A 0.4-m3 rigid tank contains 0.6 kg of N2 and 0.4 kg of O2 at 300 K. Determine the partial pressure of each gas and the total pressure of the mixture. The gas constant for N2 is 0.2968 kPa·m3/kg·K and the gas constant for O2 is 0.2598 kPa·m3/kg·K.

pN2 = 133.56 kPa

pO2 = 77.94 kPa

Total pressure = 211.5 kPa

Explanation:

Step 1: Data given

Volume of the tank = 0.4 m³

Mass of N2 = 0.6 kg

Mass of O2 = 0.4 kg

Temperature = 300 K

The gas constant for N2 is 0.2968 kPa*m3/kg*K

The gas constant for O2 is 0.2598 kPa*m3/kg*K

Step 2: Calculate the partial pressures

pN2 = MRT / V = (0.6 * 0.2968 * 300) / 0.4

pN2 = 133.56 kPa

pO2 = (0.4 * 0.2598 * 300) / 0.4

pO2 = 77.94 kPa

Step 3: Calculate total pressure

Total pressure = 133.56 kPa + 77.94 kPa

Total pressure = 211.5 kPa

Total pressure → 2.08 atm

Partial pressure N₂ → 1.31 atm

Partial pressure O₂ → 0.76 atm

Explanation:

To determine the total pressure of the mixture we need to know the total moles of the gases:

Sum of moles from gases at the mixture = Total moles (Dalton's law)

We convert the mass from kg to g and then, we states the moles of each:

0.6 kg. 1000g / 1kg = 600 g / / 0.4g. 1000g / 1kg = 400 g

600 g. 1 mol/28g = 21.4 moles of N₂

400 g. 1mol/32g = 12.5 moles of O₂

Total moles → 21.4 + 12.5 = 33.9 moles

Before to replace the data in the Ideal Gases Law, we notice that the volume is in m³. (1000 dm³ = 1 m³ and 1dm³ = 1L)

0.4m³. 1000 dm3 / 1m³ = 400 dm³ → 400L

Now, we can put the data on the Ideal Gases Law:

400L. P = 33.9 mol. 0.082L. atm/mol. K. 300K

P = (33.9 mol. 0.082L. atm/mol. K. 300K) / 400L → 2.08 atm

We apply the mole fraction for the partial pressures of each gas:

Moles of N₂ / Total moles = Partial pressure N₂ / Total pressure

Moles of O₂ / Total moles = Partial pressure O₂ / Total pressure

Partial pressure = Total pressure. (Moles of the gas / Total moles)

Partial pressure N₂ = 2.08 atm. (21.4 mol / 33.9 moles) → 1.31 atm

Partial pressure O₂ = 2.08 atm. (12.5 mol / 33.9 moles) → 0.76 atm