Question

In a mixture of 1 g H\(_2\) and 8 g O\(_2\) the mole fraction of hydrogen is

• A. 0.667
• B. 0.5
• C. 0.33
• D. None of the above

Hint:

Mole fraction is dimensionless and between 0 and 1.

Answer 1

The Correct Option is A

To find the mole fraction of hydrogen in the mixture, we need to first determine the moles of hydrogen (\( \text{H}_2 \)) and oxygen (\( \text{O}_2 \)) in the given mixture.

1. Calculate the number of moles of hydrogen (\( \text{H}_2 \)):
   • Molar mass of \( \text{H}_2 \) = 2 g/mol
   • Given mass of \( \text{H}_2 \) = 1 g
   • Number of moles of \( \text{H}_2 \) = \(\frac{\text{Given mass of } \text{H}_2}{\text{Molar mass of } \text{H}_2} = \frac{1}{2} = 0.5 \, \text{mol}\)
2. Calculate the number of moles of oxygen (\( \text{O}_2 \)):
   • Molar mass of \( \text{O}_2 \) = 32 g/mol
   • Given mass of \( \text{O}_2 \) = 8 g
   • Number of moles of \( \text{O}_2 \) = \(\frac{\text{Given mass of } \text{O}_2}{\text{Molar mass of } \text{O}_2} = \frac{8}{32} = 0.25 \, \text{mol}\)
3. Calculate the total number of moles in the mixture:
   • Total moles = Moles of \( \text{H}_2 \) + Moles of \( \text{O}_2 \)
   • Total moles = \(0.5 + 0.25 = 0.75 \, \text{mol}\)
4. Calculate the mole fraction of hydrogen (\( \text{H}_2 \)):
   • Mole fraction of \( \text{H}_2 \) = \(\frac{\text{Moles of } \text{H}_2}{\text{Total moles}}\)
   • Mole fraction of \( \text{H}_2 \) = \(\frac{0.5}{0.75} = \frac{2}{3} \approx 0.667\)
5. Conclusion:
   • The mole fraction of hydrogen (\( \text{H}_2 \)) in the mixture is approximately 0.667.

Hence, the correct answer is 0.667.