Question

In a gas mixture consisting of hydrogen, nitrogen and carbon dioxide, the partial pressures are 25 kpa for hydrogen, 35 kpa for nitrogen and 140 kpa for co2 . for 50 m3 of the gas mixture at 400 k, determine the following:

(a)the number of moles of the mixture
(b)the number of moles and mole fraction of hydrogen
(c)the mass and mass fraction of hydrogen
(d)the pure-component volume of hydrogen
(e)the average molecular weight of the mixture

Answer 1

The mass of hydrogen is found to be 7.562 g using the ideal gas law and its molar mass. The mass fraction of hydrogen requires the total mass, which involves calculating the mass of all gases in the mixture. The average molecular weight of the mixture is based on the molar masses and mole fractions of the individual gases.

Step-by-step explanation:

To determine the mass and mass fraction of hydrogen, we use the ideal gas law in combination with the given partial pressures. The ideal gas law is PV = nRT, where P is pressure, V is volume, n is moles of gas, R is the gas constant, and T is temperature. The mass of hydrogen can be calculated by multiplying the number of moles of hydrogen by its molar mass.

To find the moles of hydrogen: n(H2) = P(H2)V / RT = (25 kPa)(50 m3) / (8.314 J/mol·K)(400 K) = 3.753 mol. The molar mass of hydrogen is 2.016 g/mol, so the mass of hydrogen is approximately 3.753 mol × 2.016 g/mol = 7.562 g.

The mass fraction of hydrogen is calculated by the formula mass fraction = mass of component / total mass. To find the total mass, we would need to calculate the masses of nitrogen and carbon dioxide using their respective partial pressures and molar masses in the same manner.

For the average molecular weight of the mixture, we need the mass and mole fraction of each gas. The average molecular weight can be calculated by summing the product of each gas's molar mass and its mole fraction in the mixture.