A `2.18` g sample contains a mixture of XO and `X_(2)O_(3)`. It reacts with `0.015` moles of `K_(2)Cr_(2)O_(7)` to oxidize the sample completely to form `XO_(4)^(-) " and " Cr^(3+)` . If `0.0187` mole of `XO_(4)^(-)` is formed , what is the atomic mass of X ?

Explanation

To find the atomic mass of element X in the compounds XO and X2O3, we will follow these steps:

### Step 1: Write the balanced chemical reactions
The reactions involved in the oxidation of XO and X2O3 by K2Cr2O7 are:
1. \( 6 \text{XO} + 5 \text{Cr}_2\text{O}_7^{2-} + 34 \text{H}^+ \rightarrow 6 \text{XO}_4^{-} + 10 \text{Cr}^{3+} + 17 \text{H}_2\text{O} \)
2. \( 3 \text{X}_2\text{O}_3 + 4 \text{Cr}_2\text{O}_7^{2-} + 26 \text{H}^+ \rightarrow 6 \text{XO}_4^{-} + 8 \text{Cr}^{3+} + 13 \text{H}_2\text{O} \)

### Step 2: Define variables for the mixture
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