A gaseous mixture contains 436.0 Torr of H2(g), 341.5 Torr of N2(g), and 79.7 Torr of Ar(g). Calculate the mole fraction, X, of each of these gases.
To calculate the mole fraction of each gas in a gaseous mixture, you need to know the partial pressure of each gas.
The mole fraction (X) of a gas can be calculated using the formula:
X = (Partial Pressure of the Gas) / (Total Pressure of the Mixture)
Given the partial pressures of H2(g), N2(g), and Ar(g) in the mixture as follows:
Partial Pressure of H2(g) = 436.0 Torr
Partial Pressure of N2(g) = 341.5 Torr
Partial Pressure of Ar(g) = 79.7 Torr
The total pressure of the mixture can be calculated by summing the partial pressures of the gases:
Total Pressure of the Mixture = Partial Pressure of H2(g) + Partial Pressure of N2(g) + Partial Pressure of Ar(g)
Total Pressure of the Mixture = 436.0 Torr + 341.5 Torr + 79.7 Torr
Total Pressure of the Mixture = 857.2 Torr
Now, we can calculate the mole fraction of each gas:
Mole Fraction of H2(g) = (Partial Pressure of H2(g)) / (Total Pressure of the Mixture)
Mole Fraction of H2(g) = 436.0 Torr / 857.2 Torr
Mole Fraction of H2(g) ≈ 0.5086
Mole Fraction of N2(g) = (Partial Pressure of N2(g)) / (Total Pressure of the Mixture)
Mole Fraction of N2(g) = 341.5 Torr / 857.2 Torr
Mole Fraction of N2(g) ≈ 0.3985
Mole Fraction of Ar(g) = (Partial Pressure of Ar(g)) / (Total Pressure of the Mixture)
Mole Fraction of Ar(g) = 79.7 Torr / 857.2 Torr
Mole Fraction of Ar(g) ≈ 0.0930
Therefore, the mole fraction (X) of each gas in the mixture is approximately:
Mole Fraction of H2(g) ≈ 0.5086
Mole Fraction of N2(g) ≈ 0.3985
Mole Fraction of Ar(g) ≈ 0.0930