A 0.0251-L sample of a solution of Cu+ requires 0.0322 L of 0.129 M KMnO4 solution to reach the equivalence point. The products of the reaction are Cu2+ and Mn2+. What is the concentration of the Cu+ solution?

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Identify the balanced chemical equation for the reaction: \[ 5 \text{Cu}^+ + \text{MnO}_4^- + 8\text{H}^+ \rightarrow 5\text{Cu}^{2+} + \text{Mn}^{2+} + 4\text{H}_2\text{O} \]

Calculate the moles of \( \text{KMnO}_4 \) used: \[ \text{moles of } \text{KMnO}_4 = 0.0322 \text{ L} \times 0.129 \text{ M} \]

Use the stoichiometry of the balanced equation to find the moles of \( \text{Cu}^+ \): \[ \text{moles of } \text{Cu}^+ = 5 \times \text{moles of } \text{KMnO}_4 \]

Calculate the concentration of \( \text{Cu}^+ \) in the original solution: \[ \text{Concentration of } \text{Cu}^+ = \frac{\text{moles of } \text{Cu}^+}{0.0251 \text{ L}} \]

Review the steps to ensure all calculations align with the stoichiometry and the given data.

Key Concepts

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

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate the amounts of substances consumed and produced in a reaction based on balanced chemical equations. Understanding stoichiometry is essential for determining the concentration of solutions and the volumes of reactants needed to reach equivalence points in titrations.

Titration

Titration is a laboratory technique used to determine the concentration of a solute in a solution by reacting it with a solution of known concentration. The point at which the reaction is complete is called the equivalence point, which can be identified using indicators or pH meters. In this question, the titration of Cu+ with KMnO4 allows us to find the concentration of the Cu+ solution based on the volume and molarity of the titrant used.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in units of moles per liter (M). In this problem, the molarity of the KMnO4 solution is crucial for calculating the moles of KMnO4 used in the titration, which can then be related to the moles of Cu+ in the original solution to find its concentration.