A solution is 0.010 M in Ba²⁺ and 0.020 M in Ca²⁺. a. If sodium sulfate is used to selectively precipitate one of the cations while leaving the other cation in solution, which cation will precipitate first? What minimum concentration of Na₂SO₄ will trigger the precipitation of the cation that precipitates first?

Verified step by step guidance

1. Identify the possible precipitates and their solubility products (Ksp). For this problem, the possible precipitates are BaSO4 and CaSO4. The Ksp values are typically found in a chemistry reference or textbook.
2. Write the solubility product expressions for each potential precipitate. For BaSO4, the expression is Ksp = [Ba2+][SO42-]. For CaSO4, the expression is Ksp = [Ca2+][SO42-].
3. Calculate the ion product (Q) for each cation with the initial sulfate concentration from Na2SO4. The ion product Q is calculated using the concentrations of the ions in the solution. For example, Q for BaSO4 is [Ba2+][SO42-] and for CaSO4 is [Ca2+][SO42-].
4. Compare the ion product (Q) with the solubility product (Ksp) for each compound. Precipitation occurs when Q exceeds Ksp. Determine which cation forms a precipitate first by comparing which Q reaches or exceeds its respective Ksp first as the concentration of sulfate ion increases.
5. Calculate the minimum concentration of Na2SO4 needed to initiate precipitation for the cation that precipitates first. This can be done by setting up the equation Q = Ksp and solving for [SO42-], then using the stoichiometry of Na2SO4 to find its concentration.

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 indicates the extent to which the compound can dissolve. For precipitation to occur, the product of the concentrations of the ions in solution must exceed the Ksp value of the compound formed.

Selective Precipitation

Selective precipitation is a technique used to separate ions in a solution based on their solubility differences. By adding a reagent that forms a precipitate with one ion while leaving others in solution, it allows for the isolation of specific cations. The order of precipitation is determined by the Ksp values of the potential precipitates, with lower Ksp values precipitating first.

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 calculation of reactants and products in chemical reactions based on their molar ratios. In the context of precipitation, understanding the concentration of the sulfate ions from sodium sulfate is crucial to determine the minimum amount needed to initiate the precipitation of a specific cation.