14. Estimation of Distance between the Metal Complex Ion and the Closest Solvent Water Molecules from Density Data

Katsumi Kurotaki

Keywords: aqueous solution, metal complex, density

Contrary to Archimedes' principle, the level of water in a test tube drops when electrolytes such as CuSO₄ are dissolved in the water and dissociate into ions. This is due to the interaction between ions and water molecules around the ions; water molecules in the hydrogen-bonded network of water are oriented toward an ion by the strong electrostatic force of the ion leading to an increase of packing fraction of water molecules and an abnormal negative V⁰ calculated from density data for these ions, where V⁰ is the molar volume of ion at infinite dilution in water. Electrolyte solution theory predicted the magnitude of the electrostatic effect on V⁰. However, the V⁰ of multivalent metal ion deviates from the theoretical one because multivalent metal ions interact with water molecules by coordination bond formation as well as electrostatic force. On the other hand, the metal complex ions and peroxyanions, [ML_n]^z± whose M have no electrons for a bond with water molecules, interact with water in a purely electrostatic way (where M is metal ion of all kinds, L is NH₃, diamine/2, F^-, Cl^-, CN^-, NO₂^- and O, 1z4). Then the V⁰ of [ML_n]^{z ±} was analyzed on the basis of electrolyte solution theory and scaled particle theory (SPT). For a series of [ML_n]^{z ±} having an identical L, linear relationships are observed between the M-X bond distance, r_MX and the intrinsic volume, V_cav(ML_n) which is equal to the volume of water displaced by them, where X is the coordination atom. The value of dV_cav(ML_n)/dr_MX increased with increasing r_MX. These data were analyzed with the model of an MX_n core where the sphere M* (radius r_M*) is overlapped by n spheres (radii r_X) which are apart by r_MX from M. Assuming that r_M* = (r_MX + r_X)cos, a self-consistent set of r_M* and is determined from the experimental value of dV_cav(ML_n)/dr_MX which is equal to cos dVcav(M*_sphere)/dr_M*, whereis the angle between the MX bond and the closest water molecules in contact with M*. The sum of r_M* and the radius of water molecule (155 pm), r_w is equal to the distance between M and the closest water molecules, r_Mw'2. Table 2 shows the values of r_Mw'2, n_w'2 and dV_cav(ML_n)/dr_MX, where n_w'2 is the hydration number. These data are consistent with the structural data determined by X-ray diffraction. This is the first evidence that there is a clear relationship between thermodynamic and structure data for aqueous electrolyte solution.

Publications:
Kurotaki, K. and Kawamura, S.: J. Chem. Soc. Faraday Trans., 94, 2939- 2943, 1998.