A solution of Na₂SO₄ is added dropwise to a solution that is 0.010 M in Ba²⁺(aq) and 0.010 M in Sr²⁺(aq). (a) What concentration of SO₄^2- is necessary to begin precipitation? (Neglect volume changes. BaSO₄: Ksp = 1.1⨉10^-10; SrSO₄: Ksp = 3.2⨉10^-7.)

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Identify the relevant chemical reactions for the precipitation of BaSO_4 and SrSO_4: Ba^{2+} + SO_4^{2-} \(\rightarrow\) BaSO_4(s) and Sr^{2+} + SO_4^{2-} \(\rightarrow\) SrSO_4(s).

Use the solubility product constant (K_{sp}) expressions for each salt: K_{sp, BaSO_4} = [Ba^{2+}][SO_4^{2-}] and K_{sp, SrSO_4} = [Sr^{2+}][SO_4^{2-}].

Substitute the given concentrations of Ba^{2+} and Sr^{2+} into the K_{sp} expressions: 1.1 \(\times\) 10^{-10} = 0.010 \(\times\) [SO_4^{2-}] for BaSO_4 and 3.2 \(\times\) 10^{-7} = 0.010 \(\times\) [SO_4^{2-}] for SrSO_4.

Solve each equation for [SO_4^{2-}] to find the concentration required to begin precipitation for each salt.

Compare the [SO_4^{2-}] values obtained for BaSO_4 and SrSO_4 to determine which salt will precipitate first.

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주요 개념

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Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of ionic compounds. It represents the maximum concentration of ions in a saturated solution at a given temperature. For a salt like BaSO4, Ksp is calculated as the product of the molar concentrations of its constituent ions, each raised to the power of their coefficients in the balanced equation. Understanding Ksp is crucial for predicting when a precipitate will form in a solution.

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 cannot remain dissolved in the solution. In this context, the addition of sulfate ions (SO4^2-) to a solution containing Ba^2+ and Sr^2+ ions can lead to the formation of BaSO4 or SrSO4 precipitates, depending on the concentration of sulfate ions and the respective Ksp values.

Ion Product (Q)

The ion product (Q) is a measure of the current concentration of ions in a solution compared to the Ksp of a potential precipitate. It is calculated similarly to Ksp but uses the actual concentrations of the ions present at any given moment. If Q exceeds Ksp, precipitation occurs; if Q is less than Ksp, the solution remains unsaturated. In this problem, calculating Q for BaSO4 and SrSO4 as sulfate ions are added will determine the concentration of SO4^2- needed to initiate precipitation.

A solution of Na2SO4 is added dropwise to a solution that is 0.010 M in Ba2+(aq) and 0.010 M in Sr2+(aq). (a) What concentration of SO42- is necessary to begin precipitation? (Neglect volume changes. BaSO4: Ksp = 1.1⨉10-10; SrSO4: Ksp = 3.2⨉10-7.)