Isothermal Diffusion in the Dilute Range of the System Ca(OH)₂ - H₃PO₄ - H₂O: Theory

The equations describing isothermal diffusion in the dilute range of the ternary system Ca(OH)₂ - H₃PO₄ - H₂O are derived in two ways, first, assuming that the components are electroneutral species and, second, considering the actual ionic species present in solution. It is shown that the two models are thermodynamically equivalent. The theory permits the calculation of the four fundamental diffusion coefficients (phenomenological coefficients) in the concentration range where the Debye-Hückel theory suffices for the calculation of ionic activity coefficients. The equations can be used to test the Onsager reciprocal relations for the diffusion process in the above system. The ionic model was used to calculate practical diffusion coefficients for the electroneutral components from the limiting equivalent conductances of the ions in solutions saturated with respect to hydroxyapatite, Ca₁₀(OH)₂(PO₄)₆. Large diffusion interferences, as revealed by relatively large values for the cross-terms in D , are predicted even for solutions with total molarity in the order of 10^-5. Therefore, diffusion models based on independent fluxes of the components appear to be invalid.