(Solved): Potassium permanganate in acidic solution is used to titrate a solution of copper(I) ions, with whi ...

Potassium permanganate in acidic solution is used to titrate a solution of copper(I) ions, with which it reacts according to \[ \mathrm{MnO}_{4}{ }^{-}(\mathrm{aq})+5 \mathrm{Cu}^{+}(\mathrm{aq})+8 \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq}) \longrightarrow \mathrm{Mn}^{2+}(\mathrm{aq})+5 \mathrm{Cu}^{2+}(\mathrm{aq})+12 \mathrm{H}_{2} \mathrm{O} \text { (I) } \] A potassium permanganate solution is prepared by dissolving \( 18.21 \mathrm{~g}^{\text {th }} \mathrm{KMnO}_{4} \) in water and diluting to a total volume of \( 1.000 \mathrm{~L} \). A total of \( 15.95 \mathrm{~mL} \) of this solution is required to reach the endpoint in a titration of a 200.0-mL sample containing \( \mathrm{Cu}^{+}(\mathrm{aq}) \). Determine the concentration of \( \mathrm{Cu}^{+} \)in the original solution.