Resumen de Solution Mixing Calculations for Saturated AC–BC Solutions: A General Analytical Analysis
A closed-form, analytical analysis of the physical and chemical processes that occur when a saturated solution of a slightly soluble ionic salt, AC, is titrated with a saturated solution of a slightly more soluble ionic salt, BC, is developed and applied to the two example systems considered by Schrier in the preceding paper (Schrier, J. J. Chem. Educ. 2021, 10.1021/acs.jchemed.0c01456). The analysis assumes ideal solutions and complete ionization of the dissolved AC and BC ionic compounds. A simple inequality involving the ratios of the respective solubility constants and volumes for AC and BC is derived. This inequality describes when and if a precipitate of the less soluble salt, AC, will occur during the titration. The chemical amount of AC precipitate, if any, and the ion-product Q are obtained as functions of the volume ratio, α. Both of these quantities exhibit maxima at some value of α which is determined in the analysis. The present analytic analysis is compared with the diagrammatic approach presented by Schrier. It is found that some aspects of the system are best addressed by one method. For different aspects, the second method is preferable. In general, the two approaches are found to be highly complementary. It is suggested that the study of this system can be a powerful pedagogical tool in the teaching of the principles involved in dilution, equilibrium, and coupled chemical reactions involving a common ion.
