Chapter 5, Problem 95FP

Manganese is derived from pyrolusiteore, an impure manganese dioxide. In the procedure used to analyze apyrolusite ore for its ${\text{MnO}}_{\text{2}}$ content, a 0.533 g sample is treated with 1.651 g oxalic acid ${\text{(H}}_{\text{2}}{\text{C}}_{\text{2}}{\text{O}}_{\text{4}}\cdot {\text{2H}}_{\text{2}}\text{O)}$ in an acidic medium. Following this reaction, the excess oxalic acid is titrated with 0.1000 M KMnO_4. 30.06 being required. What is mass percent ${\text{MnO}}_{\text{2}}$ in the ore?
${\text{H}}_{\text{2}}{\text{C}}_{\text{2}}{\text{O}}_{\text{4}}{\text{+MnO}}_{\text{2}}{\text{+H}}^{\text{+}}\to {\text{Mn}}^{\text{2}}{\text{+H}}_{\text{2}}{\text{O+CO}}_{\text{2}}$ (not balanced)
${\text{H}}_{\text{2}}{\text{C}}_{\text{2}}{\text{O}}_{\text{4}}{\text{+MnO}}_{\text{2}}{\text{+H}}^{\text{+}}\to {\text{Mn}}^{\text{2}}{\text{+H}}_{\text{2}}{\text{O+CO}}_{\text{2}}$ (notbalanced)