Solubility and Precipitation Reactions | General Chemistry 3

Solubility (S):

Solubility refers to the maximum amount of a substance that can dissolve in a solvent to form a saturated solution, typically expressed in g.L^-1. At saturation, a dynamic equilibrium is established between the undissolved solid and its dissolved ions, meaning that the rate of dissolution equals the rate of precipitation.

Molar solubility (s):

Molar solubility is the amount of a compound that dissolves in 1 liter of solution, expressed in mol.L^-1, to form a saturated solution. The relationship between solubility and molar solubility is given by:
 

Solubility product constant:

The solubility product constant (K_sp) is the equilibrium constant for the dissolution reaction of a sparingly soluble salt. It represents the product of the molar concentrations of the dissolved ions, each raised to the power of its stoichiometric coefficient.

For a general salt M_mX_x​, that dissociates as follows:

M_mX_x (s) $\rightleftharpoons$ m Mⁿ⁺ (aq) + x X^y- (aq)

The solubility product constant is expressed as:
 

Since the solid phase of the salt is considered pure, its concentration is treated as 1 and does not appear in the K_sp expression.

• 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-]

General steps for calculating molar solubility:

1. Write the balanced dissociation equation for the salt.
2. Define molar solubility s, where s moles of the salt dissolve per liter to form a saturated solution.
3. Set up the K_sp expression by substituting the ion concentrations in terms of s into the K_sp expression.
4. Solve for s by rearranging the K_sp expression.
5. Calculate solubility S in g.L^-1, if required, using the molar mass of the salt: S = s x M.

Solubility of AgBr:

• Dissociation: AgBr (s) $\rightleftharpoons$ Ag⁺ (aq) + Br^- (aq)
• Since [Ag⁺] = [Br^-] = s, we have:
  K_sp = [Ag⁺] [Br^-] = s² ⇒ s = $\sqrt{{\mathrm{K}}_{\mathrm{sp}}}$
• Solubility S in g.L^-1 = s x M_AgBr = $\sqrt{{\mathrm{K}}_{\mathrm{sp}}}$ x M_AgBr

Expressions of the solubility may be more complex, involving s³ or higher powers, depending on the stoichiometry.
 

Solubility of MgF₂:

• Dissociation: MgF₂ (s) $\rightleftharpoons$ Mg²⁺ (aq) + 2 F^- (aq)

• 	MgF2 (s)	Mg2+ (aq)	2 F- (aq)
  Initial Concentration (M)		0	0
  Equilibrium Conc. (M)		s	2s

• K_sp = [Mg²⁺] [F^-]² = s (2s)² = 4s³
  s = $\sqrt[3]{\frac{{\mathrm{K}}_{\mathrm{sp}}}{4}}$

Reaction quotient (Q):

The reaction quotient Q is calculated in the same way as the solubility product constant K_sp​, but it uses the current ion concentrations rather than the concentrations at equilibrium.
 

Predicting precipitation:

By comparing Q to K_sp, we can determine whether a precipitate will form:

• If Q > K_sp: The solution is supersaturated, and a precipitate will form as excess ions combine until Q decreases to match K_sp.
• If Q < K_sp: The solution is unsaturated, so no precipitation occurs; additional solute can dissolve until Q increases to K_sp​.
• If Q = K_sp: The system is at equilibrium; the solution is saturated with no net precipitation or dissolution.

When equilibrium is disturbed:

If the equilibrium is disturbed by concentration changes, Q shifts accordingly:

• If Q > K_sp: More precipitate forms to reduce ion concentrations until Q = K_sp.
• If Q < K_sp: The precipitate dissolves, increasing ion concentrations until Q = K_sp or the precipitate fully dissolves.

The common ion effect:

• A common ion is an ion that is already present in the solution before the addition of a new compound containing the same ion.
• The common ion effect refers to the decrease in solubility of an ionic solid when a common ion is present, as the equilibrium shifts to favor the undissolved solid.
   

• Consider the solubility of CaF₂​ in water:
  CaF₂ ​(s) ⇌ Ca²⁺ (aq) + 2 F⁻ (aq)
• If NaF (which provides additional F⁻ ions) is added to the solution, the increased F⁻ concentration shifts the equilibrium to the left, reducing the solubility of CaF_2​.

The pH of the solution:

The solubility of compounds containing basic anions (e.g., OH⁻, CO₃²⁻​, PO₄³⁻​) increases in acidic solutions. In these cases, H⁺ ions react with the anions, reducing their concentration and shifting the equilibrium to dissolve more of the compound.
 

• Consider the solubility of CaCO₃ in water:
  CaCO₃​ (s) ⇌ Ca²⁺ (aq) + CO₃^2−​ (aq)
• In an acidic solution, CO₃²⁻​ ions react with H⁺ to form HCO³⁻ or H₂CO₃​, lowering the CO₃²⁻ concentration. This shift increases the solubility of CaCO₃​ by driving the equilibrium to the right.

The formation of complex ions:

•  A complex ion is a metal ion with small molecules or ions (ligands) attached to it.
• Some metal ions form complex ions in solution, increasing their solubility. When a ligand (like NH₃ or CN⁻) binds to a metal ion, it forms a soluble complex, shifting the equilibrium to dissolve more of the compound.
   

• Consider the solubility of AgCl in water:
  AgCl (s) ⇌ Ag⁺ (aq) + Cl⁻ (aq)
• If NH₃​ is added, it forms a complex ion with Ag⁺:
  Ag⁺ (aq) + 2 NH₃ (aq) → [Ag(NH₃)₂]⁺ (aq)
• This reaction reduces the Ag⁺ concentration, shifting the equilibrium to dissolve more AgCl ⇒ The formation of [Ag(NH₃)₂]⁺ increases the solubility of AgCl in the presence of NH₃​. 

Amphoterism:

Amphoteric substances can act as either acids or bases, depending on the pH of the solution. Some metal hydroxides, such as Al(OH)₃​, Zn(OH)_2​, and Cr(OH)₃, are amphoteric and dissolve in both acidic and basic environments due to their ability to react with both H⁺ and OH⁻ ions.
 

Amphoteric behavior allows Al(OH)₃ to dissolve in both acidic and basic solutions, enhancing its solubility depending on the pH:

• In acidic solutions, it dissolves by reacting with H⁺:
  Al(OH)₃ (s) + 3 H+ (aq) → Al³⁺ (aq) + 3 H₂O (l)
• In basic solutions, it dissolves by forming a soluble hydroxy complex:
  Al(OH)₃ (s) + OH⁻ (aq) → [Al(OH)₄]⁻ (aq)

Fractional precipitation:

Fractional precipitation is a method used to separate ions in a solution by adding a reagent that selectively causes one ion to precipitate while leaving others in solution. This technique is based on differences in the solubility products (K_sp​) of the ionic compounds formed, allowing for the targeted removal of specific ions.
 

• Separation of Cl⁻ and SO₄²⁻​ by addition of Ba(NO₃)₂:

In a solution containing both Cl⁻ and SO₄²⁻​ ions, adding Ba(NO₃)₂ selectively precipitates SO₄^2−​ as BaSO₄​ due to its low K_sp​ ⇒ BaSO₄​ precipitates first, leaving Cl⁻ in solution, as BaCl₂ is more soluble. Filtering out the BaSO₄ precipitate effectively separates the two ions.
 

• Separation of Ag⁺ and Zn²⁺ by addition of dilute HCl:

In a solution containing Ag⁺ and Zn²⁺ ions, adding dilute HCl selectively precipitates Ag⁺ as AgCl due to its low K_sp​ ⇒ ZnCl₂​ remains soluble, so Zn²⁺ stays in solution. Filtering out the AgCl precipitate leaves Zn²⁺ ions in the solution, effectively separating the two cations.

Steps for fractional precipitation:

1. Identify the K_sp​ values of possible precipitates. Ions with lower K_sp​ values will precipitate first, as they reach saturation at lower ion concentrations.
2. Add a precipitating agent to the solution gradually. As the reagent concentration increases, the ion with the lowest K_sp​ reaches its threshold for precipitation first.
3. Monitor the reaction quotient Q in relation to K_sp​ for each ion. Precipitation occurs when Q = K_sp for a particular ion, allowing for selective separation based on solubility.

Qualitative analysis:

Qualitative analysis is a procedure for identifying the ions present in an unknown solution. Specific chemical tests identify each ion, but interference between ions can complicate testing. Therefore, ions are first separated into groups by selective precipitation. In the traditional qualitative analysis scheme for metal cations, about 20 cations are initially divided into 5 groups.
 

The 5 groups of metal cations:

Metal cations are categorized into 5 groups based on their behavior in qualitative analysis. Each group precipitates under unique conditions, allowing selective separation:

• Group 1: Includes Ag⁺, Pb²⁺, and Hg₂²⁺, which precipitate as chlorides when dilute HCl is added.
• Group 2: Includes Pb²⁺, Cu²⁺, Hg²⁺, Cd²⁺, Bi³⁺, and Sn⁴⁺, which form insoluble sulfides in acidic conditions with hydrogen sulfide (H₂S).
• Group 3: Includes Mn²⁺, Fe³⁺, Co²⁺, Ni²⁺, Zn²⁺, Al³⁺, and Cr3+, which precipitate as hydroxides or sulfides in basic conditions (using NH₃ with H₂S).
• Group 4: Includes Ca²⁺ and Ba²⁺, which precipitate as carbonates when (NH₄)₂CO₃ is added.
• Group 5: Includes Na⁺, K⁺, and Mg²⁺, which do not precipitate under conditions used for Groups 1-4 and remain in solution. Alkali metal ions are often identified by the characteristic colors they produce in a Bunsen flame.

Flowchart for the separation of cations:

• Step 1: Add dilute HCl to the sample ⇒ Group 1 precipitates (AgCl, Hg₂Cl₂, PbCl₂).
• Step 2: Add H₂S ⇒ Group 2 precipitates (PbS, CuS, HgS, CdS, Bi₂S₃, SnS₂).
• Step 3: Add NH₃ ⇒ Group 3 precipitates (MnS, FeS, CoS, NiS, ZnS, Al(OH)₃, Cr(OH)₃).
• Step 4: Add (NH₄)₂CO₃ ⇒ Group 4 precipitates (CaCO₃, BaCO₃).
• Remaining ions in solution: Group 5 cations (Na⁺, K⁺, Mg²⁺) stay in solution and can be identified by flame tests or further testing.