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Inclusion compounds of n-hexane with naphthalene derivatives
J. Chem. Thermodynamics 1971, 3, 243-250
Inclusion compounds of n-hexane with naphthalene derivatives W. L. MASTERTON, C. H. CHEN, C. E. WARING, R. OKSALA, L. BEATTY, and A. KRAUSE Department of Chemistry, University of Connecticut, Storrs, Conn. 06268, U.S.A. (Received 14 August 1970, in revisedform 11 October 1970) Phase diagrams at temperatures above 0 °C are presented for the three systems n-hexane-k 2-methylnaphthalene, n-hexaneq- 2-chloronaphthalene, and n-hexane + 2,3-dimethylnaphthalene. The existence in each of these systems of inclusion compounds of definite stoichiometry is established by thermal analysis and vapor pressure measurements. Compositions and thermal stability ranges of the various complexes were deduced from results obtained by these techniques. Equilibrium constants for decomposition of the complexes and their enthalpies of solution and fusion were also calculated from the results. 1. Introduction During the past 20 years, a great deal of research has been devoted to so-called inclusion compounds, in which molecules of a volatile guest are enclosed within the crystal lattice of a second substance known as the host. Among the first compounds of this type to be studied were the fl-hydroquinone clathrates. Powell and coworkers (1'2) carried out extensive X-ray studies on these substances. They found that small molecules such as argon, methane, and methanol were trapped in a cage formed by three hydroquinone molecules held together by hydrogen bonds, giving the stoichiometric composition M.3CrH4(OH)2, where M is the guest molecule. Another class of clathrates is the gas hydrates, in which water serves as the host. c3- 5) Empirical hydrate formulae such as M ' 1 7 H a O , 3 M ' 1 7 H 2 0 , 3M'23H20, and 4M .23H20 were explained when it was shown that water molecules joined together by hydrogen bonds form cages of different sizes in which small (e.g. Ar, CH4, CO2) or large (e.g. C2HsI, C3Hs) guest molecules are trapped. Another type of inclusion compound is that formed by urea (6'7) and thiourea (s' 9) with aliphatic hydrocarbons. In these species, the guest molecules fit into hollow channels in the host crystal. In the case of urea, the channel is just wide enough to accommodate unbranched hydrocarbon molecules; with thiourea, the somewhat larger channels are capable of accommodating branched-chain and cyclic paraffins. In 1959 Milgrom °°) characterized a series of inclusion complexes formed by n-heptane with 2-methylnaphthalene. He reported three different compounds containing approximately 11, 27, and 50 moles per cent of n-heptane. The complex containing 11 moles per cent of n-heptane (which had two different crystal forms) is
244
W. L. MASTERTON E T AL.
stable between 6 and 25 °C; that containing 27 moles per cent of n-heptane is stable over the narrow range 1 to 6 °C, while the 1 : 1 complex exists below 1 °C. On the basis of X-ray powder patterns, Milgrom suggested a layer structure for these inclusion compounds. Milgrom reported that a variety of compounds in addition to n-heptane can serve as guests in this type of complex; toluene and decalin were mentioned specifically. Moreover, he suggested that other naphthalene derivatives could substitute for 2-methylnaphthalene as a host; 1-methylnaphthalene was cited as an example. No quantitative results were given for these systems. This interesting class of compounds does not appear to have been investigated further during the past decade. It seemed desirable to follow up Milgrom's work by attempting to prepare a variety of inclusion compounds containing an aliphatic hydrocarbon as a guest and a naphthalene derivative as the host. We studied several systems of this type; those which were most accurately characterized were ones in which the guest was n-hexane and the host was 2-methylnaphthalene, 2-chloronaphthalene, or 2,3-dimethylnaphthalene, hereafter referred to as 2-MN, 2-C1N, and 2,3-DMN respectively.
2. Experimental The n-hexane used was "chromatoquality" reagent with a purity greater than 99 moles per cent. Reagent grade 2-CIN (melting temperature 58.9 °C, literature value 55 to 56 °C) was used without further purification. The compounds 2-MN and 2,3-DMN were recrystallized twice from absolute ethanol; the/ products melted at 34.6 and 104.4 °C respectively (literature values are 35.1 °C for 2-MN and 104 to 104.5 °C for 2,3-DMN). Phase diagrams for the three systems were determined from results obtained from thermal analysis and vapor pressure measurements. Final melting temperatures were determined to _ 0.1 °C using a simple thermal analysis cell.t Samples to be analyzed by this and other techniques were allowed to stand overnight in a dry-ice + acetone bath. This procedure was suggested by Milgrom (1°) to allow for the equilibration of any metastable phase. Initial melting temperatures (the temperature at which the first liquid appears upon warming) were measured by two different techniques. One employed a Mettler FP1 melting point apparatus, which detects the onset of melting by an increase in the amount of light passing through the sample, located between a light source and a photocell. The other used a Kofier cold stage microscope enclosed in a glove bag to prevent condensation of moisture. Initial melting temperatures determined by these two methods checked to within -t- 1 °C. The vapor pressure of n-hexane in equilibrium with solid phases at a given temperature was determined by a dew-point method similar to that used by Redlich ~ Details of experimental procedures and tables of original data have been deposited as NAPS document number 01229 from ASIS National Auxiliary Publications Service, c/o CCM Information Sciences Inc., 22 West 34th Street, New York, New York 10001. A copy may be secured by citing the document number and remitting $5.00 for photocopies or $2.00 for microfiche in advance by check or money order payable to ASIS-NAPS.
INCLUSION COMPOUNDS
245
et aL (xt) for h y d r o c a r b o n + urea systems. Starting with a sample containing both
liquid and solid phases, increasing amounts of n-hexane were removed by evacuation until only pure host remained. Dew temperatures were measured (___0.2 °C) as a function of composition; a sharp drop in dew temperature was taken as evidence for the appearance of a new solid phase. Dew temperatures could be translated into vapor pressures by using the equation: (1~) loglo(p/Torr) = - 1654.6 K / T + 7 . 7 2 4 ,
(1)
where T is the dew temperature and p is the vapor pressure at that temperature.t Compositions of complexes, deduced from thermal analysis and vapor pressures, were confirmed by analysis of solid phases isolated at various temperatures. The relative amounts of n-hexane and host in a given solid sample were determined by vapor-phase chromatography.
3. Results
and discussion
Phase diagrams for the three systems, drawn so as to be consistent with the thermal analysis and the vapor pressures, are shown in figures 1 to 3. These diagrams extend only to 0 °C, the lowest temperature at which melting temperatures were measured. I
I
I
[
I
_ 30
joJ
J" J ° L i q u i d + 2-MN •
Liquid i• "~ I O CY ~o-l°Complex I + JComplex I + 2-MN J liquid O I
20 --
Q - -
10
~
o j e ' ~ C o m p l e x II + liquid
/"
o
© i
i
0.5
0.6
FIGURE
1.
I
ComplexII + 2-MN
o I
I
0.7 0.8 x (2-MN)
i
0.9
n-Hexane+2-methylnaphthalene phase diagram.
From both thermal analysis and vapor pressures, it appears that the horizontal transition lines in the diagrams extend all the way to the right-hand axis (pure host). In every case, the observed drop in vapor pressure corresponded to the disappearance of a liquid phase in equilibrium with a particular complex. In none of the systems was there a drop in vapor pressure once the system became completely solid, which t Torr = (101.325/760)kN m-L
246
W. L. M A S T E R T O N E T AL.
[
I
I
I
--T-
I
I
60
Liquid
'1
./'/
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I
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.0
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110
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I
I
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,
~:
I
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-
0.6 0.8 x (2-CIN) n-Hexane-l-2-chloronaphthalenephase diagram.
F I G U R E 2.
%
OI
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/o/Complex II + liquid @ r ' ~ £ ,, I¢° 0 ...... el.... + ...-CIN
80
Liquid o / e j e
60
o /
Liquid + 2,3-DMN
./
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, ,~
o' ComplexI + liquid
°
Complex II + liquid
20
rCeComplexIII +liqui~lO
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©
@ ComplexII + 2, 3- DMN
.O Complex llI + 2, 3:DMN ..]
0 F I G U R E 3.
0.2
0.4 0.6 0.8 x (2, 3-DMN) n-Hexane+2,3-dirnethylnaphthalenephase diagram.
1
INCLUSION COMPOUNDS
247
would have been evidence for a solid-to-solid transition. Similar behavior was noted by Milgrom (1°) for n-heptane + 2-MN. On the basis of figures 1 to 3, one can identify inclusion compounds having the compositions and thermal stability ranges listed in table 1. The estimated uncertainty in composition of the various complexes is + 2 to + 5 moles per cent. The temperature limits within which a given complex is stable are believed to be accurate to + 2 °C. TABLE. 1. Inclusion complexes with n-hexane. The temperatures h and t2 between which the complex, with mole fraction x of n-hexane, is stable are given x
Complex I Complex II Complex I Complex II Complex III Complex I Complex II Complex III
h/°C
n-Hexane + 2-MN 17 14 27 5 n-HexaneW2-C1N 11 25 40 15 67 4 n-Hexane+2,3-DMN 20 30 50 12 67 4
t21 °C
20 14 36 25 15 39 30 12
Vapor pressure measurements were carried out at bath temperatures of 12 and 18 °C for n-hexane + 2 - M N , at 10, 18, and 30 °C for n-hexane +2-C1N, and at 10, 20, and 35 °C for n-hexane + 2,3-DMN. In general, they substantiate the compositions of the various complexes reported in table 1. For example, for n-hexane + 2-MN at 18 °C, a drop in vapor pressure occurs between 12 and 17 moles per cent of n-hexane. This can be associated with complex I, stable between 14 and 20 °C, containing about 17 moles per cent of n-hexane. Again, in n-hexane + 2-C1N at a bath temperature of 10 °C, the break in dew pressure falls between 62 and 68 moles per cent of n-hexane. Referring to table 1, we find that the complex which is stable at this temperature contains about 67 moles per cent of n-hexane. The only serious divergence between dew pressure and thermal analysis results occurs for n-hexane + 2,3-DMN at 35 °C. The transition in vapor pressure at this temperature appears to occur in a sample containing about 30 moles per cent of n-hexane. F r o m thermal analysis (table 1), the complex stable at 35 °C should contain only about 20, and certainly no more than 25, moles per cent of n-hexane. The results of v.p.c, analyses of the solid phases are in general agreement with thermal analysis and vapor pressure results. In n-hexane+ 2,3-DMN, for example, it was possible to identify three complexes containing about 20, 50, and 70 moles per cent of n-hexane. These numbers coincide almost exactly with those reported in table 1 for complexes I, II, and III. Difficulties were experienced in n-hexane + 2-C1N, where adsorption of n-hexane on the host crystals led to v.p.c, analyses of relatively poor reproducibility. 17
248
W.L. MASTERTON ET AL.
In comparing the various systems, the most obvious trend is that of the thermal stability of n-hexane inclusion complexes in the sequence: 2-MN < 2-C1N < 2,3-DMN. From table 1 we find that complex I, containing a relatively small amount ofn-hexane, decomposes at 20 °C for 2-MN, at 36 °C for 2-C1N, and at 39 °C for 2,3-DMN. This trend, as one might expect, correlates with the melting temperatures of the hosts, which increase in the same sequence (2-MN, 35 °C; 2-C1N, 59 °C; 2,3-DMN, 104 °C). The compositions and thermal stabilities of inclusion compounds in n-hexane + 2-MN are roughly comparable to those reported by Milgrom(1°) for n-heptane+ 2-MN. Compare, for example, complex I in n-hexane + 2-MN (17 moles per cent of n-hexane, decomposition temperature 20 °C) with the corresponding complex found by Milgrom, which contains 11 moles per cent of n-heptane and decomposes at 25 °C. Complex II, containing 27 moles per cent of n-hexane, is stable between 5 and 14 °C; the corresponding complex in n-heptane + 2-MN contains the Same mole fraction of guest and is stable in a somewhat lower range, 1 to 6 °C. Results that we have obtained for n-heptane + 2-C1N and n-heptane + 2,3-DMN indicate the existence of inclusion compounds with properties quite similar to those reported in table 1 for n-hexane complexes with these two hosts. The equilibrium constant for the decomposition of a complex: MX,(s) = M(1) + nX(s),
(2)
where MX, represents an inclusion complex and n the stoichiometric number of the host X, can be calculated from the equation :(i 1) K = p/pO, (3) where p is the vapor pressure of guest M in equilibrium with complex and pure host, and p° is the vapor pressure of pure guest M at the same temperature. Values of p, obtained from dew-point measurements, were used to calculate the equilibrium constants listed in table 2. TABLE 2. EquilibriumconstantsK for the decompositionof the complexes according to equation (2) n-Hexane+ 2-MN t] °C K Complex I Complex II
18 12
0.66 0.60
n-Hexane+2 - C 1 N t/°C
ComplexI ComplexII Complex III
30 18 10
K
0.79 0.85 0.90
n-Hexane+2,3-DMN t] °C K ComplexI ComplexII ComplexIII
35 20 10
0.90 0.93 0.94
The equilibrium constant for reaction (2) is, of course, a measure of the stability of a complex at a particular temperature. Values of K much less than unity imply relatively stable complexes; the more nearly K approaches unity, the less stable is the complex. It appears that complex stability in these systems increases in the sequence: 2,3-DMN < 2-C1N < 2-MN. The complexes discussed here are somewhat less stable than hydrocarbon + urea complexes, for which Redlich(11) found equilibrium constants as low as 0.3.
INCLUSION COMPOUNDS
249
Enthalpies o f solution o f the various complexes in excess guest (n-hexane) can be calculated starting with the differential relation: d In x 2 / d T = AHsoln/RT 2,
(4)
where x2 is the mole fraction o f host~ in a saturated solution at temperature T and AHsoln is the molar enthalpy o f solution. Integration gives the equation: In x2 = - AHsoln/RT + C,
(5)
where C is the constant o f integration. F r o m the slope o f a plot of logto x2 against I/T, AHsoln can be evaluated. TABLE 3. Enthalpies of solution AHsol~ of the various complexes in excess guest and enthalpies of fusion AHm of the various complexes AHsoI~ kcalmo1-1
AHm kcalmo1-1
Host Complex I Complex II
n-Hexane+2-MN 3.5 5.1 4.2
2.94 a 4.6 3.8
Host Complex I Complex II Complex III
n-Hexane + 2-C1N 6.4 10.6 9.6 7.5
3.33 b 7.9 7.8 6.4
Host Complex Complex Complex Complex
n-Hexane+2,3-DMN 7.0 I 5.8 I 5.8 II 6.0 III 6.7
4.51 b 3.8 3.8 4.8 5.9
a Taken from reference 10. Measured in this laboratory with a differential scanning calorimeter. Equation (5) was applied to the final melting temperatures presented graphically in figures 1 to 3. (Note that the upper curve o f the phase diagram gives the mole fraction o f host in the saturated solution.) Least-squares analysis o f the solubilities in the temperature range over which a particular complex is stable leads to the enthalpies o f solution given in table 3. Included for comparison are the enthalpies of solution o f the three hosts, obtained by analyzing solubilities at temperatures where the pure host is the only stable solid phase. The estimated accuracy o f the various enthalpies o f solution is + 2 per cent, based u p o n an uncertainty in the final melting temperatures o f ___0.1 °C. t In principle, equation (4) should involve the mole fraction xo of complex in the saturated solution rather than the mole fraction x2 of the host. However, it is readily shown that xo = xa/x~, where x~ is the mole fraction of host in the complex. Since x~ is a constant in the temperature range over which the complex is stable, it follows that d logloxo/dt = d loglox~/dT.
250
w . L . MASTERTON E T AL.
If the liquid solutions were ideal, the enthalpy of solution would be identical with the enthalpy of fusion of the complex, i.e. the enthalpy change for the process: complex(s) = guest(l) + host(l), In practice, a correction should be applied for the non-ideality of the liquid solutions. An estimate of this correction can be obtained by comparing the enthalpies of solution and of fusion of the pure hosts using the relation: AHm(complex) = AHsol,(complex) + x2 {AHm(host)- AHsol,(host)},
(6)
where x2 is the mole fraction of host in the complex. Enthalpies of fusion of the several complexes, calculated from equations (5) and (6), are listed in the last column of table 3. The enthalpies of fusion relative to those of the pure host are largest for the 2-C1N complexes and smallest for the 2,3-DMN complexes. They are of about the same order of magnitude as those reported by Milgrom for n-heptane + 2-MN, namely 4 to 10 kcal tool - I . Incidentally, it should be kept in mind that the enthalpies of fusion in table 3 are quoted for unit amount of c o m p l e x . The calculated enthalpies of fusion for unit amount of h o s t would be larger, particularly for those complexes containing relatively small amounts of host. In n-hexane + 2,3-DMN, for example, the enthalpies of fusion for unit amount of 2,3-DMN would be 4.1 kcal mo1-1 for complex I, 7.0 kcal mo1-1 for complex II, and 12.6 kcal mo1-1 for complex III.
This research was supported by funds provided by the United States Naval Weapons Center, China Lake, California.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Palin, D. E.; Powell, H. M. J. Chem. Soe. 1947, 208. Powell, H. M. J. Chem. Soe. 1948, 61. Stackelberg, M. V. Naturwiss. 1949, 36, 327, 359. Claussen, W . F. J. Chem. Phys. 1951, 19, 259, 1425. Pauling, L.; Marsh, R. E. Proe. Nat. Aead. Sei. U.S.A. 1952, 38, 112. Schlenk, W. Jr. Justus Leibig's Ann. Chem. 1949, 565, 204. Smith, A. E. J. Chem. Phys. 1950, 18, 150. Angla, B. Ann. Chim. 1949, 4, 639. Schlenk, W., Jr. Justus Leibig's Ann. Chem. 1951, 573, 142. Milgrom, J. Y. Phys. Chem. 1959, 63, 1843. Redlich, O.; Gable, C. M.; Dunlop, A. K.; Millar, R. W . Y. Amer. Chem. Soe. 1950, 72, 4153. International Critical Tables, Vol. III, p. 222. McGraw-Hill Book Co. : New York. 1928.
Inclusion compounds of n-hexane with naphthalene derivatives W. L. MASTERTON, C. H. CHEN, C. E. WARING, R. OKSALA, L. BEATTY, and A. KRAUSE Department of Chemistry, University of Connecticut, Storrs, Conn. 06268, U.S.A. (Received 14 August 1970, in revisedform 11 October 1970) Phase diagrams at temperatures above 0 °C are presented for the three systems n-hexane-k 2-methylnaphthalene, n-hexaneq- 2-chloronaphthalene, and n-hexane + 2,3-dimethylnaphthalene. The existence in each of these systems of inclusion compounds of definite stoichiometry is established by thermal analysis and vapor pressure measurements. Compositions and thermal stability ranges of the various complexes were deduced from results obtained by these techniques. Equilibrium constants for decomposition of the complexes and their enthalpies of solution and fusion were also calculated from the results. 1. Introduction During the past 20 years, a great deal of research has been devoted to so-called inclusion compounds, in which molecules of a volatile guest are enclosed within the crystal lattice of a second substance known as the host. Among the first compounds of this type to be studied were the fl-hydroquinone clathrates. Powell and coworkers (1'2) carried out extensive X-ray studies on these substances. They found that small molecules such as argon, methane, and methanol were trapped in a cage formed by three hydroquinone molecules held together by hydrogen bonds, giving the stoichiometric composition M.3CrH4(OH)2, where M is the guest molecule. Another class of clathrates is the gas hydrates, in which water serves as the host. c3- 5) Empirical hydrate formulae such as M ' 1 7 H a O , 3 M ' 1 7 H 2 0 , 3M'23H20, and 4M .23H20 were explained when it was shown that water molecules joined together by hydrogen bonds form cages of different sizes in which small (e.g. Ar, CH4, CO2) or large (e.g. C2HsI, C3Hs) guest molecules are trapped. Another type of inclusion compound is that formed by urea (6'7) and thiourea (s' 9) with aliphatic hydrocarbons. In these species, the guest molecules fit into hollow channels in the host crystal. In the case of urea, the channel is just wide enough to accommodate unbranched hydrocarbon molecules; with thiourea, the somewhat larger channels are capable of accommodating branched-chain and cyclic paraffins. In 1959 Milgrom °°) characterized a series of inclusion complexes formed by n-heptane with 2-methylnaphthalene. He reported three different compounds containing approximately 11, 27, and 50 moles per cent of n-heptane. The complex containing 11 moles per cent of n-heptane (which had two different crystal forms) is
244
W. L. MASTERTON E T AL.
stable between 6 and 25 °C; that containing 27 moles per cent of n-heptane is stable over the narrow range 1 to 6 °C, while the 1 : 1 complex exists below 1 °C. On the basis of X-ray powder patterns, Milgrom suggested a layer structure for these inclusion compounds. Milgrom reported that a variety of compounds in addition to n-heptane can serve as guests in this type of complex; toluene and decalin were mentioned specifically. Moreover, he suggested that other naphthalene derivatives could substitute for 2-methylnaphthalene as a host; 1-methylnaphthalene was cited as an example. No quantitative results were given for these systems. This interesting class of compounds does not appear to have been investigated further during the past decade. It seemed desirable to follow up Milgrom's work by attempting to prepare a variety of inclusion compounds containing an aliphatic hydrocarbon as a guest and a naphthalene derivative as the host. We studied several systems of this type; those which were most accurately characterized were ones in which the guest was n-hexane and the host was 2-methylnaphthalene, 2-chloronaphthalene, or 2,3-dimethylnaphthalene, hereafter referred to as 2-MN, 2-C1N, and 2,3-DMN respectively.
2. Experimental The n-hexane used was "chromatoquality" reagent with a purity greater than 99 moles per cent. Reagent grade 2-CIN (melting temperature 58.9 °C, literature value 55 to 56 °C) was used without further purification. The compounds 2-MN and 2,3-DMN were recrystallized twice from absolute ethanol; the/ products melted at 34.6 and 104.4 °C respectively (literature values are 35.1 °C for 2-MN and 104 to 104.5 °C for 2,3-DMN). Phase diagrams for the three systems were determined from results obtained from thermal analysis and vapor pressure measurements. Final melting temperatures were determined to _ 0.1 °C using a simple thermal analysis cell.t Samples to be analyzed by this and other techniques were allowed to stand overnight in a dry-ice + acetone bath. This procedure was suggested by Milgrom (1°) to allow for the equilibration of any metastable phase. Initial melting temperatures (the temperature at which the first liquid appears upon warming) were measured by two different techniques. One employed a Mettler FP1 melting point apparatus, which detects the onset of melting by an increase in the amount of light passing through the sample, located between a light source and a photocell. The other used a Kofier cold stage microscope enclosed in a glove bag to prevent condensation of moisture. Initial melting temperatures determined by these two methods checked to within -t- 1 °C. The vapor pressure of n-hexane in equilibrium with solid phases at a given temperature was determined by a dew-point method similar to that used by Redlich ~ Details of experimental procedures and tables of original data have been deposited as NAPS document number 01229 from ASIS National Auxiliary Publications Service, c/o CCM Information Sciences Inc., 22 West 34th Street, New York, New York 10001. A copy may be secured by citing the document number and remitting $5.00 for photocopies or $2.00 for microfiche in advance by check or money order payable to ASIS-NAPS.
INCLUSION COMPOUNDS
245
et aL (xt) for h y d r o c a r b o n + urea systems. Starting with a sample containing both
liquid and solid phases, increasing amounts of n-hexane were removed by evacuation until only pure host remained. Dew temperatures were measured (___0.2 °C) as a function of composition; a sharp drop in dew temperature was taken as evidence for the appearance of a new solid phase. Dew temperatures could be translated into vapor pressures by using the equation: (1~) loglo(p/Torr) = - 1654.6 K / T + 7 . 7 2 4 ,
(1)
where T is the dew temperature and p is the vapor pressure at that temperature.t Compositions of complexes, deduced from thermal analysis and vapor pressures, were confirmed by analysis of solid phases isolated at various temperatures. The relative amounts of n-hexane and host in a given solid sample were determined by vapor-phase chromatography.
3. Results
and discussion
Phase diagrams for the three systems, drawn so as to be consistent with the thermal analysis and the vapor pressures, are shown in figures 1 to 3. These diagrams extend only to 0 °C, the lowest temperature at which melting temperatures were measured. I
I
I
[
I
_ 30
joJ
J" J ° L i q u i d + 2-MN •
Liquid i• "~ I O CY ~o-l°Complex I + JComplex I + 2-MN J liquid O I
20 --
Q - -
10
~
o j e ' ~ C o m p l e x II + liquid
/"
o
© i
i
0.5
0.6
FIGURE
1.
I
ComplexII + 2-MN
o I
I
0.7 0.8 x (2-MN)
i
0.9
n-Hexane+2-methylnaphthalene phase diagram.
From both thermal analysis and vapor pressures, it appears that the horizontal transition lines in the diagrams extend all the way to the right-hand axis (pure host). In every case, the observed drop in vapor pressure corresponded to the disappearance of a liquid phase in equilibrium with a particular complex. In none of the systems was there a drop in vapor pressure once the system became completely solid, which t Torr = (101.325/760)kN m-L
246
W. L. M A S T E R T O N E T AL.
[
I
I
I
--T-
I
I
60
Liquid
'1
./'/
+~m@, 40
I
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.0
2O
/C%n~exdiIll
,'~~,~~ 0.2
110
0.0Complex iii + 2 _C1N
I
I
0.4
~
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I
I
t
~
I ¸
,
~:
I
l
I
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w
-
0.6 0.8 x (2-CIN) n-Hexane-l-2-chloronaphthalenephase diagram.
F I G U R E 2.
%
OI
©
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80
Liquid o / e j e
60
o /
Liquid + 2,3-DMN
./
4o •
, ,~
o' ComplexI + liquid
°
Complex II + liquid
20
rCeComplexIII +liqui~lO
Q~Q~---.
©
@ ComplexII + 2, 3- DMN
.O Complex llI + 2, 3:DMN ..]
0 F I G U R E 3.
0.2
0.4 0.6 0.8 x (2, 3-DMN) n-Hexane+2,3-dirnethylnaphthalenephase diagram.
1
INCLUSION COMPOUNDS
247
would have been evidence for a solid-to-solid transition. Similar behavior was noted by Milgrom (1°) for n-heptane + 2-MN. On the basis of figures 1 to 3, one can identify inclusion compounds having the compositions and thermal stability ranges listed in table 1. The estimated uncertainty in composition of the various complexes is + 2 to + 5 moles per cent. The temperature limits within which a given complex is stable are believed to be accurate to + 2 °C. TABLE. 1. Inclusion complexes with n-hexane. The temperatures h and t2 between which the complex, with mole fraction x of n-hexane, is stable are given x
Complex I Complex II Complex I Complex II Complex III Complex I Complex II Complex III
h/°C
n-Hexane + 2-MN 17 14 27 5 n-HexaneW2-C1N 11 25 40 15 67 4 n-Hexane+2,3-DMN 20 30 50 12 67 4
t21 °C
20 14 36 25 15 39 30 12
Vapor pressure measurements were carried out at bath temperatures of 12 and 18 °C for n-hexane + 2 - M N , at 10, 18, and 30 °C for n-hexane +2-C1N, and at 10, 20, and 35 °C for n-hexane + 2,3-DMN. In general, they substantiate the compositions of the various complexes reported in table 1. For example, for n-hexane + 2-MN at 18 °C, a drop in vapor pressure occurs between 12 and 17 moles per cent of n-hexane. This can be associated with complex I, stable between 14 and 20 °C, containing about 17 moles per cent of n-hexane. Again, in n-hexane + 2-C1N at a bath temperature of 10 °C, the break in dew pressure falls between 62 and 68 moles per cent of n-hexane. Referring to table 1, we find that the complex which is stable at this temperature contains about 67 moles per cent of n-hexane. The only serious divergence between dew pressure and thermal analysis results occurs for n-hexane + 2,3-DMN at 35 °C. The transition in vapor pressure at this temperature appears to occur in a sample containing about 30 moles per cent of n-hexane. F r o m thermal analysis (table 1), the complex stable at 35 °C should contain only about 20, and certainly no more than 25, moles per cent of n-hexane. The results of v.p.c, analyses of the solid phases are in general agreement with thermal analysis and vapor pressure results. In n-hexane+ 2,3-DMN, for example, it was possible to identify three complexes containing about 20, 50, and 70 moles per cent of n-hexane. These numbers coincide almost exactly with those reported in table 1 for complexes I, II, and III. Difficulties were experienced in n-hexane + 2-C1N, where adsorption of n-hexane on the host crystals led to v.p.c, analyses of relatively poor reproducibility. 17
248
W.L. MASTERTON ET AL.
In comparing the various systems, the most obvious trend is that of the thermal stability of n-hexane inclusion complexes in the sequence: 2-MN < 2-C1N < 2,3-DMN. From table 1 we find that complex I, containing a relatively small amount ofn-hexane, decomposes at 20 °C for 2-MN, at 36 °C for 2-C1N, and at 39 °C for 2,3-DMN. This trend, as one might expect, correlates with the melting temperatures of the hosts, which increase in the same sequence (2-MN, 35 °C; 2-C1N, 59 °C; 2,3-DMN, 104 °C). The compositions and thermal stabilities of inclusion compounds in n-hexane + 2-MN are roughly comparable to those reported by Milgrom(1°) for n-heptane+ 2-MN. Compare, for example, complex I in n-hexane + 2-MN (17 moles per cent of n-hexane, decomposition temperature 20 °C) with the corresponding complex found by Milgrom, which contains 11 moles per cent of n-heptane and decomposes at 25 °C. Complex II, containing 27 moles per cent of n-hexane, is stable between 5 and 14 °C; the corresponding complex in n-heptane + 2-MN contains the Same mole fraction of guest and is stable in a somewhat lower range, 1 to 6 °C. Results that we have obtained for n-heptane + 2-C1N and n-heptane + 2,3-DMN indicate the existence of inclusion compounds with properties quite similar to those reported in table 1 for n-hexane complexes with these two hosts. The equilibrium constant for the decomposition of a complex: MX,(s) = M(1) + nX(s),
(2)
where MX, represents an inclusion complex and n the stoichiometric number of the host X, can be calculated from the equation :(i 1) K = p/pO, (3) where p is the vapor pressure of guest M in equilibrium with complex and pure host, and p° is the vapor pressure of pure guest M at the same temperature. Values of p, obtained from dew-point measurements, were used to calculate the equilibrium constants listed in table 2. TABLE 2. EquilibriumconstantsK for the decompositionof the complexes according to equation (2) n-Hexane+ 2-MN t] °C K Complex I Complex II
18 12
0.66 0.60
n-Hexane+2 - C 1 N t/°C
ComplexI ComplexII Complex III
30 18 10
K
0.79 0.85 0.90
n-Hexane+2,3-DMN t] °C K ComplexI ComplexII ComplexIII
35 20 10
0.90 0.93 0.94
The equilibrium constant for reaction (2) is, of course, a measure of the stability of a complex at a particular temperature. Values of K much less than unity imply relatively stable complexes; the more nearly K approaches unity, the less stable is the complex. It appears that complex stability in these systems increases in the sequence: 2,3-DMN < 2-C1N < 2-MN. The complexes discussed here are somewhat less stable than hydrocarbon + urea complexes, for which Redlich(11) found equilibrium constants as low as 0.3.
INCLUSION COMPOUNDS
249
Enthalpies o f solution o f the various complexes in excess guest (n-hexane) can be calculated starting with the differential relation: d In x 2 / d T = AHsoln/RT 2,
(4)
where x2 is the mole fraction o f host~ in a saturated solution at temperature T and AHsoln is the molar enthalpy o f solution. Integration gives the equation: In x2 = - AHsoln/RT + C,
(5)
where C is the constant o f integration. F r o m the slope o f a plot of logto x2 against I/T, AHsoln can be evaluated. TABLE 3. Enthalpies of solution AHsol~ of the various complexes in excess guest and enthalpies of fusion AHm of the various complexes AHsoI~ kcalmo1-1
AHm kcalmo1-1
Host Complex I Complex II
n-Hexane+2-MN 3.5 5.1 4.2
2.94 a 4.6 3.8
Host Complex I Complex II Complex III
n-Hexane + 2-C1N 6.4 10.6 9.6 7.5
3.33 b 7.9 7.8 6.4
Host Complex Complex Complex Complex
n-Hexane+2,3-DMN 7.0 I 5.8 I 5.8 II 6.0 III 6.7
4.51 b 3.8 3.8 4.8 5.9
a Taken from reference 10. Measured in this laboratory with a differential scanning calorimeter. Equation (5) was applied to the final melting temperatures presented graphically in figures 1 to 3. (Note that the upper curve o f the phase diagram gives the mole fraction o f host in the saturated solution.) Least-squares analysis o f the solubilities in the temperature range over which a particular complex is stable leads to the enthalpies o f solution given in table 3. Included for comparison are the enthalpies of solution o f the three hosts, obtained by analyzing solubilities at temperatures where the pure host is the only stable solid phase. The estimated accuracy o f the various enthalpies o f solution is + 2 per cent, based u p o n an uncertainty in the final melting temperatures o f ___0.1 °C. t In principle, equation (4) should involve the mole fraction xo of complex in the saturated solution rather than the mole fraction x2 of the host. However, it is readily shown that xo = xa/x~, where x~ is the mole fraction of host in the complex. Since x~ is a constant in the temperature range over which the complex is stable, it follows that d logloxo/dt = d loglox~/dT.
250
w . L . MASTERTON E T AL.
If the liquid solutions were ideal, the enthalpy of solution would be identical with the enthalpy of fusion of the complex, i.e. the enthalpy change for the process: complex(s) = guest(l) + host(l), In practice, a correction should be applied for the non-ideality of the liquid solutions. An estimate of this correction can be obtained by comparing the enthalpies of solution and of fusion of the pure hosts using the relation: AHm(complex) = AHsol,(complex) + x2 {AHm(host)- AHsol,(host)},
(6)
where x2 is the mole fraction of host in the complex. Enthalpies of fusion of the several complexes, calculated from equations (5) and (6), are listed in the last column of table 3. The enthalpies of fusion relative to those of the pure host are largest for the 2-C1N complexes and smallest for the 2,3-DMN complexes. They are of about the same order of magnitude as those reported by Milgrom for n-heptane + 2-MN, namely 4 to 10 kcal tool - I . Incidentally, it should be kept in mind that the enthalpies of fusion in table 3 are quoted for unit amount of c o m p l e x . The calculated enthalpies of fusion for unit amount of h o s t would be larger, particularly for those complexes containing relatively small amounts of host. In n-hexane + 2,3-DMN, for example, the enthalpies of fusion for unit amount of 2,3-DMN would be 4.1 kcal mo1-1 for complex I, 7.0 kcal mo1-1 for complex II, and 12.6 kcal mo1-1 for complex III.
This research was supported by funds provided by the United States Naval Weapons Center, China Lake, California.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Palin, D. E.; Powell, H. M. J. Chem. Soe. 1947, 208. Powell, H. M. J. Chem. Soe. 1948, 61. Stackelberg, M. V. Naturwiss. 1949, 36, 327, 359. Claussen, W . F. J. Chem. Phys. 1951, 19, 259, 1425. Pauling, L.; Marsh, R. E. Proe. Nat. Aead. Sei. U.S.A. 1952, 38, 112. Schlenk, W. Jr. Justus Leibig's Ann. Chem. 1949, 565, 204. Smith, A. E. J. Chem. Phys. 1950, 18, 150. Angla, B. Ann. Chim. 1949, 4, 639. Schlenk, W., Jr. Justus Leibig's Ann. Chem. 1951, 573, 142. Milgrom, J. Y. Phys. Chem. 1959, 63, 1843. Redlich, O.; Gable, C. M.; Dunlop, A. K.; Millar, R. W . Y. Amer. Chem. Soe. 1950, 72, 4153. International Critical Tables, Vol. III, p. 222. McGraw-Hill Book Co. : New York. 1928.