Step-by-step explanation:
We have a mixture of gases and we have to find the mole fraction of oxygen.
The mole fraction can be calculated by dividing the number of moles of oxygen by the total number of moles of the mixture.
mole fraction of O₂ = moles of O₂/total number of moles
To answer our problem we will have to find the number of moles of each compound and then the total number of moles.
To calculate the number of moles of each compound we have to use the molar mass of them.
atomic mass of H = 1.01 amu
atomic mass of O = 16.00 amu
atomic mass of He = 4.00 amu
molar mass of H₂ = 2 * 1.01 g/mol
molar mass of H₂ = 2.02 g/mol
molar mass of O₂ = 2 * 16.00 g/mol
molar mass of O₂ = 32.00 g/mol
molar mass of He = 4.00 g/mol
mass of H₂ = 10 g
mass of O₂ = 10 g
mass of He = 10 g
moles of H₂ = 10 g/(2.02 g/mol)
moles of H₂ = 4.95 moles
moles of O₂ = 10 g/(32.00 g/mol)
moles of O₂ = 0.3125 moles
moles of He = 10 g/(4.00 g/mol)
moles of He = 2.5 moles
We found that our mixture has 4.95 moles of hydrogen, 0.3125 moles of oxygen and 2.5 moles of helium. Now with this information we can find the total number of moles and finally the mole fraction of oxygen.
total number of moles = moles of H₂ + moles of O₂ + moles of He
total number of moles = 4.95 moles + 0.3125 moles + 2.5 moles
total number of moles = 7.7625 moles
mole fraction of O₂ = moles of O₂/total number of moles
mole fraction of O₂ = 0.3125 moles/(7.7625 moles)
mole fraction of O₂ = 0.040