What is the mole fraction of hydrogen in a tank of gas containing 10-kg hydrogen and 220-kg oxygen?
The mole fraction of hydrogen in the tank of gas is 0.42. To find the mole fraction of hydrogen in the tank of gas, we need to calculate the ratio of the moles of hydrogen to the total moles of gas in the tank.
Calculating Mole Fraction of Hydrogen
Step 1: Convert the mass of hydrogen and oxygen into moles using their respective molar masses.
Molar mass of hydrogen (H₂) = 2 g/mol
Molar mass of oxygen (O₂) = 32 g/mol
Moles of hydrogen:
10 kg = 10000 g
Moles of hydrogen = 10000 g / 2 g/mol = 5000 mol
Moles of oxygen:
220 kg = 220000 g
Moles of oxygen = 220000 g / 32 g/mol = 6875 mol
Step 2: Calculate the total moles of gas in the tank by summing the moles of hydrogen and oxygen.
Total moles of gas = Moles of hydrogen + Moles of oxygen
Total moles of gas = 5000 mol + 6875 mol
Total moles of gas = 11875 mol
Step 3: Calculate the mole fraction of hydrogen by dividing the moles of hydrogen by the total moles of gas.
Mole fraction of hydrogen = Moles of hydrogen / Total moles of gas
Mole fraction of hydrogen = 5000 mol / 11875 mol
Mole fraction of hydrogen = 0.42
Therefore, the mole fraction of hydrogen in the tank of gas is 0.42.