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A \(3.00\text{ g}\) sample containing \(\ce{Fe3O4}\), \(\ce{Fe2O3}\) and an inert impure substance, is treated with excess of \(\ce{KI}\) solution in presence of dilute \(\ce{H2SO4}\). The entire ion is converted into \(\ce{Fe^{2+}}\) along with liberation of Iodine. The resulting solution is diluted to \(100\text{ mL}\). A \(20\text{ mL}\) of the dilute solution requires \(11.0\text{ mL}\) of \(0.5\text{ M}\) \( \ce{Na2S2O3}\) to reduce iodine present. A \(50\text{ mL}\) of dilute solution, after complete extraction of Iodine requires\(12.80\text{ mL}\) of \(0.25\text{ M}\) \(\ce{KMnO4} \) solution in dilute \(\ce{H2SO4}\) medium for oxidation of \(\ce{Fe^{2+}}\). Calculate the percentage of \(\ce{Fe2O3}\) in the mixture.

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