To determine the mass of oxygen that reacted, we need to calculate the difference in the oxygen content between the initial mixture of Fe3O4 and FeO and the final product, Fe2O3.

1. Calculate the moles of Fe3O4 and FeO in the initial mixture:

The molar mass of Fe3O4 = 55.845 g/mol

Moles of Fe3O4 = 3.970 g / 55.845 g/mol = 0.0710 mol

The molar mass of FeO = 71.844 g/mol

Moles of FeO = 3.970 g - 0.0710 mol * 231.53 g/mol = 0.0116 mol

2. Calculate the moles of oxygen in the initial mixture:

For Fe3O4, there are 4 oxygen atoms per molecule.

Moles of oxygen from Fe3O4 = 0.0710 mol * 4 = 0.284 mol

For FeO, there is 1 oxygen atom per molecule.

Moles of oxygen from FeO = 0.0116 mol * 1 = 0.0116 mol

Total moles of oxygen in the initial mixture = 0.284 mol + 0.0116 mol = 0.2956 mol

3. Calculate the moles of oxygen in the final product, Fe2O3:

The molar mass of Fe2O3 = 159.69 g/mol

Moles of Fe2O3 = 4.195 g / 159.69 g/mol = 0.0263 mol

For Fe2O3, there are 3 oxygen atoms per molecule.

Moles of oxygen in Fe2O3 = 0.0263 mol * 3 = 0.0789 mol

4. Calculate the difference in moles of oxygen:

Moles of oxygen reacted = Moles of oxygen in initial mixture - Moles of oxygen in final product

Moles of oxygen reacted = 0.2956 mol - 0.0789 mol = 0.2167 mol

5. Calculate the mass of oxygen reacted:

The molar mass of oxygen = 16 g/mol

Mass of oxygen reacted = 0.2167 mol * 16 g/mol = 3.467 g

Therefore, the mass of oxygen that reacted is 3.467 g.