A 35.0-mL sample of 1.00 M Co(NO₃)₂ and an 80.0-mL sample of 0.600 M Co(NO₃)₂ are mixed. The solution is then heated to evaporate water until the total volume is 50.0 mL. Calculate the volume, in mL, of 0.20 M H₃PO₄ that is required to precipitate out cobalt(III) phosphate in the final solution.

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Calculate the total moles of Co(NO_3)_2 in the initial solutions by using the formula: \( \text{moles} = \text{concentration} \times \text{volume} \).

Add the moles from both solutions to find the total moles of Co(NO_3)_2 before evaporation.

Determine the concentration of Co(NO_3)_2 in the final 50.0 mL solution by dividing the total moles by the new volume.

Write the balanced chemical equation for the reaction between Co(NO_3)_2 and H_3PO_4 to form cobalt(III) phosphate, CoPO_4.

Use stoichiometry to calculate the volume of 0.20 M H_3PO_4 needed to react with the moles of Co(NO_3)_2 in the final solution.

Key Concepts

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

Molarity and Dilution

Molarity (M) is a measure of concentration defined as moles of solute per liter of solution. When mixing solutions of different volumes and concentrations, the total moles of solute remain constant, but the final concentration can be calculated using the dilution formula, M1V1 = M2V2. Understanding how to calculate the final concentration after mixing and diluting is essential for determining the amount of reactants needed in subsequent reactions.

Precipitation Reactions

A precipitation reaction occurs when two soluble salts react to form an insoluble compound, known as a precipitate. In this case, cobalt(III) phosphate (CoPO₄) is formed when cobalt ions react with phosphate ions. The stoichiometry of the reaction must be understood to calculate the required amounts of reactants, as the mole ratio between the reactants dictates how much of each is needed to fully precipitate the desired product.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced chemical equations. It allows chemists to predict how much of a substance is needed or produced in a reaction. In this problem, stoichiometry is crucial for determining the volume of 0.20 M H₃PO₄ required to precipitate cobalt(III) phosphate, as it requires knowing the mole ratio between H₃PO₄ and Co(NO₃)₂ in the reaction.

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