Part V – May 1969 - Papers - Enthalpy Interaction Coefficients of Silver, Cadmium, and Gold in Dilute Quaternary Tin-Rich Solutions

Equations for the heat effects of additions of mixtures of multicomponent phases to a solution have been derived in terms of the enthalpy interaction coefficients. By these equations and the measured composition dependence of the heat effects on addition of mixtures of Ag-Cd solid solutions and elemental gold to liquid tin-rich solutions, values of the enthalpy in-teraction coefficients in tin-rich solutions at 541°K have been obtained. Analysis of these results in terms of the regular solution theory and the quasichemical theory suggests that near the melting point of the solvent association in the solution becomes important. SEVERAL recent papers have discussed the nature of dilute solutions on the basis of measured enthalpy interaction coefficients. l-3 These coefficients contribute to the understanding of the constitution of solutions and can be used for the evaluation of thermo-dynamic data of multicomponent systems. Their experimental determination, however, is laborious. This communication reports values of the enthalpy interaction coefficients of silver, cadmium, and gold in liquid tin-rich solutions obtained from the measured heat effects of additions of mixtures of Ag-Cd solid solutions and elemental gold to liquid tin-rich solutions. These measurements were made in the course of the determination of the heats of formation of Ag-Cd solid solutions reported in a concurrent publication.4 THE HEAT EFFECT OF AN ADDITION TO A SOLVENT This analysis is concerned with the addition of a mixture of multicomponent phases from the temperature To to a solvent of known composition at temperature T. If Nmixture << Nsolvent, where N designates the gram-atoms involved, the heat effect per g-atom of mixture added can be expressed as (HT - HT )i = difference in heat contents of component element i in the mixture at T and To Q = heat effect on solution of the mixture at temperature T Also1 Q = S Xi [2] where ?Hi ,T,x = relative partial enthalpy per g-atom of i in solution at temperature T and composition of the solution x x = average of the atom fractions of the added material in solution before and after the addition The relative partial enthalpy ?Hi per g-atom of an element i in a dilute solution composed of a solvent 1 and the solutes j = 2, ... m is related to the interaction coefficients by the following equation5 ?Hi - ?Hi-?Hi,x1-1 + S n1ixj+ . . . +S...S...S nrixn2... Xnji...Xnmm+... [3] vhere Xj = atom fraction of solute j in the solution nri = the rth order enthalpy interaction coefficients, which can also be represented by the more general designation5 L(i)n2,n3...nm and nj may have any positive integral value or zero. For identification of various rth order interaction coefficients, nri is written as nn2i2,...nij,...nmm. Eqs. [1], [2], and [3] combine to give the following general equation for the heat effect on addition of a small quantity of a mixture to a large quantity of a dilute solution n = _?ga ?Ha,To + ? Xi(HT - HT o)i a. i + ?xi?Hi,X,i?1 + ??xnjixj + . . . + ???. . .?. . .?xinrix2n2. . . xnji. . . xnmm+ . . . [4] The first term on the right-hand side of this equation is the heat of decomposition at the addition temperature of the phases present in the mixture, the second term is the heat required to raise the temperature of