The complex formation of aluminium sulphate and scandium sulphate is studied in aqueous solution using ultrasonic relaxation techniques in the frequency range 0.23 to 1500 MHz. Two and three chemical relaxation effects are observed for solutions of aluminium sulphate and scandium sulphate respectively, which are consistent with a three step association mechanism. For scandium sulphate rate and equilibrium constants as well as volumes of reaction are obtained for all three reaction steps by analysis of relaxation times and amplitudes.Die Bildung des Aluminiumsulfat-und des Scandiumsulfatkomplexes wurde in waDriger Losung mit Ultraschall-Relaxationsmethoden im Frequenzbereich 0,23 bis 1500 MHz untersucht. Zwei bzw. drei chemische Relaxationseffekte wurden in Losungen von Aluminiumsulfat und Scandiumsulfat beobachtet. Diese Effekte konnen durch einen dreistufigen Assoziationsmechanismus erklart werden. Fur Scandiumsulfat wurden Geschwindigkeits-und Gleichgewichtskonstanten und Reaktionsvolumen aus den Relaxationszeiten und -amplituden berechnet.
IntroductionThe kinetics of formation of metal complexes in aqueous solutions has been the topic of many investigations and for these reactions the Eigen mechanism [l] of stepwise association Mm+ +c-+ k I r Mrn+(S)*Ln-2 Mrn+(S)Ln-3 M p -n ) + (1) is generally accepted. Mmt and Ln-are abbreviations for the free solvated metal ion and ligand, respectively, Mmt(S), L"-for the "outer-outer-sphere-complex" where both metal ion and ligand are solvated so that two layers of solvent molecules separate the ions, Mmt (S)Ln-stands for the "outer-spherecomplex" where only the solvation shell of the metal ion separates metal ion and ligand, and ML(m-n)+ for the contact complex or "inner-sphere-complex". The formation of the inner-sphere-complex is generally the slowest reaction step and in most kinetic studies of metal complex formation it is this step which has been measured. Usually the measurements have been evaluated assuming a two-step mechanism (i. e. neglecting the outer-outer-sphere complex) and estimating the outer-sphere equilibrium constant by means of Fuoss' equation [2].The outer-outer-sphere and outer-sphere complexes form within less than lO-*s. Their formation has been studied using ultrasonic and hypersonic chemical relaxation methods. The formation of the outer-outer-sphere complex (step 1-2) and of the outer-sphere complex (step 2-3) should both cause relaxation effects and from the concentration dependence of the experimentally measured amplitudes and relaxation times it should be possible to calculate rate constants, equilibrium constants, and volumes of reaction (AVO) for the two steps. For this purpose, however, accurate sound absorption data are needed over a wide range of frequencies. Such information is difficult to obtain, furthermore it is difficult to decide unambigiously whether the measurements should be fitted to one [3] or two [4-61 relaxation effects. The present study has been performed to obtain further insight into the formation of solvent separated i...
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