Distribution of isomorphous salts between aqueous and solid phases in ternary systems

Abstract

Distribution of isomorphous salts between aqueous and solid phases in ternary systems was studied at different concentrations of less soluble salt in the systems magnesium ammonium sulfate-copper ammonium sulfate-water, ferrous ammonium sulfate-copper ammonium sulfate-water, and nickel ammonium sulfate-copper ammonium sulate-water. Applicability of the theoretical equations developed by Doerner-Hoskins, Berthelot-Nernst, and Abu Elamayem for thg separations was investigated. Experimental results were explained by a proper choice of values for the parameters Kand m in Abu Elamayem's equation. These parameters characterize a given system over a wide range of concentrations and can be effectively used in predicting the amount of less soluble salt crystallizing out of the ternary system.Rapid crystallization of a pair of isomorphous salts from an aqueous solution results in a solid solution which changes in composition continuously. A study of the distribution of salts in the resulting system is of considerable theoretical and practical interest. Nonequilibrium states result when crystallization is carried out for short periods. Several equations have been proposed for studying the distribution of salts in ternary systems under equilibrium and nonequilibrium conditions. The Berthelot-Nernst law (Chlopin, 1925) may be written as x a -x -= Dc b -c where a and b are the total amounts of original salts, x and c are the amounts (grams) in the solid phase, (a -x ) and (b -c) are the amounts in the liquid phase, and D is the distribution constant. The logarithmic relation developed by Doerner and Hoskins (1925) for the coprecipitation of radium and barium chlorides with sulfuric acid is of the form d n In -= Xlne f where e and f are the initial amounts and d and n are the final amounts of radium and barium chlorides in solution. X is a constant. Hill et al. (1940) have given a semiempirical relation governing the distribution of a pair of isomorphous salts having a common ion, between the solid and aqueous phases -K R1 R," _ -(3)where R1 and R, are the mole ratios of salts A and B in the liquid and solid phases, respectively, m is an empirical constant, and K is the distribution constant.Abu Elamayem (1964) has worked out eq 4 and 5 for fractional crystallization of isomorphous salts in equilibrium and nonequilibrium systems, respectively y2w(K -1) -y[(w + a)(K -1) + 11 + Ka = 0 (4) r 1 1 where w = fraction by weight of original mixture separated as crystals, y = fraction by weight of less soluble salt in crystals, and a = fraction by weight of the less soluble salt in the original mixtures.MA and MB are the molecular weights of the two salts. K and m are constants employed in eq 3. As a special case when m = 1, eq 5 reduces to r 1 K \ a -wy -1Equations 1-4 are proposed for systems in equilibrium while eq 5 is applicable to a nonequilibrium system.The object of the present investigation was to study experimentally the distribution of a pair of isomorphous salts between aqueous and solid phases and examine the results from t...