The Journal of Physical Chemistry, Vol. 83, No. 21, 1979
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Communications to the Editor (2) R. D. Coombe, D. Piiipovich, and R. K. Horne, J. Phys. Chem., 82, 2484 (1978). (3) R. D. Coombe and R. K. Horne, J. Phys. Chem., 83, 2435 (1979). (4) P. P. Chegodaev, V. I. Tupikov, and E. G. Strukov, Russ. J. Phys. Chem.. 47. 746 11973). (5) V. S. Ai’zoba, F. P. Chkodaev, and V. I.Tupikov, h k / . Akad. Nauk, SSSR, 208, 143 (1977). (6) P. P. Chesodaev, V. I. TuDikov, E. G. Strukov, and S. Ya. Psherhetskii, Hiah En&w Chem.. 12: 98 (1978). (7) J.h.Kieth;-I. J. Solomon, I. Sheft, and H. H. Hyman, Inorg Chem., 7, 230 (1968). Rockwell International Science Center 1049 Camino Dos Rios Thousand Oaks, California 9 1360
R.
D. Coombe” R. K. Horne
Recelved June 14, 1979
210
200
220
230
Heat Capacity of Potassium-Crown Ether Complexes in Aqueous Solution. Manifestations and Quantitative Treatment of Important Reiaxatlonal Heat Capacity Effects
__
240
A (nm)
Figure 1. UV absorption spectrum of the gas phase decomposition products of solid O,’AsF[ (solid line). The broken llne is the absorption spectrum attributed to 0,F in ref 4 and 5, obtained from fhsh photolysis of RF -4- O2 mixtures.
I
0
I 4
I
I 8
I
I 12
I
I 16
I
1 20
TIME (mrec)
Flgure 2. Second-order plot for the decay of 0,F observed in a typical experiment. Each line represents a measurement at a given time during the course of the experiment.
+
0 2 F 02Freaction, or from the removal of O,F by AsF, via an equilibrium analogous to process (3) above: 0 2 F + AsF, +, 02+AsF( (4) This latter possibility seems unlikely, however, since the entire cell was heated well beyond the observation zone and there was no evidence of re-deposited 02’AsF6- solid downstream of the reservoirs. Hence, the present results suggest that either some discrepancy exists between the flash photolysis and thermal decomposition results or the decay mechanisms in these experiments are fundamentally different from one another. It is clear that further experiments are required to firmly establish the decay paths in each case. Acknowledgment. This work was performed under Contract F29601-78-C-0039with the Air Force Weapons Laboratory, Air Force Systems Command, United States Air Force, Kirtland Air Force Base, New Mexico. References and Notes (1) R. D. Coombe, A. T. Pritt, Jr., and D. Pllipovich, ”Electronic Transition Lasers”, Vol. 11, L. E. Wilson, S. N. Suchard, and J. I. Steinfeid, Ed., MIT Press, Boston, 1977, p 107. 0022-3654/79/2083-2806$01 .OO/O
Publlcatlon costs asslsted by the Ministh de /‘Educationdu Qu6bec
Sir: The metal ion complexes formed with macrocyclic ligands such as cyclic polyethersl and cryptates2 have generated much recent interest in various areas of chemistry. The coordination parameters of these ligands, namely, the size of the cavity which hosts the ion, allow a certain degree of ionic specificity which has been widely discussed in relation to biological ionic carrier^.^ The ability of these macrocyclic ligands to “encapsulate” metal ions has been used advantageously in organic synthesis to solubilize electrolytes in nonaqueous phasesa4 This category of complexes has also been examined as extrathermodynamic means of evaluating single ion properties in solution.6 The thermodynamic characterization of the complex formation has now been studied quite extensively for various macrocyclic “crown” ethers and equilibrium constants6 and enthalpy data7 are now available for many metal ion-crown complexes in water. Recently, the-partial molal volume (Q and isentropic compressibility ( K ) have been reported for several of these crown ether complexess with the proposal that such data could be used to evaluate the contribution to P and K of ions due to electrostriction effects. In our current workg to establish sjngle ion values of standard partial molal heat capacities C,” in water, we explored the possibility afforded by ion-macrocyclic ligand complexes. While it is yet too early to judge_theusefulness of this approach to obtain ionic values of C,”, we report below some new observations in the heat capacity behavior of aqueous solutions of a macrocyclic ether (1,4,7,10,13,16-hexaoxycyclooctadecane,18-crown-6)and KC1. Such systems exhibit heat capacity maxima similar to those observed in other aqueous-organic mixtureslO~lland micellar solutions.12 As will be shown below, this heat capacity maximum originates in the perturbation of the complexation equilibrium following the temperature rise in the heat capacity measurement. For the case examined here, the “relaxational” contribution to the heat capacity can be interpreted quantitatively from straightforward thermodynamic analysis. The macrocyclic ether 18-crown-6was purchased from BDH chemicals and recrystallized from petroleum ether; its water content (0.2% or less) was determined with an automatic titrator (Aquatest). KC1 was obtained as Analyzed Reagent (Baker) and used after vacuum drying at 80 “C for 48 h. Distilled deionized water was used in 0 1979 American Chemical Society
The Journal of Physical Chemistry, Vol. 83, No. 21, 1979 2807
Communications to the Editor
all measurements and sample solutions were prepared in Nalgene bottles to avoid ionic contaminants. Because of the reported adverse biological activity of these compounds,13 we have minimized direct manipulation of the solid macrocyclic ether compound; instead, stock solutions of 18-crown-6 (0.12 M) and KC1 (2 M) were used to prepare the working solutions by weight dilution. The molar concentration of each species in the final mixture could be calculated by using the measured densities of the stock and final solutions; the concentration of 18-crown-6was kept near 0.11 M, while that of KCl was varied in the range 0.02-0.4 M. All density measurements were carried out with a digital flow den~imeter;'~ the volumetric specific heat of the solutions was measured relative to water in a differential flow microcalorimeter described by Picker et al.15 The respective resolution of these instruments is 2 X lo4 g cmm3and 5 X J K-l ~ m - ~The , temperature rise during the heat capacity measurements was 1.8 K. The solution densities and volumetric specific heats were treated as described by Hoiland et a1.8 to evaluate the apparent molal volumes ($Jand heat capacities (6,)of the electrolyte KC1 in the mixture of water and 18-crown-6; the mixture is viewed here as the solvent. The experimental details (concentrations, densities, and specific heats) will be reported later and we discuss here only the & results; our $, data was found in satisfactory agreement with that reported by Hoiland et ala8The uncertainty on the 4, data was usually &2 J K-l mol-l and the influence of the latter on A$, for complex formation is given below. By analogy to treatment of data, the apparent molal heat capacity of KC1 in a dilute solution of 18-crown-6may be represented as8 (1) $c,soln = A,H~O + a&, + B'c where &HzO is the apparent molal heat capacity of KC1 in water at the same molar concentration and A&, the change in heat capacity for complex formation; c is the molar concentration of electrolyte and a is the fraction of complexed metal ions. Since the ionic strength is unchanged for the complexation, long-range ion-ion Coulombic interactions should not contribute to A$,; however, contributions from changes in other solute-solute interactions may be expected and these are represented by the B'c term. Hence, in the limit of low salt concentration, - $,,H~O) should yield A$,", the the quantity (l/a)($c,so~n standard heat capacity of complexation. With $v data, the above procedure leads to the same result as that given by the method of Hoiland et a1.,8 though the latter is significantly more elaborate. With 4, data, a plot of ( l / c ~ ) [ $-, $c,H20] , ~ ~ ~vs. KC1 concentration (Figure 1) exhibits a sharp maximum at MKclnear 0.1 ( a 0.8). This important concentration dependence can only be attributed to perturbation of the complexation equilibrium and such effects can be accounted for explicitly as outlined in the following treatment. The complexation reaction between the polyether ligand (L) and the potassium cation (M+) is given L + M+ is LMt with
-
Keq
= [LM+I/([Ll[M+I)
a = [ML+l/[M+l,
where [M+], is the total concentration of M+ in the solution. To simplify, we note [ML+] = x, [M+Io= a, and [L], = b; hence, we can write X Keq = ( a - x)(b - x )
a =x/a
e" I C
d
8
U
I
I
I
I
1
2
3
4
M K C ~ (Mol
Figure 1. Left ordinate: (0)apparent molal heat capacity of transfer of KCI (from water to a 0.1 1 M solution of 18-crown-6 ether) divided by a , the fraction of complexed ions; right ordinate: (---) relaxational contribution to q5c, calculated as (AH"/aXda/d r); the offset between ordinate scales represent the constant term A 4 of eq 2; error bars represent estimated uncertainties.
By analogy to eq 1,and drawing from earlier discussions of the heat capacity of water,16J7we can write an apparent molal enthalpy ($H) for KC1 in dilute solutions of 18crown-6 as follows: + BH'C d",soln = d",HzO + where AH" is the standard heat of complexation and BH'c will again account for minor contributions from changes in other solute-solute interactions. Taking the derivative dcjH/dT, we recover eq 1with, in addition, the relaxational contribution:
The last term can be neglected at this point and d a / d T can be evaluated from K,, and AH' values
with x = l/z{(a+ b + K, -l) - [ ( a + b + K , -lI2 - 4 ~ b ] ~ / ~ ) . The value of Kegis availalle as 107 L mol-l and AH' has been reported as -25.8 kJ mol-l.' From these data and eq 2, we computed the relaxational contribution A&* = (AH"/a)(da/dT); the dashed curve in Figure 1 shows the result for K,, = 110 and AH' = -26 kJ mol-l. Although no attempt was made to obtain a best fit over the entire curve, the agreement with experimental data is remarkable and suggests that, in similar cases, Kq and lAHol (the sign of AHo is not specified) could be evaluated simultaneously from the heat capacity data. Finally, substraction of the relaxational heat capacity A&* from the data (Figure 1, offset between ordinate scales) yields A$,' for the K+/ 18-crown-6 complexation as 55 J K-l mol-'. Judging from the magnitude of the heat capacity changes and the agreement between calculated and ex-
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The Journal of Physical Chemistty, Vol. 83, No. 21, 1979
Additions and Corrections
perimental values, the cation/polyether complexes appear as exceptionaly favorable cases to study relaxational heat capacities. Such quantities, in themselves, are of limited interest since they can be predicted quantitatively for any fast reaction for which equilibrium thermodynamic data are available. However, the possibility of deriving equilibrium constants and/or enthalpies for solute-solute interactions in more complex systems from heat capacity measurements provides sufficient incentive for further investigation. For example, in other aqueous-organic mixtures, where relaxational heat capacity has been found (e.g., alkylammonium sa1ts,16 tert-butyl alcohol,1° tertbutoxyethano1,ll or surfactants,12) such data can serve to characterize solute association in a way complementary to other thermodynamic or relaxation (T-jump, P-jump, and ultrasonic relaxation) measurements.
K. H. Wong, K. Yagl, and J. Srnid, J. Membr. Biol., 18, 379 (1974); D. H. Busch, Acc. Chem. Res., 11, 392 (1978). C. J. Pedersen, J. Am. Chem. Soc., 92, 388-391 (1970). S. Viliermaux and J. J. Delpuech, J. Chem. Soc., Chem. Commun., 478 (1975). H. K. Frensdorff, J. Am. Chem. Soc., 93, 600 (1971). R. M. Izatt, R. E. Terry, B. L. Hayrnore, L. D. Hansen, N. K. Daliey, A. G. Avondet, and J. J. Cristensen, J. Am. Chem. Soc., 98, 7620 (1976). H. Hoiland, J. A. Ringseth, and E. Vikingstad, J . Solution Chem., 7 , 515 (1978). C. Joiicoeur and J. C. Mercier, J . Phys. Chem., 81, 1119 (1977). C. devisser, G. Perron, and J. E. Desnoyers, 55, 856 (1977). G. Roux, 0.Perron, and J. E. Desnoyers, J. Solution Chem., 7 , 639 ( 1976). G. M. Musbally, G. Perron, and J. E. Desnoyers, J. ColloM Interface Sci., 54, 80 (1976). Chem. Eng. News, p 5 (Jan 27, 1975). P. Picker, E. Trembhy, and C. Jolicoeur, J . Solution Chem., 3 , 377 (1974). P. Picker, P. A. Leduc, P. Philip, and J. E. Desnoyers, J. Chem. Thermodyn., 3 , 631 (1971). P. Phillp and C. Joiicoeur, J . Phys. Chem., 77, 3071 (1973). S. W. Benson, J . Am. Chem. Soc., 100, 5640 (1978).
Acknowledgment. The authors gratefully acknowledge financial support from the MinistGre de 1'Education du Quebec and the Universitg de Sherbrooke.
Dgpartement de Chirnle Universit6 de Sherbrooke Sherbrooke, Qu6bec J 1K 2R 1
References a n d Notes (1) C. J. Pedersen, J . Am. Chem. SOC.,89, 7017 (1967). (2) J. M. Lehn, Acc. Chem. Res., 11, 57 (1978).
Received May 16, 1979
ADDITIONS AND CORRECTIONS 1979, Volume 83 Gerald R. Stevenson,* Gary Caldwell, a n d Elmer Williams, Jr.: Anion Radical Solvation Enthalpies. Pages 643-644. In Table I1 the enthalpy of sublimation for 2 mol of anthracene should be -46.8 kcal/mol. This means that the enthalpies for the final reaction in Table I1 and for the reactions depicted in eq 3-7 are incorrect. The following enthalpies of reaction are correct. AN-.,
+ Na+,
-
AN-*HM~A + Na+HMpA
AHo = -179.8 kcal/mol
AN-.,
+ Nat,
-
AN-v,Na+THF
AHo = -178.7 kcal/mol AN-.,
-+
AN-SHM~A
AHo = -72 kcal/mol
Carmel Jolicoeur Luc-Lln Lemelln Rlchard Lapalme
