Consider two solutions, the first being 50.0 mL of 1.00 M CuSO₄ and the second 50.0 mL of 2.00 M KOH. When the two solutions are mixed in a constant-pressure calorimeter, a precipitate forms and the temperature of the mixture rises from 21.5 to 27.7 °C. (a) Before mixing, how many grams of Cu are present in the solution of CuSO₄?

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Determine the molarity of the CuSO_4 solution, which is given as 1.00 M.

Calculate the number of moles of CuSO_4 in the solution using the formula: \( \text{moles} = \text{molarity} \times \text{volume in liters} \).

Convert the volume from mL to L: 50.0 mL = 0.0500 L.

Calculate the moles of CuSO_4: \( 1.00 \text{ M} \times 0.0500 \text{ L} = 0.0500 \text{ moles of CuSO_4} \).

Determine the mass of Cu in the solution by using the molar mass of Cu (63.55 g/mol) and the stoichiometry of the reaction, knowing that 1 mole of CuSO_4 contains 1 mole of Cu.

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Key Concepts

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

Molarity and Moles

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. To find the number of moles in a solution, you can multiply the molarity by the volume in liters. In this case, knowing the molarity of CuSO4 allows us to calculate the moles of copper present in the solution before mixing.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. In the context of this question, understanding the stoichiometric relationships in the dissociation of CuSO4 is essential to determine how many moles of copper ions (Cu²⁺) are produced from the given moles of CuSO4, which directly relates to the mass of copper present.

Precipitation Reactions

A precipitation reaction occurs when two solutions are mixed, resulting in the formation of an insoluble solid, or precipitate. In this scenario, the mixing of CuSO4 and KOH leads to the formation of copper(II) hydroxide (Cu(OH)₂), which is a precipitate. Understanding this concept helps in recognizing the significance of the reactants and products involved in the reaction.

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