Solubility and Precipitation Reactions | General Chemistry 3

Solubility (generally in g.L^-1): quantity of a substance that is dissolved in a saturated solution
Solubility-product constant K_sp: equilibrium-constant of a dissolution reaction
The solid does not appear in the K_sp expression because it is a pure solid so equal to 1
 

AgBr (s) $\rightleftharpoons$ Ag⁺ (aq) + Br^- (aq)
K_sp = [Ag⁺] [Br^-]

Ag₂CO₃ (s) $\rightleftharpoons$ 2 Ag⁺ (aq) + CO₃^2- (aq)
K_sp = [Ag⁺]² [CO₃^2-]

 The solubility s of an ionic solid can be determined using K_sp
 

AgBr (s) $\rightleftharpoons$ Ag⁺ (aq) + Br^- (aq)
According to the reaction stoichiometry: [Ag⁺] = [Br^-]

Solubility s of AgBr (s) in mol.L^-1 = [Ag⁺] = [Br^-]
⇒ K_sp = [Ag⁺] [Br^-] = s²
⇒ s = $\sqrt{{\mathrm{K}}_{\mathrm{sp}}}$

Solubility S of AgBr (s) in g.L^-1 = s x M_AgBr = $\sqrt{{\mathrm{K}}_{\mathrm{sp}}}$ x M_AgBr

Common ion: ion already contained in the solution
Common ion effect: the solubility of an ionic solid decreases when a common ion is present in solution

Complex ion: metal ion with small molecules or ions attached to it
Complexation reaction: reaction between a metal ion and a molecular or ionic entity called ligand that forms a complex
Formation constant K_f: equilibrium-constant of the formation of a complex ion
 

Formation of the complex ion [Ag(NH₃)₂]⁺:

Ag⁺ (aq) + 2 NH₃ (aq) $\rightleftharpoons$ [Ag(NH₃)₂]⁺ (aq)

K_f = $\frac{\left[\mathrm{Ag}{{\left({\mathrm{NH}}_3\right)}_2}^{+}\right]}{\left[{\mathrm{Ag}}^{+}\right] {\left[{\mathrm{NH}}_3\right]}^2}$

 The solubility of an ionic solid is increased by the formation of a soluble complex ion

Solubility-product concentration quotient Q_sp: same form as K_sp but is expressed in terms of arbitrary concentrations

Q_sp and K_sp can be used to predict whether an ionic solid can precipitate:
Q_sp > K_sp: precipitate forms
Q_sp < K_sp: no precipitate forms
At the equilibrium: Q_sp = K_sp

When equilibrium is disturbed:
Q_sp > K_sp: more precipitate forms until Q_sp = K_sp
Q_sp < K_sp: precipitate dissolves (until Q_sp = K_sp or until the complete dissolution of precipitate)

Amphoteric metal hydroxides: metal hydroxides insoluble in neutral aqueous solutions but soluble in both acidic and basic solutions

In neutral aqueous solutions: no reactions occur
In acidic solutions: reaction similar to an acid-base neutralization reaction
In basic solution: formation of a soluble hydroxy complex ion
 

Al(OH)₃ is an amphoteric metal hydroxides:

Neutral solution: insoluble
Acidic solution: Al(OH)₃ (s) + 3 H₃O⁺ (aq) $\rightleftharpoons$ Al³⁺ (aq) + 6 H₂O (l)     [acid-base neutralization]
Basic solution: Al(OH)₃ (s) + HO^- (aq) $\rightleftharpoons$ [Al(OH)₄]^- (aq)     [formation of a soluble hydroxy complex ion]