Final answer:
In gravimetric analysis, useful precipitation reactions favor the formation of insoluble products, indicated by a Ksp that is less than one (Ksp < 1). This reflects the solid phase being favored over the dissolution into ions in the aqueous phase.
Step-by-step explanation:
For a precipitation reaction to be useful in a gravimetric analysis, the product formed must be insoluble in water. The equilibrium constant (Kc) for a reaction signifies whether products or reactants are favored in a reversible reaction. For precipitation reactions that form an insoluble product, we actually refer to the solubility product constant (Ksp) rather than Kc.
(a) For the precipitation reaction AgCl(s) = Ag+(aq) + Cl¯(aq), the Ksp expression is [Ag+][Cl¯]. Since AgCl is insoluble, once the concentration of Ag+ and Cl¯ reaches a certain level, AgCl begins to precipitate, keeping the ions in their solubility limit. Thus, for AgCl, Ksp < 1 because it is a sparingly soluble salt, and the equilibrium lies to the left favoring the solid.
(b) For the reaction Pb²+¯(aq) + 2Cl¯(aq) = PbCl²(s), the Ksp expression is [Pb²+][Cl¯]². PbCl² is also insoluble, and thus it has a Ksp < 1, indicating a reaction favoring the formation of solid PbCl² over its ions in solution.
A crucial point to remember is that in the context of gravimetric analysis and precipitation reactions, the solubility product, Ksp, is used instead of Kc. The value of Ksp, being less than one, indicates that the solid phase is favored in the equilibrium, which is the goal for a useful precipitation reaction in gravimetric analysis.