Hard water often contains dissolved Ca²⁺ and Mg²⁺ ions. One way to soften water is to add phosphates. The phosphate ion forms insoluble precipitates with calcium and magnesium ions, removing them from solution. A solution is 0.050 M in calcium chloride and 0.085 M in magnesium nitrate. What mass of sodium phosphate would you add to 1.5 L of this solution to completely eliminate the hard water ions? Assume complete reaction.

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Identify the chemical reactions involved: \( \text{Ca}^{2+} + \text{PO}_4^{3-} \rightarrow \text{Ca}_3(\text{PO}_4)_2 \) and \( \text{Mg}^{2+} + \text{PO}_4^{3-} \rightarrow \text{Mg}_3(\text{PO}_4)_2 \).

Calculate the moles of \( \text{Ca}^{2+} \) in the solution: \( 0.050 \text{ M} \times 1.5 \text{ L} \).

Calculate the moles of \( \text{Mg}^{2+} \) in the solution: \( 0.085 \text{ M} \times 1.5 \text{ L} \).

Determine the moles of \( \text{PO}_4^{3-} \) needed to react with both \( \text{Ca}^{2+} \) and \( \text{Mg}^{2+} \) using stoichiometry from the balanced equations.

Calculate the mass of \( \text{Na}_3\text{PO}_4 \) required using the moles of \( \text{PO}_4^{3-} \) and the molar mass of \( \text{Na}_3\text{PO}_4 \).

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Key Concepts

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

Hard Water Composition

Hard water is characterized by the presence of dissolved minerals, primarily calcium (Ca²⁺) and magnesium (Mg²⁺) ions. These ions can form insoluble compounds with certain anions, leading to the formation of scale in pipes and appliances. Understanding the concentration of these ions is crucial for determining how to treat hard water effectively.

Precipitation Reactions

A precipitation reaction occurs when two soluble salts react to form an insoluble product, or precipitate. In this case, phosphates react with calcium and magnesium ions to form insoluble calcium phosphate and magnesium phosphate. This concept is essential for calculating the amount of sodium phosphate needed to remove hard water ions from the solution.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. It allows us to determine the exact amounts of substances needed for a complete reaction. In this scenario, stoichiometry is used to calculate the mass of sodium phosphate required to react with the given concentrations of calcium and magnesium ions in the solution.

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