A Comparative Study by Gas-Liquid Chromatography, Nuclear Magnetic Resonance, and Optical Spectroscopy of n-Complexing in Organic Solvents J.
H. P u r n e l l a n d 0. P. S r i v a s t a v a
Department of Chemistry. University College of Swansea. Singleton Park, Swansea, Wales
Complexing between benzene, toluene, ethyl be.nzene, and the three xylenes, respectively, with 2,4,7-trinitro-9fluorenone (TNF) in e a c h of the solvents di-n-butyl succinate, di-n-butyl adipate, and di-n-butyl sebacate, over the temperature range 40-60 "C has been studied by GLC, optical spectroscopy, and NMR spectrometry. The spectroscopically derived stability constants are shown to be questionable, although it is shown also that they are internally consistent in terms of interconversion of the various equilibrium constants which may be derived via the Benesi-Hildebrand approach. GLC derived stability constants are, in contrast, shown to be of reasonable magnitude and to have a high degree of consistency and coherence from solute to solute and from solvent to solvent. Activity coefficients at infinite dilution, based on the mole fraction scale, derived from GLC measurements do not permit rationalization of the stability constant data. However, these activity coefficients, when converted to the molarity scale, are shown to be reasonably independent of both solute and solvent. These data then allow calculation of relative values of the activity coefficient ratio for TNF and its complexes which account for the observed coherences of the original stability constant data. I t is argued that GLC, therefore, provides a m o r e reliable technique for evaluation of small stability constants than do the spectroscopic methods.
The potential of the GLC technique for the measurement of organic molecular complexes was first pointed out 10 years ago ( I ) and its likely advantages and disadvantages. along with a generalized classification, were enumerated some three years later (2). Progress, subsequently, was initially slow but is now growing fast enough to suggest that the technique has been widely accepted. In the recent past, therefore, interest has been shown in a comparison of data derived via GLC and those from other, more conventional approaches. A few papers along these lines have appeared (3, 4) but the conclusions were not very firm. However, it was apparent that discrepancy between the results obtained by the different techniques was common and this raises the question of which, if any, of the alternative values of stability constants is correct. The present study is part of a broad program designed to clarify the situation with respect to GLC. In the process, clearly, it has become necessary to formulate viewpoints regarding the alternative techniques also. Those most widely adopted are spectroscopic, being based on op-
tical or NMR techniques. We have, thus, studied a series of systems, in nominally identical conditions, by each of the three methods. A cross-section of the results is given here.
EXPERIMENTAL The complexing systems used here, benzene, toluene, ethyl benzene, and the three xylenes, each with 2,4,7-trinitro-9-fluorenone ( T N F ) , were studied by us earlier (51 but have now been restudied in different solvents. Those chosen for use were di-nbutyl succinate (DBSUCC), di-n-butyl adipate (DBA), and di-nbutyl sebacate (DBSEB). The GLC technique and comprehensive data processing methods employed have been described in detail earlier (5-8). Optical measurements were conducted with a Cary 16 spectrophotometer which allowed coverage of the range 180-800 mp with an accuracy of 0.5 mp and absorbance measurements to 0.0007 absorbance unit a t 0.5 absorbance. NMR measurements were made with a Varian HA lO0D spectrometer operating a t 100 MHz for l H . Sweep width calibrations were done with a signal generator and a Varian V4315 frequency counter. Tetramethylsilane (TMS) was used as internal reference ( C Q . 5%) for IH spectra and chemical shifts were reproducible to better than 0.3 cps. Temperature calibration was carried out by comparing the observed separation of the two major peaks of ethylene glycol with the manufacturer's calibration graph. In each technical approach, all prescribed precautions were followed and the data are, therefore, presumably free of technical error. The solvents and T M S were used as supplied. All other materials were subjected to purification procedures.
RESULTS The optical and NMR data were evaluated uia the Scott (9) and Foster (10) variants of the Benesi-Hildebrand (B-H) equation. The latter, for the equilibrium.
A+D+AD
(1)
has t h e form optical 1
1
,
for the situation c D o >> c A o I C A I ) , where c designates a molar concentration a t equilibrium and c0 an initial value. The other symbols represent the following: A = log Z0/Zt = absorbance; 1 = optical path length; t = molar extinction coefficient; .lo = 6 4 ~ 6\, the difference in chemical shifts of pure A and AD; A = dobsd - dA where 6obsd is the shift observed for the given mixture. The Scott version is
(5) D. L . Meen, F. Morris, and J. H . Purnell, J . Chromatogr Sci.. 9 ,
E . Gil-Av and J. Herling, J . Phys. Chem.. 66, 1208 (1962). J. H . Purnell, "Gas Chromatography 1966." A . B. Littlewood, Ed., Institute of Petroleum, London, 1967, p 3 . C. Eon, C. Pommier, and G . Guichon, C. R. Acad. Sci.. Ser. C. 270, 1436 (1970).
C. Eon, C. Pommier. and G . Guichon, J. Phys. Chem., 75, 2632 (1971 ) .
281 (1971). (6) D. F . Cadogan, and J. H.Purnell,J . Chem. Soc., 1968, 2133. (7) J. R . Conder, D. C. Locke, and J. H . Purnell. J . Phys. Chem.. 73, 700 (1969). (8) D. F. Cadogan. J. R. Conder, D. C . Locke, and J. H. Purnell, J . Phys. Chem., 7 3 , 708 (1969). (9) R . L. Scott, R e d Trav. Chim. Pays-Bas, 75, 787 (1956). (10) R . Foster, Nature (London). 173, 222 (1954).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 7, JUNE 1973
1111
derived by multiplying through either Equation 2 or 3 by cDO while the Foster version is derived by rearrangement to yield A _ - -K,A
+ KcA'E~
CDO
or
A = -K,A CD
+ KA,
Values of K,, t , and A0 were evaluated via a least squares based computer program which computed the relevant intercepts (I) and the ratios intercept/slope ( I / S ) and, hence, the required values of the formation constant. In common with other workers, we have found that the variants of Equations 2 and 3 proposed by Scott (9) and Foster (IO) give more consistent results than does a conventional B-H plot and so the data quoted here were derived in this way. Although the extrapolation involved in these latter approaches is to cDo = 0, rather than to cDO = m, any difference in the derived data is not to be associated with extrapolating to infinite dilution rather than to infinite concentration, it is the greater weighting given to the more accurate high cDO data points which improves the extrapolation. This point is often misunderstood., In the above equations, K , is the stoichiometric equilibrium constant defined as
(4) It is often the case that workers choose to use an alternative equilibrium constant
where x is a mole fraction. It is obvious from Equations 4 and 5 that, in any circumstances
K,cD
=
KxxD
(6)
and substitution of KxxD0into Equations 2 and 3 is therefore direct. It would then appear that a plot of Y against l / X D o should give the same intercept as does a l / C D o plot and I / S , th; value of K,. In practice, the former is rarely true for the obvious reason that again from Equations 4 and 5
K,
=
KxVmix
(7)
where Vmix is the molar volume of the mixture a t any designated concentration. Hence, the actual value of K , evaluated ( KB-H)is related (11) to K , vie
if the molar volumes of pure solvent (Vs) and pure reactant (VD) are reasonably close to the corresponding partial molar Volumes in solution a t infinite dilution. As we have shown elsewhere (121, from Equation 7 (9)
where, K," is the infinite dilution value of K,, and so K,B-H can never be a meaningful quantity except when Va = Vs. This argument rests on the view that K , is correctly (11) 1. D. Kuntz. F. P. Gasparro, M. D. Johnston, and R. P. Taylor, J Amer. Chern. Soc., 90,4778 (1968). (12) J. H. Purnell. in course of publication.
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ANALYTICAL CHEMISTRY, VOL. 45, NO. 7, JUNE 1973
evaluated, something we have also shown (12) to be an inevitable consequence of the fact that the Beer-Lambert law is essential to the derivation of the B-H equation. Equations 8 and 9 apply equally to data evaluated via the methods of Scott and of Foster (9, 10) and hence to the data quoted here, as can readily be shown. We-have shown elsewhere (12) also that an equilibrium constant
K,,
= c A D I c A ~ D = X.~D/XA@D
(10)
where 4 is the volume fraction, can be evaluated correctly via a B-H equation because, from Equations 10 and 4
KCQ~D= KccD
(11)
and further
K,
=
KcoVD
(12)
a plot of Y against l/&,will yield the same intercept as does one against l / c D o and a ratio (11s)= K,*. Table I lists both the optical and N M R derived values , , for the systems studied. The plots all of K,, K,, and Kc+ showed excellent linearity. Calculation of values of K , from K,B-H and K , uia Equations 8 and 12 yielded vqlues identical with those measured from I / S of a l / C O o plot. This clearly establishes the validity of the correlation equations and, incidentally, shows that the expression V = nV, where V is the volume occupied by n moles of liquid df (pure) molar volume V is closely obeyed in these systems. Furthermore, values of 6 and 10 derived from l / c u 0 and l / @plots ~ were, as predicted, identical, thus further establishing the validity of the data and that the error in evaluation of K is extremely small (for K , the least squares estimate is *0.02). Since the derived data are internally consistent, as explained above, no questions of a thermodynamic nature arise in the matter of conflict of results. However, a substantial discrepancy between the data stemming from the two techniques is evident and, more significantly, we see a substantial number of negative equilibrium constants in the lists. These features clearly establish that all the spectroscopic results obtained here are totally unreliable. It may be relevant, of course, that the formation constants concerned are quite small. As we have pointed out, however, this discrepancy has nothing to do with any thermodynamic or activity coefficient arguments. The discrepancy between the optical and N M R data, therefore, probably indicates shortcomings in the basic B-H approach as applied in each case, which could presumably be rectified by an appropriate analysis, but the negative K ' s can only mean that the relevant equilibria are wrongly identified. This is not surprising since the solvents must be involved somehow if solvent effects are observed whereas the B-H approach, as it is universally applied, takes no account a t all of the presence of the solvent; it is in fact an equation appropriate to the corresponding gas phase reaction. The corresponding GLC data, derived via the wellknown expression (1, 2)
K,
=
KR"(1 + K c c / )
where K R is the measured partition coefficient, K , is the stability constant, and cA0 is the concentration of A in S, relate, of course, to experiments wherein c a o >> C D O 2 CAD, the converse of the spectroscopic situation described above. The results are listed in Table I1 where we see only positive numbers of a magnitude which is, superficially,
Table I. Values of K , , K , B - H , and K,, Derived via Optical and NMR Studies at 40" Ca NMR
Optical
Toluene rn-Xylene o-Xylene Toluene rn-Xylene o-Xylene Toluene m-Xylene o-Xylene
D BS uCC'
DBA
DBSEB
+
Kc
KX
Kc
0.116 0.210 0.167 -0.030 0.082
-0.045 0.210 0.241 -0.710 -0.246
1.087 1.670 1.357 -0.272 0.654
...
...
...
-0.008 0.065 0.145
-0.730 -0.448 -0.180
-0.075 0.522 1.177
Kc
-0.019 0.072 0.105 -0.010 0.096
Kc 0
-0.168 0.565 0.850 -0.087 0.769
-0.624 -0.173 -0.033 -0.571 -0.198
... 0.053 0.041 0.098
-.
Kx
...
... -0.519 -0.448 -0.356
0.491 0.333 0.800
Data are averages of values derived via Scott [ 9 ] and Foster [IO]versions of B-H equation. Units are liters and moles. Acceptor, 2,4,7-trinitro-
9-fluorenone.
Table II. Stability Constants ( K c in I. mol-') of 1 : I Complexes of Named Donors with TNF in Named Solvents at Three Temperatures
Table 111. Fugacity Corrected GLC Measured Values of YD*- for Named Solutes in Named Solvents at Three Temperatures
Benzene Toluene Ethyl benzene p-Xylene rn-Xylene o-Xylene Benzene Toluene Ethyl benzene p-Xylene rn-Xylene o-Xylene Benzene Toluene Ethyl benzene p-Xylene rn-Xylene o-Xylene
40°C
50°C
60°C
DBSUCC
DBA
DBSEB
0.590 0.702 0.615 0.764 0.825 0.871 0.464 0.521 0.444 0.649 0.638 0.671 0.423 0.449 0.317 0.613 0.628 0.603
0.481 0.491 0.448 0.624 0.615 0.606 0.416 0.451 0.388 0.550 0.561 0.581 0.374 0.417 0.288 0.498 0.470 0.506
0.353 0.332 0.355 0.425 0.401 0.393 0.309 0.281 0.251 0.381 0.343 0.371 0.262 0.240 0.208 0.322 0.329 0.327
--0.5 O f 0
0 40° (3 50° 60°
-O"
t I
0
I -0.1
I I -0.4 -0.5 Log Kc(m-XYLENE)
I
I
-0.2 -0.3
Figure 1. Plot of log K , (benzene) against log K , (rn-xylene) for all three solvents at 40, 50, and 60 "C reasonable. It is immediately obvious that there is no agreement with the spectroscopic data. We are, therefore, required now to make a choice and, clearly, since we have rejected the spectroscopic data for good reasons, it is the
40°C
50°C
60°C
Benzene Toluene Ethyl benzene p-Xylene rn-Xylene o-Xylene Benzene Toluene Ethyl benzene p-Xylene rn-Xylene o-Xylene Benzene Toluene Ethyl benzene p-Xylene rn-Xylene o-Xylene
DBSUCC
DBA
DBSEB
0.709 0.808 0.915 0.917 0.871 0.914 0.739 0.836 0.944 0.939 0.937 0.926 0.731 0.816 0.919 0.924 0.919 0.906
0.641 0.700 0.800 0.780 0.747 0.776 0.656 0.727 0.824 0.807 0.810 0.797 0.612 0.678 0.766 0.791 0.796 0.780
0.537 0.569 0.644 0.620 0.589 0.613 0.517 0.568 0.639 0.619 0.626 0.614 0.516 0.559 0.633 0.619 0.617 0.610
GLC data which are the more acceptable. It remains to be proved, however, that they are correct, or a t least meaningful. The only approach open to us a t this point is to analyze the GLC data in some detail. In order to do so it is valuable to list the values of fugacity corrected, mole fraction based activity coefficients a t infinite dilution, yDxm.,derived from KRO as described by us elsewhere (5, 6). These activity coefficients, listed in Table 111, being mole fraction based take the value unity at xD = 1. Cursory inspection of Table I1 shows that the sequence of K, is the same in each solvent; furthermore, there appears to be a degree of regularity. That this is real can be quantitatively established by plotting log K , (solute D) against log K, (n-xylene, e . g . ) , when excellent straight line plots encompassing the data for all three solvents are found. Figure 1 illustrates the plot for benzene (=D), the least good of the set, where even the data for the several temperatures lie close. Table IV lists the values of the slopes ( e ) and intercepts ( p ) and we see that, excepting benzene, N is very close to unity for all. A precisely similar result can be derived from our data for the same reaction in a wide range of alkyl phthalate solvents (8). If it is accepted that cy = 1, p then becomes a solvent independent ratio of K,since log [K,(D)/K,(n-X)]
=
P
=
log
P'
(13)
The data for p' derived here lie in the sequence of Table V which contains also the same averaged quantity for the ANALYTICAL CHEMISTRY, VOL. 45, NO. 7, JUNE 1973
1113
Table V. Values of p' = Antilog p of Table I V from This and Earlier [5] Work on Same Equilibria but Different Solvents
Table IV. Least Squares Values of (Y (Slope) and p (Intercept) of Plots of log Kc (solute D) YS. log K c (m-xylene) fl
Benzene Toluene Ethyl benzene p-Xylene o-Xylene
0.65 1.03 1.oo 0.89 1.oo
P Xylene
rnXylene
1.02 1.10
1.00 1.00
0-
-0.18
-0.08
This work Ref [5]
-0.17 -0.03 0.01
same equilibrium in a wide range of alkyl phthalate solvents derived by us from our earlier work (5). The numerical agreement between the data from the two studies is quite remarkable since, though rn- and p-xylene have exchanged places, even the exchange is essentially quantitative. Thus, the data show substantial consistency and a t least a relative solvent independence, as expressed by p', is established. I t is an axiom that an equilibrium constant can be expressed in terms of activities so that it is independent of all variables but temperature. Thus
(14) We now have a wide range of choices in the matter of practical definition of a. Thus, it may be expressed in terms of molarity, molality, mole fraction, volume fraction, or any other quantity thought suitable. We will restrict ourselves here to the first two of these. There is a widely held view that the representation of activity cia the relationship a = yrx, where y x is the activity coefficient based on a mole fraction scale, is superior to any alternative. The intensity of this belief is implied in the substantial section devoted to this matter in the most recent monograph on organic molecular complexes (13) and in the views expressed in several very recent publications (14, 15). This view would imply that the most appropriate way of defining Kth in practical terms is
Following the above line, it has been suggested that, since
(13) R . Foster. "Organic charge-transfer complexes." Academic Press, New York. N.Y.. 1969. (14) C. Eon, and B. L. Karger. J. Chrornafogr. Sci.. 10, 140 (1972) (15) J. Homer, M. H. Everdell, C. J. Jackson, and P. M. Whitney. J . C h e m . Soc.. Faraday Trans. 2, 68, 874 (1972)
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ANALYTICAL CHEMISTRY, VOL. 45, NO. 7, J U N E 1973
0.93 1.06
0.83 0.77
Ethyl benzene
Benzene
0.67 0.65
0.66 0.61
In fact, this is only a special case of the general statement that, for a given component
which reduces to Equation 17 when XI = y l x = 1 a t p 1 = pl0, i . e . , for the pure liquid. We can perfectly well set pZ/p1 equal to activity ratios defined in a variety of other ways since thermodynamic restrictions enter only when p2/p1 is related with AG. For our present purposes we confine ourselves to the molarity scale, thus
which, when c 1 = c j o and y1" = 1 reduces to
where eo is the molar concentration in the pure liquid, i . e . , the inverse of V , the molar volume of the pure liquid. The above definition of y on the molarity scale is not one that is commonly adopted but it has its practical merits, as seen later, and in addition is identical with y on the volume fraction scale. As is well known, volume fractions commonly offer a better description of events in solution than do mole fractions. Then from Equations 1'7 and 20 we have
the subscript D now being introduced for compatibility with previous discussion. Since, by definition, for a given system, x / c = V,,, where Vmlx is the actual molar volume of the mixture at concentration e yxv,,,
the function on the left of Equation 16 might be solvent independent, if not concentration independent, because of the likely similarity of properties of A and AD. This view has been tested a number of times in GLC complexing studies and has met with only limited success (2, 5, 8, 14). This is undoubtedly to be associated with the fact that the relevant values of yx are not themselves too well correlated as between solutes, on the one hand, and solvents on the other. No attempt has been made to convert measured GLC activity coefficients to any other scale than mole fractions or, consequently, to investigate correlations of K,. on this basis. Theoretical argument in this field always starts from the proposition that the properties of a real solution are to be described by the modified Raoult's law
pXylene Toluene
=
ycv,
(22)
and, finally, for the condition of infinite dilution
vs
where is the molar volume of solvent. Equation 22 establishes immediately that y* offers no advantage over y, on any theoretical basis since the two are always related by a simple number. Furthermore, the above derivation has no thermodynamic basis a t all and any suggestion that yx is "thermodynamically meaningful" whereas y~ is not has no more substance than the similar proposition (14, 15) with regard to K , and K,. We could have adopted a modified approach to the development of the above by defining yc' = l when e = l and p = p', a v y y commonly adopted practical approach, which leads to
We immediately see one disadvantage of this approach, yc' would not be bounded in any fixed way in the values it might take since, for the pure liquid, it must equal
Table VI. Values of V s y X m= @’/po)yc‘mfor Named Solutes in Named Solvents at Three Temperatures (Molar Volume in Liters) DBSUCC DBA DBSEB Mean f% 40°C
50°C
60°C
Benzene Toluene Ethyl benzene p-Xylene rn-Xylene o-Xylene Benzene Toluene Ethyl benzene p-Xylene rn-Xylene o-Xylene Benzene Toluene Ethyl benzene p-Xylene m-Xylene o-Xylene
0.170 0.195 0.220 0.220 0.209 0.219 0.179 0.203 0.229 0.228 0.227 0.225 0.178 0,199 0.224 0.225 0.224 0.221
-~
0.175 0.191 0.218 0.213 0.204 0.211 0.180 0.199 0.227 0.222 0.223 0.219 0.170 0.188 0.213 0.220 0.221 0.217
0.183 0.194 0.220 0.212 0.201 0.209 0.178 0.196 0.219 0.213 0.215 0.211 0.179 0.194 0.219 0.215 0.215 0.212
0.176 0.194 0.219 ,0.215 0.205 0.213 0.179 0.199 0.225 0.221 0.222 0.218 0.176 0.194 0.218 0.220 0.220 0.216
3.8 0.5 0.2 2.2 1.9 2.8 0.6 2.0 2.6 3.2 3.1 3.2 3.3 3.2 2.7 2.3 2.3 2.3
Table VI1 lists the calculated values of y C mand now we see that, with the exception of benzene, the values are within &370 of a constancy which is not only independent of solvent but of solute also. Furthermore, excluding ben2.970, a result zene, an average_ of all data gives 1.733 implying virtual temperature independence. This is a remarkable observation and represents a considerable advance in our ability to deal with solvent effects. It is frequently suggested (see, e.g., 15) that the widely noted greater environment independence of Kc than of K, is a fortuitous result of a cancellation between “real” solvent effects and the concentration dependence of Vmix. This view might equally be offered now in respect of our findings regarding y x and yc. It is, however, quite fallacious, not only because it would require an almost universal set of coincidences but because its basis is that x is “more fundamental” than c, a line of reasoning already shown here to have no substance. We thus see that the present findings offer a route to analysis of our data. Table VI11 lists values of Kc/ycm which now,.presumably, define the quantity Kth (y..\m / ? , A D % . ) . We drop the superscript c since the ratioing of y’s makes the function independent of the concentration scale adopted.
*
Table VIII. Values of K t h y * - / y * ~ - ’ Evaluated from K, and Data of Table VI1 DBSUCC
40 “C
50 “C
60 “ C
Benzene Toluene Ethyl benzene p-Xylene m-Xylene o-Xylene Benzene Toluene Ethyl benzene p-Xylene rn-Xylene o-Xylene Benzene Tolue?e Ethyl benzene p-Xylene rn-Xylene o-Xylene
0.305 0.395 0.351 0.447 0.506 0.503 0.239 0.288 0.249 0.377 0.368 0.386 0.225 0.257 0.186 0.358 0.365 0.350
Table VII. Values of ycmfor Named Solutes Calculated from Solvent Independent Average Values of Table VI
Benzene Toluene Ethyl benzene p-Xylene rn-Xylene o-Xylene
DBSEB
DBA
(0.61) (0.78) (0.70) (0.88)* (1 .OO) (0.99) (0.65) (0.79) (0.68) (1.03) (1 .OO) (1.04) (0.62) (0.71) (0.52)* (0.98) (1.00) (0.96)
40 “C
50 “C
60 “C
1.933 1.778 1.752 1.709 1.630 1.730
1.940 1.810 1.781 1.720 1.735 1.739
1.883 1.748 1.707 1.712 1.719 1.722
(pO/p’)VD,a number which would vary from substance to substance and temperature to temperature. Table VI lists values of yxmVBfor the present data and we see immediately that the Values are remarkably constant for a given solute. As seen, this constancy is, a t worst, good to &3%. If the data are compared with those of Table 111, where y’s range by more than 50% over the three solvents, we can conclude with some certainty that concentration based y’s offer some advantage over mole fraction based y’s.
0.249 0.276 0.256 0.365 0.377 0.350 0.214 0.249 0.218 0.320 0.323 0.334 0.199 0.239 0.169 0.291 0.273 0.294
(0.66) (0.74) (0.68) (0.97) (1 .OO) (0.93)* (0.66) (0.77) (0.70) (0.99) (1 .OO) (1.03) (0.73) (0.87) (0.62) (1.06) (1 .OO) (1.07)
0.183 0.187 0.202 0.249 0.246 0.227 0.159 0.155 0.141 0.222 0.198 0.213 0.139 0.137 0.141 0.188 0.191 0.190
(0.74) (0.76) (0.82) (1.02) (1 .OO)
(0.93)* (0.51) (0.78) (0.71) (1.1 2 ) * (1 .OO) (1.07) (0.52) (0.72) (0.74) (0.98) (1 .OO) (1 .OO)
Included in parentheses are values normalized to that for rn-xylene; these are obviously very reminiscent of the data of Table V. Averaging the data, but excluding the five marked with asterisks since these clearly lie widely outside the relevant bands, yields the values: o-xylene (1.02); rn-xylene (1.00); p-xylene (1.00); toluene (0.77); ethyl benzene (0.71), and benzene (0.65). These values are, in essence, those derived alternatively and listed in Table V except that here p-xylene and rn-xylene are shown equal. Inspection of the K , data in Table I1 suggests that the present finding is probably more reliable. Whatever the explanation, we have clearly found the origin of the linearity of log K,(D) us. log K,(reference solute) plots. Since Kth is a constant for any D, the coherwhich, although solvent depenence lies in y A m / y A D m dent, varies in a solvent independent way from solute to solute, at least in a related series such as used here. This, in turn, means that for a given solute, yA /yAD varies regularly from solvent to solvent also. Since, in principle, y A - can be directly measured by one or another of a number of techniques, we are now in a position to evaluate a t least relative values of ? A D m . Clearly, this offers
-
ANALYTICAL CHEMISTRY, VOL. 45, NO. 7, J U N E 1973
1115
an important route to a quantitative description of complexing reactions. The fact that all the values listed in Table VIII are substantially less than unity implies clearly that A is very much more soluble in S than is AD. It might, of course be argued that yDm/yADmis in all cases unity and that it is a variation in Kth that leads to the observed numerical changes. This can be argued for the data for a set of solutes for one solvent but, of course, by definition of Kth, it cannot apply to a given solute in different solvents. The almost twofold changes (cf. Table VIII) on going from DBSEB to DBSUCC, therefore, make it clear that this cannot be of major consequence. The above indicates to us that the line of analysis developed here is the most promising yet and that a concentration of effort on this approach could lead quickly to, first, an isolation of the true origin of solvent effects and, second, some quantitative explanation of these. We feel, equally, that progress to date has been hampered by overemphasis of the role of mole fractions. Finally, it seems clear that the K , data generated by GLC are valid and
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ANALYTICAL CHEMISTRY, VOL. 45, NO. 7, JUNE 1973
hence, a t least in the present instance, much superior to the spectroscopic data. We have shown elsewhere (16) that a correlation of the two sets of data can be achieved on the basis of solvation of A and AD as described by Carter, Murrell, and Rosch (17) and this further consolidates our view that GLC provides true stability constants. In conclusion, we should state that the approach to data analysis recently advocated by Eon and Karger (14), which is designed to take account of so-called “size effects,” when applied to our data introduces no more (indeed rather less) solvent independence of K , than is evident in the raw data. Received for review December 4, 1972. Accepted February 5, 1973. The authors thank the British Council for the award of a Colombo Plan Fellowship to 0. P. S. (16) D. L. Meen, F. Morris, and J. H. Purneil, papers in course of pubiication. (17) S. Carter, J. N. Murreli, and E. J. Rosch, J Chem. Soc. A . 1965, 2048.
