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A 0.5 g sample containing `MnO_(2)` is treated with HCl liberating `Cl_(2)` is passed into a solution of KI and 30.0 " mL of " 0.1 M `Na_(2)S_(2)O_(3)` are required to titrate the liberated iodine. Calculate the percentage of `MnO_(2)` is the sample.

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`MnO_(2) overset(HCI)rarr Cl_(2)overset(KI) rarr I_(2) overset(Na_(2)S_(2)O_(3))rarr NaI +Na_(2)S_(4)O_(6)`

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