Calculate the molar solubility of barium fluoride in each liquid or solution. b. 0.10 M Ba(NO₃)₂

Verified step by step guidance

1. Write the dissolution equation for barium fluoride (BaF₂): BaF₂(s) ⇌ Ba²⁺(aq) + 2F^-(aq).
2. Identify the initial concentrations of the ions in the solution. Since the solution already contains 0.10 M Ba(NO₃)₂, the initial concentration of Ba²⁺ is 0.10 M. The initial concentration of F^- is 0 M.
3. Set up the expression for the solubility product constant (K_sp) of BaF₂, which is given by K_sp = [Ba²⁺][F^-]². Let 's' be the molar solubility of BaF₂ in the 0.10 M Ba(NO₃)₂ solution.
4. Substitute the equilibrium concentrations into the K_sp expression. Since Ba²⁺ is already present at 0.10 M, the concentration at equilibrium will be 0.10 M + s. The concentration of F^- at equilibrium will be 2s.
5. Solve the equation for 's' to find the molar solubility of BaF₂ in the 0.10 M Ba(NO₃)₂ solution. This involves substituting the expressions for the equilibrium concentrations into the K_sp equation and solving for 's'.

Key Concepts

Molar Solubility

Molar solubility refers to the maximum amount of a solute that can dissolve in a given volume of solvent at a specific temperature, expressed in moles per liter (M). It is a crucial concept in understanding how ionic compounds dissociate in solution and is often determined through equilibrium expressions.

Common Ion Effect

The common ion effect describes the decrease in solubility of an ionic compound when a common ion is added to the solution. In this case, the presence of Ba²⁺ ions from Ba(NO₃)₂ will shift the equilibrium of barium fluoride dissolution, reducing its molar solubility due to Le Chatelier's principle.

Equilibrium Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the dissolution of sparingly soluble ionic compounds. It quantifies the product of the molar concentrations of the ions in a saturated solution, raised to the power of their coefficients in the balanced dissolution equation, and is essential for calculating molar solubility in different solutions.