Chapter 16, Problem 16.159MP

In qualitative analysis, ${\text{Ca}}^{2+}$ and ${\text{Ba}}^{\text{2}+}$ are separated from ${\text{Na}}^{+}$ , ${\text{K}}^{+}$ , and ${\text{Mg}}^{\text{2}+}$ by adding aqueous ${\left({\text{NH}}_{\text{4}}\right)}_{\text{2}}{\text{CO}}_{\text{3}}$ to a solution that also contains aqueous ${\text{NH}}_{\text{3}}$ (Figure 16.18). Assume that the concentrations after mixing are $0.0\text{8}0\text{ M }{\left({\text{NH}}_{\text{4}}\right)}_{\text{2}}{\text{CO}}_{\text{3}}$ and $0.{\text{16 M NH}}_{\text{3}}$ .

(a) List all the Bronsted—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 $K_{\text{sp}}$ 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 ${\text{CO}}_{\text{3}}{}^{\text{2-}}$ concentration is large enough to give observable precipitation of ${\text{CaCO}}_{\text{3}}$ and ${\text{BaCO}}_3$ but not ${\text{MgCO}}_{\text{3}}$ . Assume that the metal-ion concentrations are 0.010 M.

(d) Show quantitatively which of the ${\text{Mg}}^{\text{2}+}$ , ${\text{Ca}}^{2+}$ , and ${\text{Ba}}^{\text{2}+}$ ions, if any, should give an observable precipitate of the metal hydroxide.

(e) Could the separation of ${\text{Ca}}^{2+}$ and ${\text{Ba}}^{\text{2}+}$ from ${\text{Mg}}^{\text{2}+}$ be accomplished using $0.{\text{80 M Na}}_{\text{2}}{\text{CO}}_{\text{3}}$ in place of $0.0\text{8}0\text{ M }{\left({\text{NH}}_{\text{4}}\right)}_{\text{2}}{\text{CO}}_{\text{3}}$ ? Show quantitatively why or why not.