Dee., 1960
ION
PAIR-QUADRUPOLE EQUILIBRIUM
1901
THE ION PAIR-QUADRUPOLE EQUILIBRIUM. TETRABUTYLAMM0PI;IUM BROMIDE IN BENZENE-METHANOL MIXTURES' BYKURTH. STERN^
AND
EDWIN A. RICHARDSON
Department of Chemistry, University of Arkansas, Fayetteville, Arkansas Received June 8, 1960
An improved equation for the calculation of the ion pair-quadrupole equilibrium constant from dielectric data3 is derived. An electrostatic model for the free energy is presented and compared with experiment. The continuum theory for the solvent is satisfactory for AF, but fails for the entropy.
We have shown recently3that the dielectric properties of tetrabutylammonium bromide-benzenemethanol solutions can be explained in terms of an increase in ion pair concentration (and a corresponding decrease in non-polar quadrupoles) as MeOH is added to benzene; further that the effect is most pronounced at low MeOH concentrations-no quadrupoles remain when the mole fraction MeOH exceeds 0.1--and cannot be explained in terms of an increase in solvent dielectric constant. The purpose of the present work is to present an improved method for the calculation of the ion pair-quadrupole equilibrium constant and to discuss the thermodynamics of the process. Equilibrium Constant.-In the original paper4 "normal" behavior, i.e., one in which no changes in the state of aggregation occur, was defined by equations 12-15 which assumed that the addition of a given amount of salt to a methanol-benzene mixture would increase the polarization aq, much as the same amount, of salt to pure benzene. This assumption cannot be quite correct since the former solvent mould produce more ion pairs for the same amount of salt. This leads us to substitute for equation 14 pi23
=
PIZ
+ dX3
(14')
At X , = Xzc,F C ( p ) = F ( p ) and K + a,i e . , the solute is completely dissociated into ion pairs. At X,= 0, F ( p ) = 0 and
The effect of changing MeOH concentration (X,) on K a t 25" is shown in Table I. All values in this paper have been recalculated on the molarity scale-from the mole fraction scale of the original paper-to facilitate comparison with the ion pairfree ion equilibrium data in the literature. TABLE I
Xs X 10' 0.5 1.0 1.5 2.0 2.5 3.0
EFFECT OF MeOH ON K(25')" KO K K (xz = 0) ( X = 0.005) ( X z = 0.010) X 105
x
104
x IO*
..
5.1
..
5.1 6.2 8.8 5.1
5.7
4.6
6.6 7.0 5.6
3.7
lc
(Xi = 0.015) x 109
.. ..
..
3.3 2.3 2.2 1.1 .. .. 3.3 1.4 XZ,X3 represent the mole fractions of MeOH, Bu4NBr, respectively, but K values are calculated on the molarity scale. For a comparison of the dependence of K on X a with the mole fraction scale, cf ,Tahle VI of ref. 3.
where the subscripts 1,2,3 refer to the non-polar solvent, the polar molecule, and the electrolyte, respectively, and the p's are volume polarizations. On this basis an equilibrium constant for the formal Thermodynamics.-In Table I1 are listed values equilibrium Q 21 can be derived by a method of K a t three temperatures in pure benzene and quite analogous to that given previously. For three benzene-MeOH solutions Each of these F ( p I 5 we then have values has been obtained by averaging K values over all salt concentrations in Table I. The SenF ( p ) = dZ - bZ0 (1) Further, from equation 1 we have at the critical sitivity of the equilibrium to small concentrations point ( i e . , the lowest MeOH concentration a t which of RleOH is rather striking. Thus a change in dielectric constant from 2.27 (X,= 0) to 2.31 ( X , = no quadrupoles remain) 0.01) changes K by a factor of 200. This is a far FC ( p ) = daXa - bZ0 (2) greater change than has been observed for the ion pair-free ion equilibrium. However, it is clear that Eliminating the term b l o from (1) and (2) gives the change in K cannot be attributed to a change in F ( p ) dCX3 Fo(p) Z = E. Thus, for example, for pure benzene a change in d temperature of 20" (2545") gives a Ae of 0.035. from which Yet in t,his solvent K increases with a decrease in E . [F(p) dcX3 - W p ) The effects are thus in the opposite direction. This has also been noted for the ion pair-free ion 'h = __ = x*1 -2 z xa- [ F ( P ) ddoX3 F c ~ ) ] (') equilibrium of BurNPi in the chlorobenzenes.6 d It is of some interest to calculate the thermodynamic functions for the process since particularly (1) Based in part on the M.S. Thesis of E. A. Richard-on. entropies give some indication of changes in the (2) Electrochemistry Section, National Bureau of Standards, Washington 2 5 , D. C. solvent. The molar entropy in pure benzene is (3) E. A. Richardson and K. H. Stern, J . Am. Chem. Soc., 82, 1296 thus 2.4/2 = 1.2 e.u. From a doubling of particles (1960).
+
+
+
-
(4) For terminology and definitions this paper should be consulted. ( 5 ) F ( p ) = ( ~ i r s pi%) (pia - pi).
-
-
(6) P. H. Flaherty and K. H. Stern, J . Am. Chem. Soc., 80, 1034 (1958).
KURTH. STERNAND EDWINA. RICHARDSON
1902
1101. 64
TABLE I1 ing spheres, but that in their interactions they beEQUILIBRIUM CONSTANTS FOR Q e 21 IN THE BENZENE- have as point charges. Since the free energy of solution for the uncharged ions is independent of METHANOL SYSTEM (MOLARITY SCALE) 1
(“C.)
25 35 45
A-9
9.3 9.3 12.G
X I = 0.005
= 0
x
10-5 6 . 0 6.2 6.6
THERMODYNAMIC
X2
x
X i = 0.010
10-4 3 . 4 2.6 2.4
x
10-3
Xz
= 0.015
1.8 x 10-2 1.1 0.9
TABLE I11 QUANTITIES FOR THE EQUILIBRIUM Q & 21 (MOLARITYSCALE)^
AFOise(koa1.)
AH0 (kcal.)
A S 0 (ca1.P)
5.7 (5.5 2.4 - 12 4.4 0.8 3.4 -3.3 22 .010 -31 .015 2.4 -7.0 Thermodynamic values are given for two moles of electrolyte. 0.000 .005
-
distance and cancels we have omitted it.. It is assumed that the ion pairs are separated to large distances. There are two distances in a quadrupole for ions of nearly equal size : rl = anion-cation distance, r2 = distance between ions of like charge. a+ and a- are the cation and anion radii, respectively. The work of forming a quadrupole in vacuo1oand charging the four ions is 2e2 ea e2 - 4e2 -tl +--+-+a a+
and therefore the work done on the system in moving a quadrupole from the medium to a vacuum is
0
U-
alone one would expect R In 2 = 1.4 e.u. This is The work of forming two ion pairs in vacuo from a excellent evidence that the effect on the solvent is quadrupole is virtually negligible, Le., at least no change in solva- W I I = 2 -+-A)e2 tion occurs as quadrupoles separate to ion pairs. 2arl The situation becomes strikingly different when MeOH is added. For every change in X 2of 0.005 r1 rz a+ the entropy decreases by roughly 10 e.u. indicating and the increasing solvation of ion pairs over quadrupoles. Up to a MeOH concentration of 0.015 the ion pairs do not seem to be “saturated” with MeOH since the entropy decrease Ehows no leveling off. The net process The enthalpy decrease is also fairly regular. I n WI” = WI F I X W I I I = 2e2 pure benzene a positive AHo is to be expected if only ion pair-ion pair (electrostatic) “bonds” are broken. With increasing MeOH the greater attrac- For one mole of electrolyte tion of MeOH-electrolyte forces over those of Ne2 1 AFIV= 7( 6 MeOH-MeOH leads to an increasingly negative AHo. More direct evidence for the solvation of BurNBr ion pairs by MeOH has recently been To test this model some choice of distances is necessary. r1 should approximate the usual ion pair obtained from infrared spectra.’ The continuum theory applied to the solvent will contact distance a. For equal anion-cation radii also yield an entropy decrease for the processes r2 = r1.\/2. For other size relationships a particdescribed without requiring a solvation model. ular model must be postulated. The model used For the ion-ion pair equilibrium this has been here is already somewhat simplified since in general worked out by Denison and Ramsey.8 Although anion-anion and cation-cation distances will not the predicted dependence of AFO for this equilib- be equal. This is particularly true for rigid ions of rium on the dielectric constant agrees very well with widely different sizes. At the present stage of the e~perinient,~ there have been very few tests for theory it does not seem worthwhile to introduce too AHo and A S o . In ethylene chloride and ethylidene many arbitrary parameters. The theory can be chloride agreement appears to be satisfactory8; used in two ways: (a) using experimental distances in the chlorobenzenes experimental entropie,0 are to calculate AFO, (b) using experimental AFo’s to about half the predicted ones.6 In order to test the calculate distances. In either case we shall assume continuum theory for the higher equilibrium we that the experimental ion-pair distance for Budwrite, rnalogous to the cycle used by Denison and NBr3 is valid. (a) For a square array in the quadRamsey* rupole r1 = 2.90 k., r2 = r 1 d = 4.90A., AFOca1, = 20.6 kcal. (b) AFOexp (XZ= 0 ) = 2.83 kcal., r2 = Quadrupole IV Separated ion pairs in medium + in medium 3.1 ?i. This calculation indicates that the assumption of a square array for the quadrupole gives quite I11 poor agreement for AFO. An examination of moI1 lecular models shows that the accommodation of the Quadrupole + Separated ion pairs large cations in the quadrupole to an r2 of 3.1 A. in vacuo II in vacuo leads to a tight but not impossible structure. As We assume, as did Denison and Ramsey, that in has been found previously for the ion pair case“ it charging the ions they may be considered conduct-
(&:
+
(i;k)
+
k)
t
(7) J. Bufalini and IC. H. Stern, Science, 1S0, 1249 (1959). ( 8 ) J. T. Denison and J. B. R a m e y . J . Am. Chem. SOC.,77, 2615 (1955). (9) E.&. E . Hirsch and R. M. Fuoss. ibid., 83. 1018 (1960).
(IO) G. P. Hamwell, “Principles of Electricity and Electromagnetism,” 2nd Ed., RfcCraw-Hill Book (20.. New York, N. Y., 1949. p. 48.
(11) K. 1%.Stern, 19, 1114 (1951).
F. H. Healey and A. E. Martell. J. Cham. I’hys.,
SORPTION OF NITRIC OXIDEBY A
Dec., 1960
would require that the anions be in contact with the nitrogen atom of the quaternary ammonium ion, the butyl groups moving out of the way to permit this. Considering the rather crude model used for the electrostatic free energy calculation the agreement must be regarded as satisfactory. The situation is strikingly different as far as the enthalpies and entropies are concerned. A test of the continuum theory for these quantities requires no detailed model. Using experimental AFO's we simply write,* assuming independence of ion size parameters with changing temperature AS0 = AFO (d In D/dT) = ( A F o / T ) ( d In D/d In AH0 = AFo (1 d In D/d In T )
+
T)
2
~GEL~
x
~
~
~
1903
Table I11 shows that agreement is quite poor. This is particularly true of the entropy in which the trend predicted is actually the reverse of the observed one. Also the observed positive entropy in pure benzene is not accounted for by the continuum theory. Clearly the discontinuous nature of the solvent and its specific interactions with the electrolyte must be taken into account. TABLE IV TESTO F
THE x1
CONTINUUM
THEORY' ASOC~IO. (e.".
(25') ; hsOAND AHo AHOoala. (kosl.1
0.0 -4.8 .005 -3.7 .010 -2.7 .015 -2.0 For all solvents d In D/d In T = -0.25.
4.3 3.4 2.5 1.8
and use the values of AFO derived from Table 11. a Calculated enthalpies and entropies are shown in Table IV. This is the test previously applied to Acknowledgment.-We would like to thank the the ion-ion pair equilibrium.6 National Science Foundation for the financial supComparison with the experimental quantities in port of this work.
SORPTION ,4ND MAGNETIC SUSCEPTIBILITY STUDIES ON NTRIC OXIDE-ALUMINA GEL SYSTEMS ,4T SEVERAL TEMPERATURES BY AAGESOLBAKKEN' AND LLOYD H. REYERSON School of Chemistry, University of Minnesota, Minneapolis, Minnesota Received June 18, 1960
Sorptions of nitric oxide by alumina gel were determined a t 181, 102, 207 and 273°K. Magnetic susceptibility of the sorbed nitric oxide was followed by a movable magnet. A rapid physical adsorption of the nitric oxide was in each case followed by a slow chemisorption. This was definitely shown by the magnetic studies, for the susceptibility rose rapidly during the physical adsorption and then remained almost constant or fell slightly during the long period of chemisorption. Desorption of the physically sorbed nitric oxide causes the magnetic suscentibility to fall tzothe starting point. The slow desorption of the chemisorbed gas produces no further change in the susceutibility of the system. Here is a system exhibiting both physical and chemisorption under the same conditions. Further, the rate of chemisorption was found to be faster a t lower temperatures, indicating B negative energy of activation if calculated in the usual manner. The data indicate that the transmission coefficient for the chemisorption is very low.
Introduction Early studies in this Laboratory2on the magnetic susceptibility and sorption of nitrogen dioxide on alumina gel had strongly indicated that NO2 was chemisorbed by alumina gel, and the magnetic studies indicate that aluminum nitrate was formed on the surface. More recent studies3 on the sorption of nitric oxide on silica gel showed marked differences between the behavior of NO2 and KO on this gel. Where the NO2 was physically sorbed and dimerized on the gel, the KO was physically sorbed but showed definite 2rIna/r character until the surface was nearly covered with a monolayer a t lower temperatures. These results suggested that the sorption of NO should be studied on alumina gel under conditions similar to those reported on silica1 gel. The following experiments show markedly different results from those previously reported. Experimental Using the same sorption and magnetic equipment as described earlier,3 isotherm and magnetic susceptibilities
-
(1) Graduate Norwegian Fellow at the University of Minnesota from the Norwegian Institute of Technology, Trondbeim, Norway. ( 2 ) L. H. Reyeraon and John Wertz, THISJOURNAL, 63, 234 (1949). (3) Aage Solbaliken and Lloyd H. Reyeraon, ibid., 63, 1G22 (1958).
were determined a t 181, 192,207 and 273°K. The alumina gel was prepared by the same identical method as in the former study.2 Its area, as determined by the BET-nitrogen method, was found to be 368 m.2/g. In contrast, the silica gel used in the recent worka had an area of 562 m.*/g. The same high purity nitric oxide was sorbed and a t no time during the whole investigation did the sorbed gas show any color, as reported by J. H. deBoer on work done in the laboratories of the States' Mines in Holland.' The very first experiments a t 192'K. showed that a very different process was going on than had been previously observed. A rapid physical adsorption occurred which was followed by a very slow chemisorption. The magnetic susceptibility rose rapidly, following the physical adsorption, until the slow chemisorption began. The susceptibility then remained almost constant or fell slightly during chemisorption. This showed that the physically adsorbed gas behaved in a way similar to that adsorbed by silica geLs The chemisorption which followed was of a very different character from previous chemjsorptions observed in this Laboratory. The initial rate de ended on the pressure of the gas and the temperature. sowever, for similar pressures, the rate increased as the temperature was lowered. The rate for a given pressure and temperature declined slowly with time. If after several hours the gas preseure was reduced to zero, the physically sorbed gas quirkly desorbed and the magnetic susceptibility fell to the initial value. A slow desorption of the chemisorbed gas followed with no change in magnetic susceptibility. Because of this slow desorption, it was found desirable to warm the sample and remove all the adsorbed nitric (4) Personal communication from Professor .J. H. deBoer.
