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Solution:
Step 1: Calculate the molar mass of each gas.
For O₂
molar mass = 16.00 g/mol × 2
molar mass = 32.00 g/mol
For N₂
molar mass = 14.01 g/mol × 2
molar mass = 28.02 g/mol
For H₂
molar mass = 1.008 g/mol × 2
molar mass = 2.016 g/mol
Step 2: Calculate the number of moles of each gas.
[tex]n_{\text{O}_{2}} = \text{15.1 g O₂} × \frac{\text{1 mol O₂}}{\text{32.00 g O₂}} = \text{0.472 mol}[/tex]
[tex]n_{\text{N}_{2}} = \text{8.18 g N₂} × \frac{\text{1 mol N₂}}{\text{28.02 g N₂}} = \text{0.292 mol}[/tex]
[tex]n_{\text{H}_{2}} = \text{2.46 g H₂} × \frac{\text{1 mol H₂}}{\text{2.016 g H₂}} = \text{1.22 mol}[/tex]
Step 3: Calculate the mole fraction of O₂.
[tex]X_{\text{O}_{2}} = \frac{n_{\text{O}_{2}}}{n_{\text{O}_{2}} + \: n_{\text{N}_{2}} + \: n_{\text{H}_{2}}}[/tex]
[tex]X_{\text{O}_{2}} = \frac{\text{0.472 mol}}{\text{0.472 mol + 0.292 mol + 1.22 mol}}[/tex]
[tex]\boxed{X_{\text{O}_{2}} = 0.238}[/tex]
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