To calculate the mole fractions of helium (He) and oxygen (O₂) in the Heliox mixture, we can follow these steps:

1. Determine the mass fractions of He and O₂:

The problem gives the following mass percentages:

• O₂: 6.11% by mass
• He: 93.89% by mass

2. Convert mass percentages into grams:

To simplify calculations, let's assume we have 100 g of the mixture. This means:

• Mass of O₂ = 6.11 g
• Mass of He = 93.89 g

3. Calculate the number of moles of each component:

We use the molar masses of O₂ and He:

• Molar mass of O₂ = 32.00 g/mol
• Molar mass of He = 4.00 g/mol

Now, calculate the moles of each gas:

• Moles of O₂ = $\frac{6.11 \, \text{g}}{32.00 \, \text{g/mol}} = 0.1903 \, \text{mol}$
• Moles of He = $\frac{93.89 \, \text{g}}{4.00 \, \text{g/mol}} = 23.4725 \, \text{mol}$

4. Calculate the total number of moles in the mixture:

Total moles = Moles of O₂ + Moles of He $\text{Total moles} = 0.1903 \, \text{mol} + 23.4725 \, \text{mol} = 23.6628 \, \text{mol}$

5. Calculate the mole fraction of each gas:

• Mole fraction of O₂ = $\frac{0.1903 \, \text{mol}}{23.6628 \, \text{mol}} = 0.00804$
• Mole fraction of He = $\frac{23.4725 \, \text{mol}}{23.6628 \, \text{mol}} = 0.99196$

6. Final Answer:

• Mole fraction of O₂ = 0.00804
• Mole fraction of He = 0.99196

Recap:

• Mole fraction of O₂: 0.00804
• Mole fraction of He: 0.99196

Would you like a detailed explanation of any specific part of the calculation or have additional questions? Here are some related questions for further exploration:

1. How does the mole fraction relate to partial pressures of gases in mixtures (Dalton's Law)?
2. What would the result be if the composition of the gas mixture changed (e.g., 10% O₂)?
3. How can you calculate the density of a gas mixture using its mole fractions?
4. What is the difference between mole fraction and mass fraction in gas mixtures?
5. How do changes in temperature affect mole fractions in gas mixtures?

Tip: When calculating mole fractions, it's important to remember that they sum up to 1.