Solubility and Mass-Transfer Factors

The smaller the size, the larger is the interfacial area between the solid and liquid and, therefore, the higher is the rate of transfer of material moreover, the shorter is the distance the solute must diffuse with the solid. Nevertheless, fine particles may impede the subsequent particle-liquid separation and liquid circulation. To achieve a uniform dissolution and facilitate the separation, it is generally desirable to choose particles of a narrow size range. 

The ultimate leaching efficiency in the absence of mass-transfer limitations is governed by the solubility of the solute in the solvent the extent to which solid can dissolve in liquids vary enormously. The solubility can be either experimentally determined or, alternatively, it can be estimated based on thermodynamics principles. If the pure solute is a solid at the extraction temperature, the following relates the fugacity of this pure solid solute to its fugacity in the liquid solution  

Equations (15) and (16) suggest that for ideal solutions, i.e., for the solutions involving molecules of similar sizes and intermolecular forces, Yj = 1 and the solubility can be estimated based on enthalpy of fusion, heat capacities of solute in solid and liquid states, and triple point temperature. Moreover, Eqs. (15) and (16) imply that solubility increases with temperature. 

The activity coefficient has to be estimated for nonideal solutions. There is no general method for predicting activity coefficients of solid solutes in liquid solvents. For nonpolar solutes and solvents, however, a reasonable estimate can frequently be made with the regular solution theory, or the Scatchard-Hildebrand relation. 

In using Eqs. (17) and (18), the molar liquid volume of the solvent, can be estimated by resorting to generalized density correlation chart (17). The solubility parameter of the solvent can be determined based on its definition, or. 

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