On being heated in air, a mixture of Feo and `Fe_2O_4` picks up oxygen to convert completely to `Fe_2O_3`. If the observed weight gain is `5%` of the initial weight, what must have been the composition of the initial mixture?

Explanation

To solve the problem, we need to determine the composition of a mixture of FeO (iron(II) oxide) and Fe3O4 (iron(II,III) oxide) that, upon heating in air, converts completely to Fe2O3 (iron(III) oxide) with a weight gain of 5%.

### Step-by-Step Solution:

1. **Define Variables**:
Let the weight of FeO in the mixture be \( X \) grams. Therefore, the weight of Fe3O4 in the mixture will be \( 100 - X \) grams, since the total weight of the mixture is 100 grams.

2. **Write the Reactions**:
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