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11 August, 07:10

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.

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  1. 11 August, 07:48
    0
    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
  2. 11 August, 07:57
    0
    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
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