3849
CONCURRENT SQLUTION AND ADSORPTION PHENOMENA IN CHROMATOGRAPHY
Concurrent Solution and Adsorption Phenomena in Chromatography.
111.
The Measurement of Formation Constants of
H-Bonded Complexes in Solution by D.F. Cadoganl and J. H.Purnell Department of Chemistry, University College, Swansea, Wales, U.K.
(Received April 7,1969)
A gas-liquid chromatographic method for the quantitative evaluation of the stoichiometricformation constants of H-bonded complexes in nonaqueous solution is described. Theory is developed for the situation where multiple sorption occurs and methods for correcting for surface effects are described. The theory is tested by study of systems involving individual Cs-Cs alcohols and didecyl sebacate in squalane. It is established that 1:1 complexes only are formed and formation constants and associated thermodynamic parameters are presented. The data are shown to be self-consistentand to compare well with values for other systems studied spectroscopically. The results indicate a quantitative relationship between the activity coefficients of the alcohols in squalane and the corresponding formation constants. The advantages of the glpc technique are outlined.
We have recently described2 a gas-liquid partition chromatographic (glpc) method for the accurate and rapid measurement of formation constants of organic complexes in nonaqueous solution. A series of columns, each containing a complexing additive ( A ) dissolved in an inert solvent (8) is employed, the columns differing only in the concentration (cA) of additive. Measurement of the retention volume of small samples of volatile complexing species ( X ) with each column allows calculation, sometimes directly and otherwise by extrapolation, of the corresponding apparent infinite dilution partition coefficients, KL, via the well known infinite dilution retention equation connecting fully corrected (net) retention volume, V,, and column liquid volume, V L VB = KLVL
(1)
Formation constants, for 1: 1 complexes (KI), may then be evaluated via the equation3
+
K L = K L " ( ~ KiCA)
(2)
rect. It was established also that, for any volatile species, an extended form of the infinite dilution equation (1)
+ KIA, + K s A s
VN = KLVL
(3)
which takes into account the surface contributions, is applicable. KI and Ks are the infinite dilution partition coefficients relevant to liquid-gas and solid-gas interface adsorption, respectively, and A I and A s are the corresponding surface areas. When the surface terms are all zero, V N = V,. I n the case where, also, complexing occurs in solution, KL in eq 3 is again defined by eq 2. Evidently, if the method is to be generally applied to H-bonding studies, much more comprehensive experimentation is required than with the more amenable systems previously studied1 if dependable values of KL and, in turn, K1, are to be extracted from the retention data. The first extension of the approach demanded is immediately evident if eq 3 is rewritten in the form
+
+
V N / V L= K L ( K I A , K s A s ) / V L (4) where KLo is the relevant infinite dilution partition coefficient (C,,/C,,) for distribution of X between S and Thus, given that values of V Ncorresponding to infinite the gas phase. dilution can be obtained, a plot of VN/VL against VL-l I n principle, the above approach is applicable to the should then give a curve extrapolating to KL at VL-l = evaluation of K I for complex formation via hydrogen 0. It is thus necessary to employ extra sets of columns, bonding, and one such study has been d e ~ c r i b e d . ~ However, almost by definition, any solvent which can (1).Department of Chemistry, University of California, Riverside, Calif. be regarded as inert toward volatile H-bonding species (2) D. F. Cadogan and J. H. Purnell, J . Chem. Soc., A , 2133 (1968). is almost certainly a very poor solvent for such sub(3) J. H.Purnell, "Gas Chromatography 1966," A. B. Littlewood, stances. I n consequence, liquid bulk solubility of X Ed., Institute of Petroleum, London, 1967,p 3. will be low and contributions to retentionfrom liquid sur(4) A. B. Littlewood and F. W. Wilmott, Anal. Chem., 38, 1031 (1966). face and exDosed solid surface adsomtion will be sub(6) (a) J. R.Conder, D. C. Locke, and J. H . Purnell, J. Phys. Chem., stantial. This .view has recently been subjected to 73, 700 (1969); (b) D.F. Cadogan, J. R. Conder, D. C. Locke, and rigorous examination5"and shownSbto be generally corJ. H. PurnelI, ibid., 73, 708 (1969). volume 78,Number 11
November 1969
3850 of varying solvent/support ratio, i e . , V L ,for each value of CA desired, to derive the information necessary to the use of eq 4. The second extension of the experimentation arises because, unfortunately, the occurrence of multiple sorption generally brings with it very marked peak asymmetry, which persists at even the smallest sample size which can be handled, as a consequence of the char& ~ ~ there is, acteristics of the surface e f f e c t ~ . ~ Hence, generally, no simple route to the determination of the infinite dilution value of V , for any multiple sorption system but, more important, because peak-maximum retention is not necessarily thermodynamically significant in these circumstances, some means to measure meaningful values of V , with asymmetric peaks is also required. These problems have been considered a t some length by us previously6 and have been the subject of an elegant analysis by Conder.' Briefly, Conder considers the situation that a solute (X) is eluted in turn from each of a set of columns, identical in a11 but V,, arbitrarily numbered j = 0 , 1 , 2 , 3 . . . , to produce with each column a large asymmetric peak. He shows that a set of retention volumes corresponding to elution at a fixed gas-phase concentration of X from all columns can be obtained by finding corresponding points on the diffuse side of each peak a t which the ratio [height of point above baseline: adjusted retention (from air peak)], (hj/VN,), is the same. This involves finding sets of hj which fit
D. F. CADOGAN AND J. H. PURNELL offers a means of measurement of formation constants. Despite the added experimentation, the method is still likely to be far more rapid than alternative procedures. This paper describes a test of the theory and methods described by study of some specific systems.
Experimental Section The low solubility of H-bonding species in inert solvents, s, previously mentioned in relation to solutes, also applies to the involatile additive A . Thus, some difficulty may be experienced in finding a, suitable noncomplexing diluent but it is hardly likely ever to be seriously limiting. Since in the present instance our intent was establishment of the viability of the technique, we have chosen to look for a liquid likely to Hbond with the chosen solutes (the Ca-Cs aliphatic alcohols) which has satisfactory solubility in squalane rather than t o search for a suitable diluent for some chosen additive. We find that didecyl sebacate (DDS), a widely used glpc substrate, is suitable and this has been used throughout this work. All columns used were 50 cm X 0.5 cm o.d., and the solid support was 100-120 mesh (A.S.T.M.) hexamethyldisilazane-treated Sil-O-Cel. Columns of about 18% w/w solution/support were constructed with the concentration of DDS in squalane (cA) ranging from 0 to 0.55 mol 1.-l while, for the experiments a t fixed cA, columns ranging from about 7 to 32% w/w solution/support were used. I n all other respects the experimental details were exactly as previously described. 2,5
Results where the zero subscript signifies arbitrarily chosen reference data. Our experience is that this procedure, for any value of hor can be carried out numerically very readily; only rarely, with the systems studied, were more than two successive approximations needed. Calculating sets for different values of ho yields values of V,, for each column as a function of gas-phase concentration, the data can then be corrected for pressure drop and extrapolated to yield the infinite-dilution value of V Nfor each column for insertion in eq 4. An alternative procedure to that suggested by Conder is, from the data derived by analysis of the diffuse side of each of the set of peaks, to plot a set of curves of h, against V N ,for each column. Straight lines from the origin, which correspond to fixed values of ho/VNo, may be drawn to intersect the curves, the points of intersection along each straight line yielding the required sets of data. This procedure is undoubtedly the more effective if many data points are desired or if the numerical method requires three or more successive approximations. We thus see that although the experimental and dataprocessing procedures are more tedious when H-bonding systems are under study, the glpc method again The Journal of Physical Chemistry
Detailed preliminary studies of the dependence of peak shape on injected sample size established that, in every case, the trailing (diffuse) edges of the elution peaks for any solute with any given column lay on a common curve. Figure 1 shows a set of peaks corresponding to elution a t 50" of 0.03 to 0.11-pl liquid samples of 2-methyl-l-propanol from a pure squalane column, which illustrates the point. This behavior, which may of course not be general, means that, for such systems, the data required in the application of Conder's method of evaluation of infinite dilution V N can be obtained either, as he suggests, from a single massive peak or from the peali-maximum retention data of a series of peaks of different size. Conder's method is clearly more economical, but because of the exploratory nature of this study and the greater reliability of multiple measurements, we have used the pealr-maximum method. Thus, in place of the single large injection we have carried out a minimum of ten elutions per system. (6) D. E. Martire, R. L. Pecsok, and J. H. Purnell, Trans. Faraday Soc.,61,2496 (1965).
(7) J. R. Conder, J . Chromatogr., 39,273 (1969).
3851
CONCURRENT SOLUTION AND ADSORPTION PHENOMENA IN CHROMATOGRAPHY
Liquid sample ( ~ 1 )
\I
I
1
1200
0
I
I
I
I
I
I
2
4
6
8
10
12
c-',g Inject ion peaks
I
0
mi-',
Figure 2. Plots of ' f " j / V ~against VL-I for various values of ho. Data for elution of 1-butanol a t 60" from a column of 9.4% w/w DDS in squalane (cA = 0.14 mol l.-l). To compensate for small differences in the various columns, V L is taken as the volume of solvent per gram of total packing.
Time.
Figure 1. Illustration of dependence of peak shape on injected sample size for elution of 2-methyl-1-propanol from pure squalane at 50".
700
600
Data processing, following Conder, was carried out as follows. For a given solute, temperature, and cA, the data for a set of columns of differing solvent/support ratio were tabulated as sets in terms of h , / V , ratios corresponding to hi = 5 , 10, 15,20, and 30 chart mm peak height. The recorder attenuation setting and detector operating conditions were, of course, maintained constant a t all times. The values for the most heavily loaded column were then designated ho and ho/VN,in each set, and the tabulated values of h,/VNj for all other columns were then used as a guide to carry out the numerical approximation necessary to find for each the values of h, and V N ,yielding h,/VN, = ho/VNO. As stated, this procedure was found to be quite straightforward. Having derived sets of values of Vu, corresponding to constant h,/VN,,Le., constant gas-phase concentration, two approaches are open. First, the data may be plotted as a function of h, and extrapolated to h, = 0 t o yield an infinite dilution value of V N for each column. These data can be plotted, according to eq 4,as V N / V Lagainst VL-l t o give a single curve which must then be extrapolated to VL-l = 0 to yield KL. The accuracy with which KL can be determined is clearly dependent on the adequacy of extrapolation of a single curve. The alternative method, adopted here, is to plot V N , / V Lagainst VL-l curves for the sets of VN3calculated for each ho. Since, a t VL-l = 0, all practical sample sizes, in the range employed here at least, correspond to infinite dilution, the curves for all ho should extrapolate to the same value of KL. This we find to be true in practice and the extrapolation is undoubtedly more accurate when a number of curves can be used to locate the common point. Figure 2 illustrates one set of such plots, those for 1-butanol eluted at 60" from a series of columns of cA = 0.14 mol 1.-l. The difference quantity [(V,/VL) - K L ]measures
50 0
400
k4 300
200
100
c I
01 0
I
0.1
0.2
,
1
I
,
0.3
0.4
0.5
0.6
c,, mol I.-! Figure 3. Plots of K L against c, (DDS in squalane) for (i) 2-pentanol, lines: B, 50"; D,60'; F , 70'; and (ii) 3-methyl-1-butanol, lines: A, 50"; C , 60'; E,70".
the contribution of the surface terms. While KL for any alcohol was found to depend on the value of cA, it was found also that, for any given solvent/support ratio, the above difference was effectively independent of cd, Thus, if this quantity is determined for a series of pure squalane columns, it can be used directly with the data for squalane-DDS columns to evaluate KL, If this behavior is found to be general it will much reduce the volume of experimental work required. Figure 3 illustrates typical sets of plots of derived values of K L against cA, for two of the alcohols, a t each of three temperatures. The lines drawn are leastsquares fits to the data and there is no doubt that eq 2 well describes the results. Plotted also, a t c, = 0 , are data points obtained with squalane columns, and the agreement with the extrapolated value is excellent. These observations offer strong confirmation of the theory and procedures presented here. Formation Volume 73. Number 11 November 1969
D. F. CADOGAN AND J. H. PURNELL
3852 constants evaluated from the slopes of such plots are listed in Table I. I n order to establish that the slopes of the lines in plots such as Figure 3 do not result from mix-solvency or other effects, experiments identical with those already described were carried out with saturatedhy drocarbons as solutes. Figure 4 shows a plot of K L against Table I: Formation Constants K1 at 50, 60, and 70" for 1 : l Hydrogen-Bonded Complexes between Didecyl Sebacate and Aliphatic Alcohols ----&, Alcohol
50°
2-Propanol 1-Butanol 2-Butanol 2-Methyl-1-propanol 2-Met hyl-2-propanol
1.80 1.89 1.48 1.77 1.48 1.51 1.83 1.23
2-pent an
3-Methyl-1-butanol 1,l-Dimethyl-1-propanol
1. mol-I---60'
(1.63) 1.67 1.31 1.57 1.32 1.37 1.65 1.10
Table I1 : Thermodynamic Data for 1:1 Hydrogen Bonding between Aliphatic Alcohols and Didecyl Sebacate a t 60"
2-Propanol 1-Butanol 2-Butanol 2-Methyl-1-propanol 2-Methyl-2-propanol 2-Pentanol 3-Methyl-1-butanol 1,l-Dimethyl-1-propanol
-ASo,
-AHo,
- AUO,
kcal mol-'
kcal mol-'
deg-1
2.1 2.4 2.5 2.8 2.5 2.4 2.1 2.3
0.33 0.34 0.18 0.30 0.18 0.21 0.33 0.06
5.3 6.2 6.9 7.5 6.9 6.5 5.3 6.6
OR1
mol-]
70'
1.48 1.51 1.18 1.37 1.18 1.21 1.51 1.00
260 24 0 220 200
cAfor n-hexane which establishes that K Lis independent of C, for such substances since the spread of the data is within the range 3=1.25% which must be within any reasonable estimate of experimental and procedural error. An indication of the errors introduced by failing to follow the procedures outlined is illustrated in Figure 5 in which we plot VNi/VLagainst C, for a range of ho for elution of 2-methyl-1-propanol a t 50". We see that a series of lines is obtained and that both KLo and KI vary by more than 10% over this small range of effective sample size. If larger samples of alcohol were used the errors could well approach 100%. Further, and most important, if data for a single howere plotted, the linearity would be sufficiently good as to give no indication of error. As a final check on our procedures the data of Figure 5 can be corrected by subtracting from each the quantity [(V,/V,) - K L ]derived from against VL-l. When the appropriate plots of VN,./VL this is done, the four lines of Figure 5 collapse into one, with a maximum spread of i1% on the points for any value of cA. Plots of log K1 against 2'-l yield good straight lines; Figure 8 illustrates this with the data for four of the alcohols. The thermodynamic data derived from such plots are listed in Table 11.
'04 0
0.1
0.3
0.5
c,. mol I-'.
Figure 4. Plot of K L against ,C for elution of n-hexane from DDS-squalane columns at 60". The Journal of Physical Chemistry
180 160 1401 0
,
,
0.1
0.2
,
,
,
,
0.3
0.4
0.5
0.6
c,,mol I-', Figure 5. Plots of V N j / V sagainst ,C (DDS in squalane) for data corresponding to various ho, uncorrected for surface effects. Elution of 2-methyl-1-propanol a t 50".
0.25
-
I
2.95
3.00
3.05
3.10
lO'/T, deg-'
Figure 6. Log K I against T-' plots for A , 1-butanol; B, 2-propanol; C, 2-pentanol; D, 2-methyl-2-propanol.
Discussion The glpc method enjoys the considerable advantage that work a t high dilution of X in X is readily possible because of the high sensitivity of available detector systems. Thus, both self-association and formation of complexes of high stoichiometry are likely to be encountered only infrequently and, further, concentration dependence of KI due to activity changes will be of little consequence. These assumptions underlie the basic theory adopted here and its validity is confirmed
3853
CONCURRENT SOLUTION AND ADSORPTION PHENOMENA IN CHROMATOGRAPHY
I
c
I
,
16
-
15
-
14
-
13
-
I3
a,
p L 0 E
0 0
12 11
-
h-
J
r'
e
++
+ -AG~', kcal mol-' at 50".
a 0
Figure 8. Plot of partial molal excess free energy of solution (&e) of alcohols in squalane (50') against free energy of formation of alcohol-DDS complexes (AGO) a t 50". Key: 1, 2-propanol; 2, 1-butanol; 3, 2-butanol; 4, 2-methyl-1-propanol; 5, 2-methyl-2-propanol; 6, 2-pentanol; 7, 3-methyl-1-butanol; 8, 1,l-dimethyl-1-propanol.
+t +O
5
1
10
-ASo, cal mol-' deg"
15
.
Figure 7 . Plots of - A H ' / l 'against - A S " . Key: e, C1-Cs alcohols/di-n-propyl ether; f , Cl-G'b alcohols/diethyl ether;l0 0,methanol, 0, ethanol, and A, Lbutanol with acetone, henzophcnone, or ethyl acetate;" X, this work.
could serve to indicate serious discrepancy, which is not apparent in the present instance. An interesting aspect of the data is that a quantitative correlation between the partial excess free energy (qZe)for dissolution of alcohols in squalane and the free energy of complex formation is indicated. Values of qze are available from our earlier work6 and these are plotted against -AGO in Figure 8. Within the very reasonable error limits indicated, the data can be represented by the expression gze = (-2.5AG"
+ 0.330)
=k
0.10 koa1 mol-'
A similar, qualitative correlation is implied in the results of an infrared study of methanol-aromatic systems by Josien and Fuson.l5 The factors leading to low solubility in the nonpolar solvent are thus, in gross terms, those which lead, in the converse sense, to increasing complex stability. The data for the 1-01s in fact would fit, with negligible error, a common linear plot, thus indicating a quite direct correlation along the lines suggested. The data for the Csand Cd 2-01s, on the other hand, show that, whereas molecular size and point of substitution affect the value of the activity coefficient of the alcohol in squalane, they have no influence on K I . This illustrates that more subtle effects are a t work in the solution process. The work described appears to us to establish that the basis of the glpc approach to H-bonding studies,
by the excellent linearity of the plots in Figure 3. There is thus little question that the alcohol-DDS interaction involves formation of a single H bond in the conditions of this work. There is, clearly, considerable self-consistency in the values of K1 obtained since they compare in magnitude with those generally found in alcoholic systems* while their sequence is the same as has been observed previously in the majority of studies.O The values of - AH" and - ASo might be regarded as somewhat low. However, they accord well with those reported for interaction of alcohols with weak bases such as dioxane, acetone, and ethyl acetate,10-12for example. There is thus little reason to doubt these values. Figure 7 (8) A. K. Chandra and A. B. Sanigrahi, J . Phys. Chem., 69, 2494 illustrates a plot of - A H " / T against -ASo for the (1965). data obtained here and for a wide variety of other data (9) A. K.Chandra and S. Basu, Trans. Faraday Soc., 56, 632 (1960). relating to alcohol interaction with dioxane, ketones, (10) M. Tsuboi, J . Chem. SOC. Japan, Pure Chem. Sect., 72, 146 (1951). esters, and ethers. Our results are obviously consistent (11) J. J. Lindberg, SOC.Sci. Fennica, 2 0 , 5 (1957). with these others. Such plots as these are not very (12) E.Grunwald and W. C. Coburn, J . Amer. Chem. Soc., 80, 1322 meaningful, as we have pointed out e l ~ e w h e r e ,since ~ ~ ) ~ ~ (1958). essentially they may merely tie together the data for (13) S.H.Langer and J. H. Purnell, J . Phys. Chem., 67,263 (1963). systems for which K1 lies within a fairly restricted range (14) S. H.Langer and J. H. Purnell, ibid., 70,904 (1966). (the broken line corresponds to K1 = 1). Even so, they (15) M.L.Joaien and N. Fuson, J . Chem. Phys., 22, 1169 (1954). Volume 73, Number 11 November 1969
3854
HENRY F. LEFEVREAND RICHARD B. TIMMONS
as developed here, is valid and that the technique offers much potential. The method is relatively rapid, can be employed with impure compounds, makes small demands on special experimental and theoretical skills, and requires moderately inexpensive equipment. Further, it is ideally employed in the region of infinite dilution and, most important, allows study over very wide temperature ranges. A special advantage over the infrared method is the fact that a wider range of solvents may be available since, in the latter technique, a clear solvent spectrum in the appropriate region is demanded. The one apparent drawback of the glpc
method, the required involatility of the solvent could presumably be largely or totally overcome by use of suitable pre-saturation or closed circuit gas flow techniques. l7
Acknowledgments. The authors are grateful to the Foxboro Go., Foxboro, Mass., for the award of a scholarship (D.F.C.) and of a grant for equipment and chemicals. (16) I. Motoyama and C. H. Jarboe, J.Phys. Chem., 71,2723 (1967). (17) E. D. Becker, Spectrochim. Acta, 17,436 (1961).
The Kinetics of the Reaction of Trifluoromethyl Radicals with Ammonia
by Henry F. LeFevre and Richard B. Timmons Department of Chemistry, The Catholic University of America, Washington, D . C. 20017 (Received April 7, 1969)
The gas-phase reaction of trifluoromethyl radicals with ammonia has been studied over the temperature range 81-252'. The trifluoromethyl radicals were generated by photolysis of CFJ. The rate constant for the reaction CF3 NH3 -t CFsH NH2 was found to be k = (3.3 f 1.3) x 1Olo exp { (-8300 f 200)/RT} in units of cm3 mol-' sec-l, A comparison of CF3 and CHa reactions with various polar and nonpolar molecules is presented. The difference in activation energy for these two radicals is consistently lower with polar molecules than with nonpolar substrates. However, there appears to be no simple systematic trend between the activation energy difference and the polarity of the substrate.
+
+
Introduction The gas-phase H-atom abstraction reactions of CH, and CF3 radicals have been studied with a large number of substrates. In reactions where the H atom is abstracted from a hydrocarbon the results of various workers consistently reveal that the CF3 reactions occur with activation energies which are of the order of 3 kcal/mol lower than the corresponding CH3 reactions. This is not surprising in view of the fact that the C-H bond-dissociation energy in C R H is larger than the C-H bond energy in CHJ. In comparing CF3 and CH3 reactions with polar inorganic molecules the above mentioned generalization of greater CF3 reactivity is not always observed. For example, in comparing the reactions of CF3 and CH3 radicals with HCl1P2and HBr,3-5 the CF3 reactions are reported to be slower than the corresponding CH, reactions. In the case of H I reactions5s6the specific rate constants reported for these two radicals are very similar, resulting from the fact that although the CH3 reaction has a higher activation energy the preexponential factor is approximately 6 times larger than The Journal of Physical Chemistry
the value obtained in the CF3 reaction. A similar situation pertains in comparing CF3 and CH3 reactions with SiHC137S8 where again a higher activation energy for the CH3 reaction is offset by a preexponential factor reported to be 20 times larger than that obtained for the CF3 reaction. Conflicting results have been reported for CH3 and CF3 reactions with HzS. The original rate constants reported for CH3 reaction with N2S9J0 are probably too high, as pointed out recently (1) R. J. Cvetanovic and E. W. R. Steacie, Can. J . Chem., 31, 158 (1953). (2) J. C. Amphlett and E. Whittle, Trans. Faraday SOC.,62, 1662 (1966). (3) G. C. Fettis and A. F. Trotman-Dickenson, J. Chem. SOC.,3037 (1961). (4) B. G. Tucker and E. Whittle, Trans. Faraday SOC.,61, 866 (1965). (6) J. C. Amphlett and E. Whittle, ibid., 63, 2695 (1967). (6) M. C. Flowers and 8. W. Benson, J. Chem. Phys., 38, 882 (1963). (7) J. A. Kerr, D. H. Slater, and J. C.Young, J . Chem. SOC.,A , 104 (1966). (8) T. N. Bell and B. B. Johnston, Aust. J. Chem., 20, 1545 (1967). (9) N. Imai and 0. Toyama, Bull. Chem. SOC.Jap., 33, 652, 1120 (1960).
