50
A Study of Ionic Association in Aqueous Lanthanide Nitrate Solutions by Ultrasonic Absorption Spectroscopy’ R. G a m e y z a and D. W. EbdonZb Contribution f r o m the Dcpartment of Chemistry, University of Maryland, College Park, Maryland 20740. Received June 10, 1968 Abstract: Ultrasonic absorption measurements over a frequency range of 10-250 MHz are reported for some trivalent lanthanide nitrates, perchlorates, and chlorides in aqueous solution. Thermodynamic and kinetic parameters for the formation of MN03*+complexes of neodymium and gadolinium have been determined. The approximations and assumptions made in this calculation are discussed. Changes in relaxation frequency with cation across the lanthanide series are discussed in terms of changes in cation coordination number.
U
ltrasonic absorption measurements have been used extensively in the study of association behavior of bi-bivalent electrolytes and the results have been comprehensively reviewed. The excess sound absorption in these solutions is attributed to a multistate association process. For magnesium sulfate Eigen and coworkers4zj have quantitatively interpreted the absorption in terms of a four-state association in which the solvated ions form solvent-separated ion pairs in which two intervening water molecules are successively replaced to form a contact ion pair. The lanthanide nitrates show maxima in excess absorption per wavelength ( p ) at frequencies between 10 and 100 MHz which are not observed for the chlorides or perchlorates. This considerable excess relaxational absorption is interpreted in terms of a three-state model illustrated in eq 1, where c = stoistep I1
step I
contact Ion
solvent-
separated ion pairs
solvated ions M3+
+ Nos-- f-
M3f. *
.NOa-
kZ1
equil concn
uc
(2
+ u)c
pairs
kzs
k12
Jr MNOs*+
(1)
k32
(1 - u)c
chiometric concentration and u is the degree of dissociation. This is the simplest model consistent with the experimental data. The excess absorption can be represented to within experimental accuracy by a single relaxation process (one which may be characterized by a single time constant or relaxation time) and is attributed to step 11. Evidence of the existence of lanthanide nitrate contact ion pairs has recently been published.6 Lanthanide sulfates show a similar excess absorption which also has been interpreted in terms of contact ion pairing. The sulfate absorption is, however, considerably more complex, and quantitative interpretation is correspondingly less certain. (1) Presented at the 155th National Meeting of the American Chemical Society, San Francisco, Calif., March 31-April 5, 1968. (2) (a) Central Electricity Research Laboratories, Leatherhead, England; (b) Department of Chemistry, Eastern Illinois University, Charleston, Ill. 61920. (3) J. Stuehr and E. Yeager, “Physical Acoustics,” Vol. 11, Part A, W. P. Mason, Ed., Academic Press, New York, N . Y., 1963, p 424. (4) H. Diebler and M . Eigen, Z . Phj,sik. Chem. (Frankfurt), 20, 299 (1959). (5) M. Eigen and I,
=
-&.,
(5)
From eq 4 and 5 the following expression for pmaxis obtained. For a discussion of approximations, see Tamm. l8
C, is the equilibrium concentration of all associated species and (1 - 7) is the degree of reaction 11. A V I , is the change in volume per mole for step 11.
(7) (17) See ref 3, p 384, (18) I
