15.1 Precipitation and Dissolution

Solubility equilibria and precipitation are key concepts in chemistry. They explain how substances dissolve and form solid precipitates in solutions. Understanding these processes helps predict chemical reactions and their outcomes in various settings.

Calculations using solubility product constants allow us to determine solubilities and ion concentrations. By comparing reaction quotients to Ksp values, we can predict when precipitation will occur. Factors like common ions and solution conditions affect solubility in important ways.

Solubility Equilibria and Precipitation

Chemical equations for solubility equilibria

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• Solubility equilibrium occurs when the rate of dissolution of a solid equals the rate of precipitation in a saturated solution
• Involves the dissociation of a slightly soluble ionic compound (e.g., $\ce{[AgCl](https://www.fiveableKeyTerm:AgCl)}$) into its constituent ions (e.g., $\ce{[Ag+](https://www.fiveableKeyTerm:Ag+)}$ and $\ce{[Cl-](https://www.fiveableKeyTerm:Cl-)}$) in a saturated solution
• General form of a solubility equilibrium equation: $\ce{A_xB_y(s) <=> xA^{y+}(aq) + yB^{x-}(aq)}$
  • $\ce{A_xB_y(s)}$ represents the slightly soluble ionic compound (e.g., $\ce{[Ca3(PO4)2](https://www.fiveableKeyTerm:Ca3(PO4)2)}$)
  • $\ce{A^{y+}(aq)}$ and $\ce{B^{x-}(aq)}$ represent the dissociated ions in the saturated solution (e.g., $\ce{Ca^2+}$ and $\ce{[PO4^3-](https://www.fiveableKeyTerm:PO4^3-)}$)
• Solubility product constant ($K_{sp}$) is the equilibrium constant for a solubility equilibrium
  • General expression: $K_{sp} = [\ce{A^{y+}}]^x[\ce{B^{x-}}]^y$
    • $[\ce{A^{y+}}]$ and $[\ce{B^{x-}}]$ are the molar concentrations of the dissociated ions at equilibrium
    • $x$ and $y$ are the stoichiometric coefficients of the ions in the balanced chemical equation
• Solubility rules help predict whether a compound will dissolve or precipitate in aqueous solutions

Calculations with solubility product constants

• Solubility is the maximum amount of a solute that can dissolve in a given amount of solvent at a specific temperature
  • Molar solubility is solubility expressed in moles of solute per liter of solution (mol/L or M)
• Calculating solubility from $K_{sp}$ involves the following steps:
  1. Write the balanced solubility equilibrium equation
  2. Set up the $K_{sp}$ expression using the equilibrium concentrations of the ions
  3. Substitute the molar solubility (s) for the concentration of each ion, considering their stoichiometric coefficients
  4. Solve the resulting equation for s
• Calculating ion concentrations from solubility is done by multiplying the molar solubility by the stoichiometric coefficient of each ion in the balanced chemical equation
  • Example: For $\ce{AgCl}$, if the molar solubility is $s$, then $[\ce{Ag+}] = [\ce{Cl-}] = s$

Prediction of precipitation reactions

• Precipitation reaction occurs when an insoluble solid (precipitate) forms upon mixing two solutions containing soluble compounds
  • Example: Mixing $\ce{[AgNO3](https://www.fiveableKeyTerm:AgNO3)}$ and $\ce{[NaCl](https://www.fiveableKeyTerm:NaCl)}$ solutions forms a white $\ce{AgCl}$ precipitate
• Reaction quotient ($[Q](https://www.fiveableKeyTerm:Q)$) is the ratio of the product of the concentrations of the products raised to their stoichiometric coefficients divided by the product of the concentrations of the reactants raised to their stoichiometric coefficients
  • For a solubility equilibrium: $Q = [\ce{A^{y+}}]^x[\ce{B^{x-}}]^y$
• Predicting precipitation involves comparing $Q$ to $K_{sp}$:
  1. If $Q < K_{sp}$, the solution is unsaturated, and no precipitation will occur
  2. If $Q = K_{sp}$, the solution is saturated, and no net precipitation will occur
  3. If $Q > K_{sp}$, the solution is supersaturated, and precipitation will occur until $Q = K_{sp}$
• Common ion effect occurs when the presence of a common ion (an ion that appears in the solubility equilibrium expression) decreases the solubility of the slightly soluble compound
  • Example: Adding $\ce{NaCl}$ to a saturated $\ce{AgCl}$ solution will decrease the solubility of $\ce{AgCl}$ due to the increased $\ce{Cl-}$ concentration
• Le Chatelier's principle can be applied to understand how changes in concentration, temperature, or pressure affect solubility equilibria

Factors affecting solubility

• Ionic strength of a solution influences the solubility of ionic compounds
• Activity coefficient accounts for the non-ideal behavior of ions in solution, especially at higher concentrations
• Fractional precipitation is a technique used to selectively precipitate ions from a mixture based on their different solubilities