Complex formation constant and hydration number change of aqua-rare earth ions

Full text: It is now well established that the inner-sphere hydration number of aqua-rare earth ions changes from nine to eight in the middle of the rare earth series. This hydration number change greatly affects the complex formation of rare earth ions as we observe irregular variations in most series behaviours of the complex formation constant (K) in aqueous solution systems when K being plotted against 1/r or r (r is ionic radius of rare earth ion). Furthermore, it shows very anomalous concentration dependence in the sense that nona-aqua Ln3+ ion increases in number with increase in salt concentration in aqueous rare earth salt solution (salt chloride, perchlorate). In this report, a theoretical derivation of the formation constant (K) for the inner-sphere complex formation of rare earth ions with a monodentate ligand was made by taking account of both the hydration number change in the middle of the series and its anomalous salt concentration dependence. The series behaviour of the formation constant against 1/r (or r) is successfully explained with using the empirical finding that K varies almost linearly with 1/r (or r) in the region where only one hydration number dominates. This success is also taken as evidence that the anomalous salt concentration dependence of the hydration number change is caused by the outer-sphere complex formation of rare earth ions with the condition that nona-aqua rare earth ions form outer-sphere complexes more easily than octa-aqua ions