Chapter 15, Problem 15.146MP

In qualitative analysis, Ca²⁺ and Ba²⁺ are separated from Na⁺, K⁺, and Mg²⁺ by adding aqueous (NH₄)₂CO₃ to a solution that also contains aqueous NH₃ (Figure 15.18). Assume that the concentrations after mixing are 0.080 M (NH₄)₂CO₃ and 0.16 M NH₃.

(a)    List all the Brønsted–Lowry acids and bases present initially, and identify the principal reaction.

(b)    Calculate the pH and the concentrations of all species present in the solution.

(c)    In order for the human eye to detect the appearance of a precipitate, a very large number of ions must come together to form solid particles. For this and other reasons, the ion product must often exceed K_sp by a factor of about 10³ before a precipitate can be detected in a typical qualitative analysis experiment. Taking this fact into account, show quantitatively that the CO₃^2– concentration is large enough to give observable precipitation of CaCO₃ and BaCO₃, but not MgCO₃. Assume that the metal-ion concentrations are 0.010 M.

(d)    Show quantitatively which of the Mg²⁺,Ca²⁺, and Ba²⁺ ions, if any, should give an observable precipitate of the metal hydroxide.

(e)    Could the separation of Ca²⁺ and Ba²⁺ from Mg²⁺ be accomplished using 0.08 M Na₂CO₃ in place of 0.080 M (NH₄)₂CO₃? Show quantitatively why or why not.