GORDON ATKINSON AND SERGIO PETRUCCI
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mechanism involves the heterolytic dissociation on a dual site consisting of an incompletely coordinated aluminum ion and another component such as a surface oxide ion, this involving what is essentially a partial reduction of the aluminum ion. The subsequent oxidation of that ion could then be the rate-determining step. This is not necessary if a modified spreading mechanism is accepted, but then the surface diffusion of an entity other than a hydrogen atom or ion is re-
quired. This could involve OH and OD species, the mass difference then not giving rise to an appreciable isotope effect. The low-temperature surface migration of hydroxyls appears unlikely, but cannot be ruled out.
Acknowledgment. Support for the work by Contract No. DA36-039-AMC-O2170(E), monitored by U. S. A.E.L., and Contract Nomr 404(19), is gratefully acknowledged.
Ion Association of Magnesium Sulfate in Water at 25”
by Gordon Atkinson and Sergio Petrncci Department of Chemistry, University of Maryland, CoEEege Park, Maryland
(Received March 16, 1966)
The ultrasonic absorption of aqueous MgS04 solutions has been measured at 25” over the frequency range 5-255 Mc. Two relaxations are found in this range. These together with the lower relaxation previously measured by others allow a complete analysis of the relaxation data in terms of the Eigen three-step association mechanism. The rate constants and equilibrium constant for the first and fastest step are consistent with a diffusioncontrolled process of the two hydrated ions. The slower steps presumably depend on the rate of exchange of solvent molecules on the anion and cation of the ion pair.
The problem of ion association, formulated in the classical theories of Bjerru” and FUOSS,~ has attracted chemists for many years. Experimental studies of ion association by many different techniques appear regularly in the scientific literature. Two recent monograph~~ have . ~ summarized the present status of the theory and the experimental progress so far achieved. The constant interest in ion association derives both from its fundamental importance in solution theory and from its practical importance in such widely different fields as live polymer growth6 and biochemFuoss in his monograph on conductance7 proposes ion association based on the sphere-ina-continuum model of the Debye-Huckel-Onsager theory. I n his theory the ions are assumed to be spheres of radius a = R where R is the hydrodynamic radius. These spheres are hydrodynamically rigid a mechanism for
The Journal of Physical Chemistry
and conform to the Stokes model* but upon ion pairing undergo loss of solvent until the ionic center-to-center distance equals a. It was clear in the picture that the solvent shell around the unassociated ions had a thickness equal to a/2. This seems in conflicte with the (1) N. Bjerrum, Kgl. Danske Vdenskab. Selskab, 7 , No. 9 (1926). (2) R.M. Fuoss, J. A m . Chem. SOC.,80, 5059 (1958). (3) C. B. Monk, “Electrolytic Dissociation,” Academic Press Inc., New York, N. Y.,1961. (4) C. W. Davies, “Ionic Association,” Butterworth and Co., Ltd., London, 1962. (5) M. Szwarc, et al., J. Phys. Chem., 69, 608. 612,624 (1965). (6) E.Q., G. L. Eichorn in “Chemistry of the Coordination Compounds,’’ J. Bailer, Ed., Reinhold Publishing Corp., New York, N. Y.,1956, Chapter 21. (7) R. M. Fuoss and F. Accascina, “Electrolytic Conductance,” Interscience Publishers, Inc., New York, N. Y., 1959. (8) G.G.Stokes, Trans. Phil. Soc., 8 , 287 (1945). (9) D. J. Karl, Ph.D. Thesis, Michigan State University, 1960.
IONASSOCIATIONOF 1LIgS04IN HzO AT 25"
general belief that solvation decreases as ion radius increases for ions of a given charge. The above theory is classical in that it assumes the solvent to be a structureless, condensed gas-like medium that can be completely characterized by its bulk properties, in particular its dielectric constant and viscosity. In the process of ion association the solvent was pushed away from between the ions until actual ion-ion contact occurred. For some of the alkali halides, this approach seemed very accurate because of the numerical correspondence between the sum of the ion radii and the experimentally determined UJ valuelo (the conductance mean distance of closest approach). However, other salts gave U J values substantially less than the sum of the ion radiia very discouraging result. It is also apparent that specific ion-solvent interactions" cannot be comfortably accommodated within such a model. Recently, more and more evidence has accumulated demonstrating that any theory that makes the solvent bulk dielectric constant the controlling factor in association cannot be a d e q ~ a t e . ' ~ Even ~ ' ~ the analysis of the various experimental data on such a simple salt as KCl14 shows marked deviations from predicted behavior. I n view of these facts two different directions have been taken in an attempt to resolve the problem. One group of workers has concentrated on reexamining the mathematics of the conductance theory so that the derived KA would be more solidly based.15*16 This has not really resolved the problem but has increased the ambiguity of the smaller derived association constants ( K A < 40). The other group of workers has taken its cue from the recent revival of mechanistic inorganic chemistry." The application of techniques such as nmr18 and relaxation technique^'^ has clearly shown ( 1 ) the existence and properties of definite solvation numbers for quite a few ions,20( 2 ) the effect of selective solvation in a solvent mixture,21( 3 ) the existence for 2 :2 electrolytes of a multistep ion-association process involving stepwise removal of solvent molecules from between ions. The important conclusions were that the different ion-pair species are in equilibrium, the contact ion pair was not energetically favored, and the conductimc.trically determined association constant included contributions from all the ion pairs present.22 I n other words, none of the three different ion-pair states examined in the above system (R/InS04in HzO) contributed to the conductance of the solution. Therefore, the primacy of the contact ion pair must be rejected for this type of salt. It should be noted that this still leaves the Bjerruni type of ion association as a possibly useful description but not the FuossRamsey contact model.2a The first model considers ions as being paired if
3123
their potential energy is greater than 2kT. The potential energy is calculated from the simple Coulomb law. All pairs of oppositely charged ions between the distance
and some minimum (contact) distance are considered paired; all pairs above a distance r are considered free and subject to the regular Debye atmosphere effects. The second model counts as ion pairs only those ions in actual physical contact. Both models seem artificial if one ever starts to think about solvent molecules. Recently, an extensive investigation of ultrasonic absorption in MnS04 solutions has been reported. Investigations were carried out as a function of temperature in waterz4and at 25" in methanol-water and dioxane-water mixtures.22 The relaxation spectra obtained are shown to be due to the stepwise association of Mn-tZand S04-z ions in the three-step process originally postulated by Eigen25 M+2(aq)
I
I1
kiz
kZ8
+ SO4-2(aq) I-[M(WW)SO,]
ha2
kri
0
0 I11 liar
[R!r(W)SO*]
[II/IS04] krs
where W represents a water molecule trapped between the ions. The postulate of two, one, and no water molecules for the three ion-pair states was not proven but chosen as the simplest picture available. Although Eigen showed the need for a three-step process, the (10) Reference 7, p 203. (11) J. B. Hyne, J . A m . Chem. Soc., 85, 304 (1963). (12) A. D'hprano and R. M. Fuoss, J . Phys. Chem., 67, 1704, 1722 (1963). (13) G. Atkinson and S. Petrucci, J . Am. Chem. SOC.,86, 7 (1964). (14) S. Petrucci, Acta Chem. Scund., 16, 760 (1962).
J. Phys. Chem., 66, 477 (1962). M.Fuoss and L. Onsager, ibid., 67, 28, 621 (1963).
(15) D. J. Karl and J. L. Dye, (16) R.
(17) F. Basolo and R. G. Pearson, "Mechanism of Inorganic Reactions," John Wiley and Sons, Inc., New York, N. Y., 1958. (18) E. F. Caldin, "Fast Reactions in Solution," Blackwell Publications, Oxford, 1964, Chapter 11. (19) Reference 18, Chapters 4, 5. (20) R. E. Connick and R. E. Poulson, J . Chem. Phys., 30, 759 (1959). (21) 2. Luz and 5. Meiboom, ibid., 40, 1058, 1066 (19134). (22) G. Atkinson and S. K. Kor, J . Phys. Chem., 69, 128 (1965). (23) J. T. Denison and J. B. Ramsey, J . A m . Chem. Soe., 77, 2615 (1955). (24) G. htkinson and S. K. Kor, submitted for publication. (25) M. Eigen and K. Tamm, Z . Elektrochem., 66, 93, 107 (1962).
Volume 70,Number 10 October 1966
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data available to him showed two relaxation frequencies (at most) for the 2 : 2 sulfate solutions instead of the required three. How-ever, Smithson and LitovitzZ6 had reported a "middle" relaxation in aqueous AlnS04 solutions at about 30 ;\ICin addition to the 3- and 200;\IC relaxations reported by Tamm. This was then verified in this laboratory.22 The existence of all three relaxation frequencies has also been demonstratedZ7vz8 for aqueous CoSO4. It was then decided to reexamine the classic case of aqueous MgS04 solutions in an attempt to find a third relaxation peak in addition to the two used by Eigen. In addition, the RlgSO4 equilibrium is inherently interesting because of its responsibility for the large excess absorption at ultrasound in sea water. Aqueous T\lgS04 solutions have been examined acoustically by several workers in the past L!O years. The pioneering work of Leonard29 and Liebermann30was followed by the more systematic measurements of B i e ~ , ~Wilson,32 l and Tamm.33 A very well-defined peak was found with a maximum in the region of 0.15 l l c . In the region above 1 ;\IC some relatively inaccurate measurements were re~ et al., ~ Over ~ the ~ range , 343 1lc,34 ported by B Then Kurtze and Tamm35 published a second paper shelving a second maximum at approximately 200 ;\ICfor a 0.1 Jl solution at about 20". I n this paper measurements are reported in 0.10, 0.15, and 0.20 JiT solutions at 25" over the frequency range 3-255 Mc.
Experimental Section Apparatur. The transmitted pulse technique36 was used for all measurements. For the frequency range 1-60 bIc the apparatus used has been previously de~cribed.~'In the range 40-200 Mc, the apparatus used consisted of a 1-in. path length interferometer cell, a Chesapeake U-100 pulser, an RDO receiver, and a Tektronix 531A oscilloscope. The calibrated comparison signal was obtained from a Hewlett-Packard 608D signal generator pulse modulated by a Dumont 256 AR scope. For the range 100-255 Mc, the Chesapeake pulser-RDO receiver combination was replaced by a Nadison PR 201 transmitter-receiver. The technique consists of displaying the received pulse train on the oscilloscope together with the standard pulse. Initially, the first received pulse and the standard pulse are adjusted to the same amplitude. The standard pulse is then decreased by a given number of decibels and the path length increased until the two signals are again equal. Usually two or three received echos can be used so as to give replicate measurements. A plot of attenuation (decibels) us. distance (centiThe Journal of Physical Chemistry
GORDON ATKINSON AND SERGIO PETRUCCI
meters) gives a straight line with the absorption coefficient as the slope. All measurements were made at 25" with the temperature controlled to *0.05". The 1-in. cell used a 0.5-in. diameter X-cut quartz crystal fronted by a 1in. length quartz delay line as a sender, and a 1-in, diameter X-cut crystal as the receiver. Crystals with fundamentals of 3, 4, 5 , 7, 10, 15, and 20 Mc were used. It should be pointed out that in water at 25", 1 db attentuation requires 20 cm path length at 5 blc but only 0.077 cm at 255 N c . This explains the necessity for the specific cell instrumentation for the different frequency ranges. Materials. The RSgS04 was AR grade dried to its anhydrous form at 200" for 3 6 4 8 hr. Analysis of the solutions by ion-exchange techniques confirmed the weighed concentrations within O.2V0. The solvent used was conductance water obtained by passing distilled water through a double ion-exchange column.
Results and Calculations Measurements of the absorption coefficient were repeated at least twice at each frequency with a fresh solution. The results reported are the averages of the replicate runs. The basic information desired is the excess absorption coefficient per wavelength p = (ax
-
asXs)
(1)
where a = absorption coefficient in solution, X = wavelength in solution, a, = absorption coefficient in solvent, and X, = wavelength in solvent. Since the velocity dispersion is quite small, we let X = A, and used the data of Greenspan and T ~ c h i e g gfor ~ ~the velocity of sound in pure water. For aswe used the average value determined in this laboratory with the three pulse (26) J. R. Smithson and T. 8.Litovitz, J . Acoust. SOC.Am., 28, 462 (1956). (27) H. Siegert, Acustica, 13, 48 (1963). (28) G. Atkinson and 9. K. Kor, Physical Chemistry Symposium "Fast Reactions in Solution," Buffalo, N. Y., 1965, to be published: (29) R. Leonard, P . Combs, and L. Stridmore, J . Acoust. Soc. Am., 21, 63A (1949). (30) L. Liebermann, ibid., 20, 868 (1948). (31) D. Bies, J . Chem. Phys., 23, 428 (1955). (32) 0. Wilson and It. Leonard, J. Acoust. Soc. Am., 26, 223 (1954). (33) G. Kurtze and K. Tamm, Acustica, 3, 33 (1953). (34) W. C. Smith, R. E. Barrett, and R. T. Beyer, J . Acoust. SOC.Am., 23, 71 (1951). (35) K. Tamm, G. Kurtze, and R. Kaiser, Acustica, 4, 380 (1954). (36) J. M. M. Pinkerton, Proc. Phys. SOC.(London), B62, 129, 286, (1949). (37) G. Atkinson, S. K. Kor, and R. L. Jones, Rev. Sci. Instr., 35, 1270 (1964). (38) M. Greenspan and C. E. Tschiegg, J . Res. S a t l . Bur. Std., 59, 249 (1957).
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IONASSOCIATION OF MgSOl IN HzO AT 25"
-
-
I
I
-
8-
1
I l l 1 1 1
"Middle"
I
I
I
I
Relaxation
--
l l l l i
F 2%
4-
g
3-
-
2-
-
f
