A solution is 0.022 M in Fe2+ and 0.014 M in Mg2+. a. If potassium carbonate 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 K2CO3 will trigger the precipitation of the cation that precipitates first? b. What is the remaining concentration of the cation that precipitates first when the other cation begins to precipitate?

Verified step by step guidance

Identify the solubility product constants (Ksp) for the carbonates of Fe2+ and Mg2+. These values are necessary to determine which cation will precipitate first.

Write the balanced chemical equations for the precipitation reactions: FeCO3(s) ⇌ Fe2+(aq) + CO3^2-(aq) and MgCO3(s) ⇌ Mg2+(aq) + CO3^2-(aq).

Use the Ksp expressions for each reaction: Ksp(FeCO3) = [Fe2+][CO3^2-] and Ksp(MgCO3) = [Mg2+][CO3^2-].

Calculate the ion product for each cation using the initial concentrations and compare them to their respective Ksp values to determine which cation will precipitate first. The cation with the ion product reaching its Ksp first will precipitate first.

Determine the minimum concentration of K2CO3 needed to reach the Ksp of the cation that precipitates first by solving for [CO3^2-] in the Ksp expression of that cation.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 at lower concentrations of its constituent ions.

Selective Precipitation

Selective precipitation is a technique used to separate ions in a solution by adding a reagent that forms an insoluble compound with one ion while leaving others in solution. This process relies on the differences in solubility of the compounds formed. In this case, potassium carbonate (K2CO3) will selectively precipitate either FeCO3 or MgCO3 based on their respective Ksp values.

Concentration and Precipitation

The concentration of ions in a solution is crucial for determining when precipitation occurs. As the concentration of a precipitating agent, such as K2CO3, increases, it can exceed the solubility product of a specific cation, leading to the formation of a solid precipitate. Understanding the minimum concentration required for precipitation helps in predicting the order in which cations will precipitate from a mixed solution.

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Selective Precipitation

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