The Precipitation of Sparingly-Soluble Alkaline-Earth Metal and Lead Salts with Slow Development of Supersaturation (Slow Anion and Hydroxyl Ion Addition): Kinetics of Nucleation and Induction Periods

Barium and lead sulphate and chromate precipitations were studied at 20° to 95°C at precipitation rates varying from 10⁻³ to 10⁻⁷ ion l⁻¹ sec⁻¹: the supersaturation was developed by slow direct addition of anion to metal nitrate solution and by neutralisation of equivalent metal salt in excess acid solution. Slow heterogeneous nucleation occurred onto particles dispersed within the aqueous solution. The nucleation rate at any time was Where k_n is the rate constant for heterogeneous nucleation, N_∞ is the maximum number of potential nuclei, n_t is the number of nuclei after time t, I. P_t is the ionic product (C_mt)(C_mt) and 2π is the number of metal salt ions in the critical nucleus, generally eight. Crystal growth started after induction periods (t̄) at times just after the times for maximum rate of formation of nuclei. The induction periods (t̄) for precipitations from solutions of initial cation concentration ^cM₀ varied with precipitation rate (R) according to the relation, where γ = π/(π + 1) and k₁ (the unit reciprocal induction period) = . Nucleation rate constants for different precipitations were estimated from the k₁ values and are tabulated. For slow precipitations by direct anion addition, the rate constants were lower for precipitation from solution of the salt of greater solubility. The rate constants for slow precipitation of metal chromates from acid solution were far lower than those for slow precipitation by direct chromate addition. Rate constants decreased somewhat with rise in precipitation temperature.