J . Phys. Chem. 1986, 90, 1143-1147 TABLE V: Interaction Parameter XI2Calculated from Experimental Results of V E and HE,and Excess Volume Calculated with XI3= 0, for n-Alkane + 2-Butanone Mixtures X I 2 .J cm-3 n (n-alkane) VE HE VE,c cm3 mol-' 7 9
10 11 12 16
31.2Ia 37.95" 30.42" 3 1.05" 32.61" 33.27"
54.56
57.66
0.06" 0.01" 0.23" 0.23" 0.21" 0.26'
"Values at 20 O C for x2 = 0.5. bValues at 25 O C for volume fraction = 0.5, from ref 40. = 0. components at 20 OC and for the molecular surface parameter S , the values given by Flory et al.2,42have been used. With these data p has theoretically been calculated as a function of the interaction parameter XI2.The results of such calculation for T = 20 O C and the fixed composition of x2 = 0.5 are as follows. (42) Flory, P. J.; and Hocker, H. Trans. Faraday SOC.1971, 67, 2258. (43) Timmermans, J. Physycal-chemical Constants of Pure Organic Compounds"; Elsevier: Amsterdam, 1950 and 1965. (44) Weissberger, A,; Proskauer, E. S.; Riddich, J. A.; Taops, E. E. "Organic Solvents Physical Properties and Methods of Purification"; Interscience: New York, 1955; Val. 111. (45) Commou, D. J.; Mackor, E. L.; Hijuraus, J. Trans. Faraday SOC. 1964, 60, 1539. (46) Aicart, E. Tesis Doctoral, Universidad Complutense, Madrid 1979. (47) Blinowska, A,; Brotow, W. J . Chem. Thermodyn. 1975, 7, 787. (48) Dusart, 0.;Piekarski, C.; Piekarski, S.; Viallard, A. J . Chim. Phys. 1976, 73, 837. (49) Messow, U.; Doye, U.; Kuchenbecker, D. Z.Phys. Chem. (Leipzig) 1978, 259, 884. (50) Rhim, J. N.; Park, S. S.; Lie, H. C. Hwahak Konghak 1973,11,41. ( 5 1 ) Naidu, G. R.; Naidu, B. R. J . Chem. Eng. Data 1981, 26, 197.
1143
In Table V the values of X12which match our experimental p ( 0 . 5 ) results are shown. There is no clear trend of XI, with n and the differences between X 1 2values for different n-alkane mixtures are, to a certain degree, due to uncertainties in the values of the characteristic and surface parameters of the pure alkanes. In Table V our XI2values calculated from are compared with those calculated by BiroS et aL4' from HE. The interaction parameter deduced from enthalpy is notably larger. That is, the excess volume observed is not as large as would be determined from the balance of enthalpy interactions. The equation of state contribution to is small in these mixtures. The last column of Table V shows the magnitude of p ( 0 . 5 ) calculated with XI, = 0, namely, the contribution to p due just to equation of state differences regardless of interactions. As can be seen this contribution is very small for n = 7 and 9 and about 20-25% for the rest. The major part of is due to the contribution arising with the exchange interactions X 1 2 . Possible conformational adjustments or arrangements between the n-alkane and the ketone existing in the mixture would be reflected in the value calculated for XI2,since in theory this parameter embodies all other effects besides equation of state contributions. It is reasonable to assume that such conformational effects can lead to a shrinking of the total volume of the mixture with respect to the volume determined by the contact interactions between molecular surfaces. The lower values of XI, calculated from p could thus be a consequence of this effect if, as it seems possible, the influence of such conformational arrangements is lower on the energetics of the system (HE) than it is on its volume.
Acknowledgment. We are indebted to C.A.Y.C.T. for financial support (Project 2293/83). Registry No. 2-Butanone, 78-93-3; n-hexane, 110-54-3; n-heptane, 142-82-5; n-nonane, 11 1-84-2; n-decane, 124-18-5; n-undecane, 112021-4; n-dodecane, 112-40-3; n-hexadecane, 544-76-3.
Ion-Pair Solvation Equilibria: Temperature Dependence from Combined Liquid Solution and Matrix-Solvation FT-IR Data Gary Ritzhaupt and J. Paul Devlin* Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078 (Received: September 3, 1985)
The existing THF and glyme matrix-solvation FT-IR data for the lithium nitrate contact ion pair have been augmented by new matrix spectra for the full range of diglyme solvates of LitNO 273 K while the cell was evacuated for use at lower temperatures. Salt solutions in the range 0.08 to 0.20 M were prepared from dried solvent and anhydrous LiNO, and loaded into the sample cell under dry nitrogen. The liquid range for the glyme solutions was limited by crystallization which occurred near 180 K, while the T H F solutions remained liquid to nearly 150 K and the diglyme solutions failed to crystallize even at 110 K. The infrared spectra were measured with a Digilab FTS-2OC vacuum spectrometer at a nominal resolution of 2 cm-I. Liquid-solution spectra were recorded for each 20' decrement between room temperature and the sample-freezing temperature. Crystal-phase solution spectra were observed immediately below the freezing point and at 110 K.S Spectra for the pure solvents at the respective temperatures were also recorded for the purpose of spectral stripping although, because deuterated solvents were used exclusively, only very minor interference from solvent bands occurred in the nitrate-ion u j stretching region. Spectroscopic Results and Discussion The new spectroscopic data are restricted to the behavior of the components of the u j mode of the nitrate ion in the contact ion pair Li+NO< at various stages of solvation. It is advantageous to first examine the results for the matrix solvation of the ion pair by diglyme since this will permit a review of the nature of matrix-solvation data and will also result in a slightly modified interpretation of the published glyme matrix-solvation results. Diglyme Solvates o f L i N 0 3 . Diglyme is a flexible triether that has a trans-trans conformation of minimum energy so that trans-cis isomerization is necessary for other than monodentate coordination to a single ~ a t i o n .Assuming ~ that such isomerization can occur in the low-temperature matrix environment, as has been reported for glyme itself, the matrix-solvation study using diglyme represents the first such investigation using a tridentate solvent. The spectrum obtained for Li+N03-in an argon matrix containing 1 mol % of diglyme is presented as curve d in Figure 1 for comparison with analogous spectra for the solvents T H F and glyme. It has previously been noted that an ion pair in an argon matrix containing 1 mol % of a solvent is typically present in comparable concentrations of the bare ion pair and the singly solvated ion pair for an initial deposit at 12 K.'s6 The annealing of such a deposit, or the use of a matrix containing a higher solvent concentration, results in the preferential formation of higher solvates (as is displayed in Figure 2 ) . Solvation of Li+NO< by one molecule of the monodentate ether T H F results in single solvent coordination with the lithium cation so that the spectrum of curve b of Figure 1 shows primarily the bands for the bare ion pair and the solvate with C N = 1. However, since glyme can act as either a mono- (trans conformation) or bidentate (cis conformation) ligand, the same concentration of glyme also gives rise to a large amount of the singly solvated ion pair but with C N = 1 or C N = 2. This situation is clearly displayed in curve c of Figure 1 and leads to the expectation that the triether diglyme, which can act as either a mono- (trans-trans), bi-(cis-trans), or tridentate (cis-cis) ligand, will, at 1% concentration, lead to single solvates (Le., glyme,.LiNO,) having C N (4) While this work was in progress a very interesting paper describing the far-infrared spectrum of the solvated lithium cation in THF, obtained by the use of a very similar technique, was published and is listed as ref 3. (5) These spectra, although informative of the infrared spectra of certain ion-pair solvates, are not described here but will be a subject of a separate paper. (6) Devlin, J. P.; Consani, K. J . Phys. Chem. 1984, 88, 3269.
The Journal of Physical Chemistry, Vol. 90, No. 6, 1986 1145
Ion-Pair Solvation Equilibria I
I
I
I
I
o
TABLE I: Frequency Assignments (cm-I) for uj, and qbfor the Glyme and Diglyme Solvates of the Lithium Nitrate Ion Pair for the Full Ranee of Cation Coordination Numbers (CN) ~~
~
~
Glyme CN
0
uja
1531" 1269" 262
1 1515" 1278" 237
0 1531" 1269' 262
1 1514" 1278" 236
~ 3 b
Au,
2 1498 I286 212
3 1467 1309 158
4 1445 1320 125
5 1419 1334 85
3 1470 1306 164
4 1448 1320 128
5 1419 1332 87
Diglyme CN uja ujb
Au~
2 1498 1288 210
"These values are from 1% solvent matrix concentrations and, unlike the values for the other solvates, reflect no influence from anion-solvent contact.
I
I
I
1500
1400 crnd
I;
1300
Figure 1. A comparison of the extent of solvent-to-cationcoordination for Li+NO< in argon matrices containing 1% of the ether solvents THF (b), glyme (c), and diglyme (d). Curve a is for lithium nitrate in a pure argon matrix. The numerical labels refer to the CN value for the solvates
S,.LiN03.
1500
1400
1300
cni' Figure 2. Infrared curves for the u j modes of Li+NO< in argon matrices containing diglyme: (a) 1%; (b) 10%;(c) to% at 25 K; (d) 5% at 40 K; (e) 25% at 40 K; (f) 100% at 100 K. The Kvalues represent annealing temperatures; all spectra were measured at 12 K.
values of 1, 2, and 3. Figure 1 is consistent with this view in all respects and certainly conveys the impression that the bands labeled 1, 2, and 3 in curve d are properly assigned to the ion pair singly solvated by diglyme but with different C N values. An
obvious conclusion is that diglyme, like glyme, undergoes considerable but incomplete isomerization during the formation of the matrix at 12 K. The effect of increasing the diglyme matrix concentration and/or annealing the mixed matrices at temperatures above 12 K is shown by the series of infrared curves in Figure 2. The evidence is that the collapse of the nitrate-ion u3 splitting from the bare ion-pair value of 262 cm-I to the completely solvated ion-pair value of 87 cm-' occurs in five distinct steps as labeled in the Figure. However, as has been noted in earlier matrixsolvation studies, it should be recognized that a transition occurs in passing from the 1 to 10 mol % solvent concentration range that causes a shifting and broadening of the individual solvate bands. This effect, which has been tentatively identified with weak solvent-anion association,'%6is emphasized by the off-vertical dashed lines connecting solvate peaks in curves a and b of Figure 2. In the earlier study using the solvent glyme one step in the solvation sequence was never fully developed (step 3 in Figure 3 of ref 1) but was nevertheless counted in arriving at the published C N values for that solvent. Since the peak frequencies for the C N values 1, 2, and 3 are clearly the same for glyme and diglyme (Figure l), as are the peak values for the completely solvated case (Table I), it is likely that the complete solvation sequence occurs very similarly for the two ethers. Thus, based on the present results for diglyme, including the increased confidence in the reality of the weak anion-solvation shift, the earlier data for glyme have been given a slightly different interpretation that is summarized, along with the diglyme results, in Table I. The principal new conclusion is that, for these two ethers, the maximum solvent coordination number is 5 (rather than 6 as suggested previously for glyme) with the corresponding maximum solvation numbers being 3 for glyme and 2 for diglyme. Sohation Equilibria in THF Solutions. The infrared spectra for the lithium nitrate ion pair in liquid T H F solutions at 300, 240, and 180 K are presented in Figure 3. Though the major u3 peaks shift slightly with the reduction in temperature, the primary effect of lower temperature is the gradual elimination of the pronounced shoulder at 1465 cm-'. The stick spectra for the C N = 3 and CN = 4 T H F solvates from matrix-solvation results show that the loss of intensity can be attributed to a shift in the equilibrium concentrations of the two solvates. The 1465-cm-' shoulder is coincident with the u3a band of the solvate THF.LiN03 while the two relatively narrow solution bands that remain at 180 K (1433 and 1325 cm-') are coincident with the published matrix-solvation values for THF4-LiN03.These results confirm the speculation that the primary difference between liquid-solution and matrix-solvation spectra (obtained by annealing the pure glassy solvent matrices) results from an equilibrium shift that favors a higher solvate C N value at law temperatures. Solvation Equilibria in Glyme and Diglyme Solutions. The infrared spectra for the lithium nitrate contact ion pair in liquid glyme solutions at 300, 240, and 180 K are presented in Figure 4. Similar temperature-dependent spectra have been obtained for diglyme solutions but they are not presented here since they
Ritzhaupt and Devlin
1146 The Journal of Physical Chemistry, liol. 90, No. 6, 1986
t I
1500
1400
1300
Cm-1
Figure 3. Liquid solution infrared spectra for Li'NOF in THF (0.09 m): (a) 300 K, (b) 240 K, and (c) 180 K. The stick spectra at the bottom of the figure represent the matrix-solvation values for THF,.LiNO, (unbroken) and THF3-LiN03(broken) from ref 1 .
isomerization and coordination of those glyme molecules that solvate the cation or the solvation of the average cation by an additional glyme molecule. The situation is different for diglyme since the change from a C N value of 4 to a C N value of 5 must occur without a change in the solvation number of 2 (Le., there is not room for 3 of the triether molecules around a single ionpaired cation). Solvation Enthalpies f r o m Temperature-Shifted Equilibria. The reason for the simplification of the spectra in the v3 region of the ion-paired nitrate ion at reduced temperatures for the ether solutions under investigation has apparently been revealed through the comparisons made with the matrix-solvation spectra. It is difficult to conceive a satisfactory alternate explanation. Assuming that the interpretation is correct it is clear that, at least in principle, the spectroscopic data can be used to deduce the enthalpy change associated with the increase in coordination number from 3 to 4 for T H F and from 4 to 5 for glyme and diglyme. Unfortunately, it appears that only estimates can be made because the individual solvate bands themselves display a slight position and bandwidth temperature dependence such that there exists no rigorous approach to the resolution of the composite bands into components assignable to specific solvates. For example, subtraction of the scaled 1432-cm-' band of the T H F C N = 4 solvate, measured at 180 K, from the corresponding band complex measured for the T H F solution at 300 K leaves a distorted band centered at the C N = 3 solvate value of 1465 cm-I. Nevertheless, a simple curve-resolution procedure has yielded approximate relative peak intensity values, for the 1465- and 1433-cm-' component bands of the THF-solution spectra, which have permitted and estimate of K( r ) for the reaction THF3.LiN03 F= THF,.LiN03. The estimated values of K ( T ) for the temperature range 300-220 K varied from 2.2 to 6.4, indicative that AH = -2.0 kcal/mol (-8.3 kJ/mol) for the incorporation of the fourth solvent molecule into the coordination shell. Similarly, K( T ) for the glyme solutions for the equilibrium glymeLiN0, (CN = 4) glyme.LiN03 (CN = 5) has been estimated to vary from 0.37 to 7.3 over the temperature range 300-180 K. This is consistent with an enthalpy change of -3.0 kcal/mol (-1 2.5 kJ/mol). The corresponding values for diglyme were deduced as 0.69 and 4.88 for K ( T ) at 300 and 200 K, suggesting that AH = -2.5 kcal/mol (-10.4 kJ/mol). The above approximate values of AH, for the binding of the last solvent functional group that enters the liquid-solution coordination shell, are unquestionably of the correct sign and order of magnitude. The greatest confidence can be placed in the T H F value since the solvate bands that required resolution (1 465 and 1433 cm-') were more widely spaced than for glyme or diglyme. It is unclear whether or not the greater magnitude indicated for AH for the polydentate ethers is significant in view of the lack of rigor used in the estimation. However, the greater exothermicity could reflect the weaker intrashell steric repulsions that have been suggested for the polydentate ligands based on the apparent tendency to assume a greater maximum CN value.6
' t
1500
1400 -1 cm
Figure 4. Liquid solution infrared spectra for Li*NO< in glyme (0.10 M). The stick spectrum at the bottom of the figure represents the matrix-solvation values for gIyme,.LiNO, (CN = 5) from Table I.
were nearly indistinguishable from those for glyme. These spectra are characterized by a pronounced narrowing of both the spacing between the doublet components and of the bands themselves. At 300 K the peak values (1438 and 1323 cm-I) are not greatly different from the suggested values (1445 and 1320 cm-') for the v j bands of the CN = 4 solvate while at 180 K the liquid solution bands are coincident with the matrix-solvation bands for the CN = 5 solvate. The evidence is substantial that the primary influence of the reduction in temperature is a shift in the solvation equilibrium from one that favors a lower coordination number (Le., 4) at room temperature to one dominated by a higher (Le., 5) CN value at 180 K. As for the case with T H F these data also reveal the major difference between the room-temperature liquid solutions and the annealed pure glassy solvent matrices. However, any complete description of the change within the solvation sphere is complicated by the fact that, in this case, a CN value of 4 can be realized by cation association with either 2 or 3 glyme molecules. Thus, the change revealed in Figure 4 may reflect either an enhanced
Summary Discussion The combination of matrix-solvation spectroscopy of the LiNO, ion pair with low-temperature liquid-solution infrared spectroscopy for LiNO, dissolved in nondissociating ether solvents has provided a unique opportunity for a rather direct spectroscopic study of solution equilibria between ion-pair solvates having coordination shells with different well-defined solvent coordination numbers. There seems to be little doubt that, structurally, the most important equilibria for these particular systems at room temperature is between these different ion-pair solvates, the recognition of which, as spectroscopically defined entities, has depended on the development of a body of data for the individual solvates using the techniques of matrix-solvation spectroscopy.' (7) Prior to this and related matrix-solvation studies it has been a practice to interpret spectra such as that for LiNO, in THF in terms of equilibria involving ion triplets and other exotic species. See, for example, Perelygin, I . S.; Klirnchuk, M. A,; Beloborodova, N. N. Russ. Phys. Chem. 1980, 54, 605.
J . Phys. Chem. 1986, 90, 1147-1152
In the present study that body of data has been expanded to include the five diglyme solvates of LiN03. These spectra represent the first matrix-solvation results for a tridentate ligand. The contrast of the diglyme spectra with those of the T H F and glyme solvates has made it particularly clear that the identification of the solvates having C N values of 1, 2, and 3 is correct in each case. However, based on the diglyme results, a correction has been necessary for the later solvation stages for glyme,.LiN03. Taken together, both the glyme and diglyme matrix-solvation data sets are each best interpreted in terms of five major cation-solvation steps plus one less substantial change that apparently reflects a small but nontrivial effect from solvent contact with the anion. Obviously such contact must occur at some stage in the solvation sequence and evidence is growing that the initial influence occurs as the solvent concentration is increased through the 5 mol % range. On the basis of this new interpretation of the polyether matrix-solvation results, it follows that the dominant room temperature solvate for both glyme and diglyme has a C N value of 4 corresponding to the formula S2.LiN03 (where S is glyme or diglyme). However, cooling of the liquid solutions or formation of the low temperature annealed pure glassy matrix samples results in solvates having identical spectra and which have, therefore, been identified as the C N = 5 ion-paired solvates. The spectroscopic observation of the response of the equilibria between different ion-pair solvates to the reduction of liquid-so-
Vapor-Liquid Equilibrium in the Xenon
1147
lution temperatures has shown that AH, for formation of the final solvent-to-cation coordinate bond, is small and negative with values ranging from -2.0 kcal/mol for T H F (CN = 4) to approximately -3.0 kcal/mol for glyme. These values may be in error by as much as 50% but the spectroscopic data are of sufficient quality to give promise of the future availability of more accurate values. Meanwhile, there appears to be no comparable published values with which to compare the change in enthalpy values. The AH value of the corresponding gas-phase hydration step for Li+ is nearly an order of magnitude greater (-17 kcal),8 a fact that merely gives emphasis to the obvious need to account for solvent-solvent as well as solvent-ion interaction energies.
Acknowledgment. Support of this research by the National Science Foundation under Grant CHE-8420961 is gratefully acknowledged. Registry No. THF, 109-99-9;LiNOI, 7790-69-4; diglyme, 11 1-96-6: glyme, 110-71-4.
(8) Kebarle, P. Ions and Ion-Solvent Molecule Interactions in the gas phase Mass Spectrometry in Inorganic Chemistry; American Chemical Society: Washington, DC, 1960;.Adv. Chem. Ser. No. 72. (9) The isomeric positions around the C-C bond(s) of glyme and diglyme are properly identified as anti, rather than trans, and gauche, rather than cis (Anderson, M.: Karlstrom, G. J . Phys. Chem. 1985, 89, 4957).
+ Ethene System
M. Nunes da Ponte,' D. Chokappa, J. C. G. Calado,t J. Zollweg, and W. B. Streett* School of Chemical Engineering, Olin Hall, Cornel1 University, Ithaca, New York 14853 (Received: September 30, 1985)
Vapor-liquid equilibrium measurements have been performed on mixtures of xenon and ethene at 17 temperatures, between 203 and 287 K, and pressures up to 5.7 MPa. This system exhibits a positive azeotrope and a critical curve with a minimum in temperature. Nine isotherms lie below this minimum, in the subcritical region, and eight above. Two out of these eight have two branches and two critical points, one on the xenon-rich side and another one on the ethene-rich side. Excess Gibbs energies were calculated by the method of Barker. They are in good agreement with earlier measurements.
Introduction A few years ago Calado, Azevedo, and Soares reported meafor surements of the three major excess functions GE,HE,and mixtures of ethane or ethene with the rare gases.' They found that, although the ethane and ethene molecules are very similar (they are often well represented by a bicentric model), their behavior when mixed with spherical molecules, xenon in particular, was very different. Whereas the ethene + xenon mixtures exhibited the behavior normally associated with simple systems the ethane xenon (small positive values for both GE and p), mixtures were found to form with negative values of all three excess functions. This anomalous behavior is unique among all the mixtures of small, simple molecules studied so far and cannot be explained on the basis of the opposite signs of the quadrupole moments of the ethane and ethene molecules. Since the measurements of Calado et al. were done, at most, at two temperatures (at, or close, to the triple point of the spherical molecule'), in the low-pressure region, it seemed worthwhile to investigate the behavior of those systems over much wider temperature and pressure ranges. In a previous paper we presented
+
+On sabbatical leave from Faculdade de CiZncias e Tecnologia, Universidade Nova de Lisboa, 2825 Monte da Caparica, Portugal. *Permanent address: Complexo I, Instituto Superior Tknico, 1096 Lisboa,
Portugal.
0022-3654/86/2090-1147$01.50/0
+
results on the vapor-liquid equilibrium for the xenon ethane mixtures up to the critical curve.* Here we report similar measurements for the xenon ethene mixtures. A comparison between the two systems can now be made on a much firmer basis. We performed vapor-liquid equilibrium measurements at 17 temperatures, ranging from 203 to 287 K, close to the critical point temperature of xenoil (289.74 K). The system exhibits a positive azeotrope at compositions ranging from xXe 0.8 mole fraction in xenon at 161 K (Calado and Soares3) to xXe 0.5 at 283 K, where it merges into the mixture critical line. This line has a minimum in temperature, below the critical temperatures of both pure components. Nine isotherms lie below this minimum, in the subcritical region, and eight above. Of these eight, two correspond to temperatures between the critical curve minimum and the critical temperature of ethene and exhibit two critical points each, one on the ethene-rich side and another one on the xenon-rich side. Excess Gibbs energies GEwere calculated as a function of composition for the eight lower isotherms, at zero reference pressure, by using Barker's method! Comparison with the results of Calado
+
--
(1) Calado, J. C. G.; Comes de Azevedo, E. J . S.; Soares, V. A. M. Chem. Eng. Commun. 1980, 5 , 149. (2) Nunes da Ponte, M.; Chokappa, D.; Calado, J . C. G.; Clancy, P.; Streett, W. B. J . Phys. Chem. 1985, 89, 2746. (3) Calado, J. C. G.; Soares, V. A. M. J . Chem. Thermodyn. 1977, 9, 91 1.
0 1986 American Chemical Society
