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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1. Identify the balanced chemical equation for the reaction: \[ 5 \text{Cu}^+ + \text{MnO}_4^- + 8\text{H}^+ \rightarrow 5\text{Cu}^{2+} + \text{Mn}^{2+} + 4\text{H}_2\text{O} \]
2. Calculate the moles of \( \text{KMnO}_4 \) used: \[ \text{moles of } \text{KMnO}_4 = 0.0322 \text{ L} \times 0.129 \text{ M} \]
3. Use the stoichiometry of the balanced equation to find the moles of \( \text{Cu}^+ \): \[ \text{moles of } \text{Cu}^+ = 5 \times \text{moles of } \text{KMnO}_4 \]
4. Calculate the concentration of \( \text{Cu}^+ \) in the original solution: \[ \text{Concentration of } \text{Cu}^+ = \frac{\text{moles of } \text{Cu}^+}{0.0251 \text{ L}} \]
5. Review the steps to ensure all calculations align with the stoichiometry and the given data.