A solution is 0.010 M in Ba²⁺ and 0.020 M in Ca²⁺. b. What is the remaining concentration of the cation that precipitates first, when the other cation begins to precipitate?

Verified step by step guidance

1. Identify the solubility products (Ksp) for possible precipitates involving Ba²⁺ and Ca²⁺. Common precipitates to consider are BaSO₄ and CaSO₄.
2. Write the solubility product expressions for each precipitate. For BaSO₄, the expression is Ksp = [Ba²⁺][SO₄^2-]. For CaSO₄, the expression is Ksp = [Ca²⁺][SO₄^2-].
3. Calculate the ion product (Q) for each cation with sulfate. Q is calculated using the initial concentrations of the cations. For Ba²⁺, Q = [Ba²⁺][SO₄^2-], and for Ca²⁺, Q = [Ca²⁺][SO₄^2-].
4. Compare the ion product (Q) with the solubility product (Ksp) for each cation to determine which precipitate forms first. The cation whose Q exceeds Ksp first will precipitate first.
5. Calculate the concentration of the cation that precipitates first when the second cation begins to precipitate. Use the Ksp value of the second cation to find the maximum concentration of sulfate ion possible before the second cation starts to precipitate, then use this sulfate concentration to find the remaining concentration of the first cation.

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is a numerical value that represents the equilibrium between a solid and its ions in a saturated solution. It is specific to a particular ionic compound and is used to predict whether a precipitate will form when two solutions are mixed. The lower the Ksp value, the less soluble the compound is, meaning it will precipitate out of solution at lower concentrations.

Precipitation Reaction

A precipitation reaction occurs when two soluble salts are mixed, resulting in the formation of an insoluble compound, or precipitate. This process is driven by the decrease in solubility of the ions involved when their concentrations exceed the Ksp. Understanding which cation precipitates first requires knowledge of the Ksp values of the potential precipitates formed from the cations in the solution.

Common Ion Effect

The common ion effect refers to the decrease in solubility of a salt when a common ion is added to the solution. In the context of precipitation, the presence of a common ion shifts the equilibrium, favoring the formation of the solid precipitate. This concept is crucial for determining which cation will precipitate first, as the concentration of one cation can influence the solubility of the other.