Exactly 1.0 L of hydrogen gas (H2) is collected over water at 292 K under a total pressure
of 152 torr. If the vapour pressure of water is 16.5 torr at this temperature, what is the
mole fraction of hydrogen in the gas sample?
Volume of CO2 = L
Mole
vp H2O = 16.5 so XH2O = 16.5/152 = ?
152-16.5 = PH2 so XH2 = 135.5/152 = ?
To find the mole fraction of hydrogen in the gas sample, we need to calculate the number of moles of hydrogen and the total number of moles in the gas mixture.
Step 1: Calculate the partial pressure of hydrogen gas.
The partial pressure of hydrogen gas is the total pressure minus the vapor pressure of water:
Partial pressure of H2 = Total pressure - Vapor pressure of water
Partial pressure of H2 = 152 torr - 16.5 torr = 135.5 torr
Step 2: Convert the partial pressure of hydrogen to atm.
Since mole fraction is expressed in atm, we need to convert the partial pressure of hydrogen gas to atm by dividing it by 760 torr (1 atm).
Partial pressure of H2 (in atm) = Partial pressure of H2 (in torr) / 760 torr
Partial pressure of H2 (in atm) ≈ 135.5 torr / 760 torr ≈ 0.1783 atm
Step 3: Calculate the moles of hydrogen gas.
Using the ideal gas equation, we can calculate the moles of hydrogen gas:
n = PV / RT
n = (Partial pressure of H2) * (Volume in liters) / (Gas constant) * (Temperature in Kelvin)
n = 0.1783 atm * 1.0 L / (0.0821 L.atm/mol.K) * 292 K
n ≈ 0.00754 moles
Step 4: Calculate the moles of water vapor.
Since the hydrogen gas is collected over water, the vapor pressure of water affects the total pressure. We need to calculate the moles of water vapor using its partial pressure.
n_water = P_water * V / (R * T)
n_water = 16.5 torr * 1.0 L / (0.0821 L.atm/mol.K) * 292 K
n_water ≈ 0.00701 moles
Step 5: Calculate the total moles of the gas mixture.
The total moles of the gas mixture is the sum of the moles of hydrogen gas and water vapor.
Total moles = Moles of H2 + Moles of water
Total moles ≈ 0.00754 moles + 0.00701 moles ≈ 0.0146 moles
Step 6: Calculate the mole fraction of hydrogen gas.
The mole fraction of hydrogen gas is the moles of hydrogen divided by the total moles of the gas mixture.
Mole fraction of H2 = Moles of H2 / Total moles
Mole fraction of H2 ≈ 0.00754 moles / 0.0146 moles ≈ 0.516
Therefore, the mole fraction of hydrogen gas in the gas sample is approximately 0.516.