Determine the minimum concentration of the precipitating agent on the right to cause precipitation of the cation from the solution on the left. a. 0.035 M Ba(NO₃)₂; NaF

Verified step by step guidance

1. Identify the cation and anion in the given solutions. In Ba(NO₃)₂, the cation is Ba²⁺ and the anion is NO₃^-. In NaF, the cation is Na⁺ and the anion is F^-.
2. Determine the possible precipitate by combining the cation from one solution with the anion from the other. Here, the possible precipitate is BaF₂ because Ba²⁺ can combine with F^-.
3. Write the solubility product expression (K_sp) for the possible precipitate. For BaF₂, the expression is K_sp = [Ba²⁺][F^-]².
4. Look up the K_sp value for BaF₂ from a reliable source such as a chemistry textbook or database.
5. Calculate the minimum concentration of F^- needed to begin precipitation. Use the formula derived from the K_sp expression, rearranging it to solve for [F^-], and substituting the concentration of Ba²⁺ from Ba(NO₃)₂.

Key Concepts

Precipitation Reaction

A precipitation reaction occurs when two soluble salts react in solution to form an insoluble compound, known as a precipitate. This process is driven by the formation of a solid that separates from the liquid phase, often governed by the solubility product constant (Ksp) of the precipitate. Understanding the conditions under which a precipitate forms is crucial for determining the minimum concentration of a precipitating agent.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that quantifies the solubility of a sparingly soluble ionic compound. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For a precipitation reaction to occur, the product of the concentrations of the ions must exceed the Ksp value, indicating that the solution is supersaturated.

Concentration and Stoichiometry

Concentration refers to the amount of a substance in a given volume of solution, typically expressed in molarity (M). Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. To determine the minimum concentration of the precipitating agent required to initiate precipitation, one must apply stoichiometric principles to relate the concentrations of the reactants to the formation of the precipitate, ensuring that the necessary conditions for precipitation are met.