A 4.0 g sample contained `Fe_2O_3,Fe_3O_4`, and inert material. It was treated with an excess of aq KI solution in acidic medium, which reduced all iron to `Fe^(2+)` ions along with the liberation of iodine . The resulting solution was diluted to 50 mL and a 10 mL sample of it was taken the iodine liberated in the small sample was titrated with 12.0 " mL of " 0.5 M `Na_2S_2O_3` solution. The iodine from another 25 mL was extracted, after which the `Fe^(2+)` ions were titrated with 16 " mL of " 0.25 M `MnO_4^(ɵ)` ions in `H_2SO_4` solution. Calculate the mass of two oxides in the original mixture.

Explanation

To solve the problem step by step, we will break down the information provided and perform the necessary calculations.

### Step 1: Understand the reactions involved
We have two iron oxides: \(Fe_2O_3\) and \(Fe_3O_4\). When treated with KI in an acidic medium, both oxides are reduced to \(Fe^{2+}\) ions, and iodine (\(I_2\)) is liberated.

### Step 2: Write the relevant reactions
1. For \(Fe_2O_3\):
\[
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