of A S us. AG (Figures 4 and 5 ) . The first observation from Table V is that all entries for alkanes other than those used to determine log r(*)are zero within the experimental error, except for the isolated case of 2,4dimethyl pentane. This doubly branched alkane behaves anomalously in other respects, and though the entry of 0.04 against it in palmitonitrile is probably significant, n e do not pursue it, further here. We conclude that the shape of an alkyl group does not affect at least not grossly. S o columns for 1-bromohesadecane have been included in Table V, because the constancy of the figures in Table IV implies that r(b) for every solute in 1-broinohesadecane is the same as that in 1-chlorohesadecane. The only difference between the two solvents (except for alkanols, q.v.) lies in the value of I n the table, sokutes have been
AH,, = 2AG,, = 2TAS,,
grouped in order of increasing dipole moment. I t is clear that log T(b) is a monotonically increasing function of dipole moment. With the weakly polar 1-hesadecene, however, this is only apparent from the last few entries in the table, where the solute dipole is large enough to give an effect appreciably greater than the error. The effect of changes in solvent dipole moment is shown by the additional two columns of the table, which give the ratios of values of log r(b) for pairs of successively more polar solvents. For l-chlorohesadecane and palmitonitrile, for which all values of log T ( b ) are much larger than the error, the ratio is close to 2.0, which is also the ratio of their dipole moments. This is done also for the other pair, though the values have more scatter because of the greater proportion of error in the data for 1-hesadecene. The effect of dipole nionients of both solvent and solute is displayed in Figure 3; it is seen that plots of log T ( b ) us. solute dipole moment lie on smooth curves, one line for each solvent, and differ only in the scale of the ordinate, which varies from solvent to solvent according to their dipole moments. The lines fit the equation log r(b)
SZ
W1!J2'"
(12)
which provides powerful evidence that determined by dipole-dipole interaction only. K e do not expect that Equation 12 should contain the same function of dipole moments as the
T ( ~ ) is
I n n-hesadecane, TAS is of the same order as AG for the majority of solutes, so that most of the solutes lie along a line in Figure 1 such that TAS = AG. The effect of substituting a polar group in the solvent is to add an increment to A G for polar solutes; if Pople's rule applies, a similar- increment is also added to TAS, with hhe result that the point an the figure for a polar solute will merely move up the line of unit slope (on a plot of TAS us. AG-i.e., a line of slope 1 / T in the figure) in a north-east direction without any gross movement south-east or north-west. Detailed comparison of Figures 2, 4, and 5 shows that this is approsimately true. A further point of similarity between Figures 2, 4, and 5 is the pattern formed by straight and branched alkanes, so that the smaller entropy of solution characteristic of the branched alkanes is unaffected by the polar groups in the solvent. The main point of difference between Figures 4 and 5 is that the entropies of solution of halogenated compounds are raised in the polar solvent relative to the entropies of solution of the majority of other compoundb. l'hue, the line for alkyl bromides, which in Figure 1 lies 1.7 entropy units below that for the alkanes, lies only 0 . i entropy unit below that for alkanes in Figure 5 , Similarly the points for the chloromethanes are raised in the 1)olar solvent. The practical conclusion to be drawn from Figures 4 and 5 is that if a pair of solutes of different dipole moment> happen to overlap on the solvent, they may be resolved on a solvent of different dipole moment, but that if a pair of different polarity overlap on a given VOL. 3 6 , NO. 8, JULY 1964
1447
.
16
BCH
15
>Mi
DBB
14
EBCI3
13
FI03 12 0-
II
1
2,.
.
.
l l
.
2 8
1
~
.
1 %
3 0
~
3 4
1
~
1 8
*o
*
1.8
-
1 0
.
4 1
polar solvent, the overlap will not be resolvable merely by changing the temperature any more than it would on a nonpolar solvent. Dipole-Induced Dipole Interactions. Induced dipole interaction will contribute to e if the polarizability of a solute or solvent group in the neighborhood of a dipole is greater than that of the methylene group which would occupy its volume if it were absent. Hence, from Equation 11, the ratio of direct dipole to induced dipole interactions is given by: Dipole 2M2 Induce dipole 3kT(cu2 -
or CYCIIJ
in which the first case compares induced dipolar interaction of a polar solvent group and a polarizable solute group, and the second case compares that of a polar solute group and a polarizable solvent group. If p ’ is the dipole moment in Debye unitz, and a’ is the “molar” polariza bilit y-i.e., the polarizability due to a “mole” of a particular group or bond in a molecule, measured in cubic centimeters-then Equation 13 becomes: Dipole Induce dipole
9 P’12 cy’*
-
or
LY’CH~
a t or near 60” C. Also, if it is assumed that cy’ is related with molar refraction, R , by the equation R = 4 ~ ‘ / 3 Equa, tion 14 becomes: Dipole 38 P‘I* or Induced dipole Rz - Rcas 38 P’22
RI - Rcna
(15)
The assumption that CY is a simple scalar is justified whenever the molar refraction of a compound is equal to the sum of the “molar” refractions of its bonds: this is true for most compountis. In the results of the previous 1448
ANALYTICAL CHEMISTRY
~
~
~
*
‘
11
i*cnl,mole).
Figure 4. Entropy of solution as function of free energy of solution for solutes in 1 -chlorohexadecane at 60” C. tine connects points for n-alkanes
:. 2
d Q
10
B
Figure 5. Entropy of solution as function of free energy of solution for solutes in palmitonitrile at 60” C. tine connects points for n-alkanes
section, the largest single bond polarizability considered was that of the C-Ih bond, for which the molar refraction is about 12.6 cc. ( 2 , 4 , 5 ) . The molar refraction of a methyl group is 6.0 cc., so that the denominator of the second form of writing of Equation 15 is about 6 cc. With dipole moments of 1 D or greater, it is clear that polarizability effects have comparatively little perturbation on our correlations of retentions with dipole moments. In particular, we are justified in neglecting the difference between the polarizabilities of the C-C1 bond and the C-Br bond in the discussion of retentions in 1-chlorohesadecane and l-bromohesadecane. The polarizabilities of benzene, dichloromethane, chloroform, and carbon tetrachloride are greater than those of the other groups considered. Log T ( ~ ) values for these four solutes are laid out in Table Vb, and points for these solutes in palmitonitrile are given in Figure 3. I t is apparent from the figures that log T ( ~ ) is greater than would be anticipated from the solute dipole momenta, which, indeed, are zero for two of the solutes. From the table, it is seen that the increment by which log T ( , ) is larger than anticipated from dipole-dipole interaction is proportional to the solvent dipole moment, as for the entries in Table Va. We therefore attribute this increment to the effect of induced dipolar interaction. We can make no simple quantitative correlation of log T ( & ) with molar refractions, and we should not espect to be able to do so without a much more precise molecular model of the solution than we consider here. The magnitude
of the effect on ref,) which we have attributed to induced dipolar interaction is equivalent in carbon tetrachloride to the effect that would be produced by a dipole moment’ of ~ 1 . 2D., and in benzene to the effect that would be produced by ~ 2 . 0D . These imply polarizabilities which are considerably greater than those derived from the molar refractions of the liquids. Figure 3 contains the points for esters in palmitonitrile, and it is seen that, like the polarizable molecules, they are well above the line for simply polar solutes. S o certain explanation can be offered for this anomaly. The ester group, however, contains two polar groups acting somewhat in opposition, so that it contains more dipoles than its overall moment suggests. If two opposing dipoles are well separated in a rigid molecule, the dipole moment gives lit’tle guide to the ability of the molecule to take part in dipolar interactions with other polar molecules. Some support for this suggestion is given by the fact that the entropies of solution of the esters are raised relative to their free energies of solution in polar solvents, as is shown in Figures 4 and 5 . EFFECT O F H Y D R O G E N B O N D I N G
Hydrogen bonds may affect specific retention volumes in three classes of solvent-solute system: (a) when the solvent contains hydrogen atoms capable of bonding and the solute contains donor atoms, ( b ) when the solute contains hydrogen atoms capable of bonding and the solvent contains donor atoms, and (c) when both solvent and solute contain hydrogen atoms and donor atoms. Table I shows esamples
from which we can study all three kinds. (‘lass (a) can be studied from the rrtcntion of polar solutes other than alkanols in 1-hexadecanol. I n this case, if hydrogen bonding provides extra retention, the retention of the halogenated solutes should be determined purely by dipole-dipole interactions, while there should be extra retention of solutes which are both polar and possess a donor atom-e.g., ethers, esters, ketones, aldehydes, and (to a lesser estent) nitriles. The figures of Table VI show this to be true. The solutes are arranged so that. in part (a) are solutes which are not expected to act as appreciable donors, and in part (b) are those that are known to do so. The first column of figures shows log r(b) for solutes in 1-hesadecanol, and the second column shows the ratio of log T ( b ) for solutes in 1-hesadecanol dividrd by the same quantity for the same solutes in 1-chlorohesadecane. I t is seen that for the first group of solutes, this ratio is very close to unity; this implies that if the electrical interactions between solute and solvent are purely dipolar, then the dipole moment of 1-hexadccanol is close to that of 1chlorohesadecane. I n fact this is true; the dipole moments of the solvents are apl)rosiniately 1.7 (-OH) and 2.0 (-Cl), and the error is such that the results would not distinguish these. The figures for the ratio for the solutes in part (b), however, are all consistently greater than unity, and are in order of the recognized donor power of the donor atoms in the niolecules to which they refer. The data of Table VI, therefore. suggest that hydrogen bonding of class ( a ) has a considerable effect on specific retention volumes. I n the case of ethers, the extra retention directly attributable to hydrogen bonding is approximately 0.2 log unit-Le., a factor of 60% in specific retention volume. Class (e) hydrogen bonding can be atudied from the retentions of alkanolr in 1-hesadccanol; the values of log T [ b ) are given in part (c) of Table VI. I t is apparent that the presence of hydrogens capable of bonding and donor atoms in both solute and solvent produces a very large extra retention of the order of a 10-fold increase in specific retention volume. Chloroform and dichloromethane, which are generally recognized to form weak hydrogen bonds, show a small extra retention which is probably due to hydrogen bonding, and this esplanation is supported by the fact that their retentions in palmitonitrile (hee points of Figure 3) are rather greater than can be attributed to their large polarizability. The evidence for the effect of class ( h ) hydrogen bonding on specific retention volumes is complicated, partly bec a u s ~no solvent other than hesadecanol
is a very effective donor. The items of evidence are : 1. I n both palinitonitrile and 1chlorohexadecane, log T ( b ) for alkanols is larger than would be anticipated from attributing a dipole moment of 1.7 D. to the alkanols. The points are included in Figure 3. I n the case of l-chlorohesadecane, log ? ( b ) is 1.8 times the value to be expected merely on the basis of dipolar int,eraction; in the case of palmitonitrile, the figure is 2.6; in neither case is the esperimental error large. 2. From Figures 4 and 5 , it is seen that entrollies of solution of alkanols in palmitonitrile are vrry much larger than in 1-chlorohexadecane, and in the latter, the entropies conform to normal behavior. 3 . In Table IV, the alkanols are the only solutes for which the ratio of specific retentions in l-chlorohesadecane and I-bromohesadecane is less than 1.2. We show immediately below that a characteristic of ordinary hydrogen bonds is a large entropy of formation, so that item 2 provides good evidence for hydrogen bonding between alkanols and palmitonitrile, and no hydrogen bonding between alkanols and l-chlorohesadecane. If, however, there is no hydrogen bonding in l-chlorohexadecane, log T ( & ) for alkanols in this solvent should be such a3 to lie on the ai)propriate line of Figure 3 , which it manifestly does not. lye note, however, that the factor by which log T ( b ) exceeds that expected from pure dipolar interaction is greater in palniitonitrile than I-chlorohesadecane. These results suggest weak hydrogen bonding to chlorine, it is usually considered that hydrogen bonding to these elements is very small indeed, we may remember that me are aiming to interpret quantities of the order bo 100 cal.,’mole, which are themselves very small. Furthermore, there is some evidence for a sort of hydrogen bonding to halogen atoms which stands in the same relation to ordinary hydrogen bonding as induced dipole interaction does to dipole-dipole interaction. In this, the hydrogen can interact with a highly polarizable groul)-e.g., phenyl or halogens as in the o-halophenols (6, 20, @)-and we may guess that the interaction is greater the greater the polarizability of such a group. If this mechanism operates here, the entropy of interaction, requ orientation of gr relatively small, and all the items above would be consistently explained. Figure 6 shows a plot of the entropies of solution of solutes in 1-hesadecanol as a function of their free energy of solution. The most notable feature is the large entropy of solution of the
Table Vi. Logarithms of Retention Increments for Solutes in 1-Hexadecanol
Log
-0.250;
Solvent dipole moment, 1.7 11. Log r ( b ) (l-hesa-
decaiiol) Log
rib)
(1-Chlorohesadecane)
Solute Log l’(b) ( a ) POLARSOLCTESSOTACTING As L)OSORS
Benzene n-Propyl chloride Ethyl bromide n-Propyl bromide sec-Butyl bromide n-Butyl bromide ( b ) PoI,.4R SoLITES Iliethyl ether Di-n-propyl ether Ethyl formate Ethyl acetate Rlethyl ethyl ketone Propionaldehyde ButyIraldeh!.de Ethyl cyanide n-Propyl cyanide Sitroethane
0.173 0.175 0.201 0.161 0.140 0.139
10 12
1.2 1.0 0.9 0 9
LkC‘TIrjG AS I)ONoRS
0 228 0.172 0.425
0.366: 0 432 0.362
0.316 0.321 0.521
0.440
3.0 3 0 1.9 1.6 1.7 1 5 1.3 1 4 1.3 1 2
SOl.lTES W I T H BONDING HYDROGEKS Methanol 0 (303 6 7 Ethanol 1.012 5 3 %-Propanol 1 065 4 7 n-Butanol 1 033 5 2 IXchloromethane 0 3117 1 5 Chloroforni 0 313 1 7 (C)
alkanols, which is about twice that of other solutes. This reflects the fact that the formation of a hydrogen bond requires more precise orientation of the interacting molecules than is the case with simple dipole-dipde interactions. The pattern adopted by the points for alkanes and alkenes in Figure 6 is similar to that of Figures 2 , 4, and 5 . The other points, however, Lhow a difference in that the scatter in the SE-SIV direction i:. much larger, which, as described above, implies that relative ret,ention volumes chanpr rapidly with change of temperature. Detailed study of the pattern of i)oints in Figure 6 s h o w that the more 1)olar a solute, the smaller it.: entro1)y of solution even among those solut..s which can act as donors for hydrogen bond formation. h-o explanation is offered for this observation, which is I)articularly noteworthy since an increase in entropy occurs in the reciprocal cas? that the solute ha:: the hydrogen a t m i and the solvent is the donor. Independent experiments in different a1q)aratus using I-dodecanol (16) as a solvent yield a similar pattern to that of Figure 6. DISCUSSION
From the di.cus-ion of the rewlt- of Table I, \\e have i h o a n that retention< can be correlated n ith the fcllon ing VOL. 36, NO. 8 , JULY 1964
1449
POH
20
E OH
0
0 z
IC
i
FCl
-0
I
15
10
0
LIIrnES
Figure 7. Chromatogram of palmitonitrile at 50" C.
many
kinds of
solute in
ECB
2 1
2 6
2 8
3 0
3 2
3 4
3 6
AG
3 8
4 0
(hc I/ o l e )
Figure 6. Entropy of solution as function of free energy of solution for solutes in 1 -hexadecanol at 60" C. Line connects points for n-alkanes Dotted lines indicate change of scale
molecular parameters: 1. a parameter,
r(,,), characteristic of the sol\.ent, defined by the ratio of the retention of an alkane in n-hesadecane to the retention of the same alkane in the solvent. From the five solvents considered, it, appears that the value of this parameter is always greater than unity, and increases the greater the proportion of the molar volume of the solvent that is not occupied by methyl or methylene groups. 2. the dipole moment of the characteristic group of the solvent. 3. the dipole moment of the characteristic group of the solute. 4. the polarizability of the solute, if unusually large. 5. the existence in either solute or solvent of hydrogen atoms capable of forming hydrogen bonds. 6. the donor power of solute groups complementary to items 5. At one extreme, changes in these parameters can make differences in specific retention volumes up to 1000%---e.g., alkanols in alkanolsand a t the other extreme, thrir effect can be seen operating to produce changes of as litt,le as 10% in specific retention volumes---e.g., alkenes in I-chlorohexadecane, Table V. From the results of Table I, it is possible to give semi-empirical numerical values to most of the ahovt, parameters. Thus, for parameter I , valurs for are given in the tahlcs. Parameters 2 and 3 may be defined by the relevant dipole moments:, togethrr with an appropriate empirical constant' t o convert 1'rol)ortionality 12 into an equation; from the results shown in Figure 3 for retention? at 60" C., the equation would be log r ( D )= 0.04 p l p ? ' . 2 Parameter 4 cannot be specified quantitatively from the fen- results 1450
ANALYTICAL CHEMISTRY
available, and is probably the most complicated to specify. Parameter 5 as written above is not numerical-it merely deppnds on the formula of solute or solvent. For parameter 6, Table S'Ib s h o w t,hat it may well be possible to correlate log r C b ) with a recognized order of donor power for hydrogen bonding, but, there are not enough results to tabulate numerical values of such a parameter. The results ?how that it i; possible t o predict the relative retentions of any pair of monofunctional solutes in any hexadecyl derivative and the ratio of the retention of a solute in a given hexadecyl derivative to its specific retention in n-hexadecane, and hence the ratio of the specific retentions of any solute in any two hexadecyl derivatives. The 'only remaining item in the scheme is to ])rediet specific retention volumes in n-hexadecane, and though we have ih0n.n (16) that specific retentions of solutes in an alkane solvent (squalane) are proportional to a function determined principally by molecular weight, the precision of this relation is very much less than the precision of the relations defined by the semienipirical parameters given above. The detcrmination of specific and rclative retentions of solutes a 1)riori can hr,ll) in choosing the appropriate stationary liquid for a given separation. It may also he used in techniques derived several years ago ( 7 , 1. H. Ilesty, ed., p. 343, .kcademic Press, Kew York, 1958. (10) Knight, H. S., ANAL. CHEM.30, 9 i1958). (11) Kovats, E., Helv. Chzm. ilcta 41, 1915 (1958). (12) Kwantes, A., Rijnders, G. W. A,, “Gas Chromatography 1958,” D. H. Destv. ed.. IJ. 125. Academic Press. New”York,’1658. ’ (13) Littlewood, A. B., “Gas Chromatography,’ p. 206, Academic Press, 1963. (14) Littlewood, A . B., J . Gas. Chromatog. 1. KO. 5, 6 (19633. isj 1Eid.i ?;o. 11,’p. 16. 16) Littlewood, A. B., Willmott, F. W., unpublished data, Xewcastle upon Tyne, 1963. 17) McXair, H. SI.,DeT’ries, T., ASAL. CHEM.33,806 (1961). 18) Perrett, R. H., Purnell, J. H., J . Chromatog. 7,455 (1962). 19) Pierotti, G.J., Deal, C. H., ])err, E. L., Porter, P. E., J . A m . Chem. Soc. 78, 2999 (1956). 20) Pimental, G. C., ?fcClellan, A. L., “The Hydrogen Bond, IT. H. Freeman and Co., San Francisco, Calif., 1960. (21) Pople, J. A , , Disc. Faraday Soc. 15, 35 (1953). (22) Prigogine, I., “The Molecular Theory of Solutions,” Sorth-Holland Publishing Co., Amsterdam, 1957. (23) Ralston, A. W., Harwood, H. J., Pool. M’, J., J . Am. Chent. SOC.59, 986 (1937). (24) Kulf, 0. R., Liddel, O., Hendricks, S.B., Ibid. 58, 2287 (1936)
LITERATURE CITED
S., Juvet, R. S., Jr., “Gas-Liquid Chromat,ography,” p. 45, Interscience, Yew York, 1962. (2) Denbigh, K. G., Trans. Faraday Soc. 36,936 (1940). (3) Evans, 34, B., Smith, J. F., J . Chromatog. 6, 293 (1961).
(1) Dal Nogare,
RECEIVEDfor review January 7, 1964. Accepted March 30, 1964. ,Presented at 2nd International Symposium on Advances in Gas Chromatography, Cniversity of Houston, Houston, Texas. March 23-26, 1964. VOL. 36, NO. 8, JULY 1964
e
1451
