Question

A mixture of gas contains 3.2 kg of Oxygen, 2.2 kg of Carbon Dioxide and 5.6 kg of Nitrogen. (a) calculate the number of moles of each component. (b) calculate the mass ratio and mole ratio of each component. (c) calculate the molar mass of the gas mixture when the gas mixture is heated from 25 ∘

C to 200 ∘
C under constant pressure, (d) calculate the change of enthalpy of the gas mixture, given that the C p
​ of O 2
​ is 0.918 kJ/kg−K,CO 2
​ is 0.839 kJ/kg−K and N 2
​ is 1.040 kJ/kg−K. (e) Calculate the change of entropy of the gas mixture given the same C p
​ value in (d).

Answer 1

(a) To calculate the number of moles of each component, we need to use the molar mass of each substance. The molar mass of Oxygen (O₂) is approximately 32 g/mol, Carbon Dioxide (CO₂) is approximately 44 g/mol, and Nitrogen (N₂) is approximately 28 g/mol.

Number of moles of Oxygen (O₂):
3.2 kg = 3200 g
moles of O₂ = 3200 g / (32 g/mol) = 100 mol

Number of moles of Carbon Dioxide (CO₂):
2.2 kg = 2200 g
moles of CO₂ = 2200 g / (44 g/mol) = 50 mol

Number of moles of Nitrogen (N₂):
5.6 kg = 5600 g
moles of N₂ = 5600 g / (28 g/mol) = 200 mol

(b) Mass ratio and mole ratio of each component:

Mass ratio of Oxygen (O₂):
Mass of O₂ / Total mass of mixture = 3200 g / (3200 g + 2200 g + 5600 g) = 0.2667

Mass ratio of Carbon Dioxide (CO₂):
Mass of CO₂ / Total mass of mixture = 2200 g / (3200 g + 2200 g + 5600 g) = 0.1833

Mass ratio of Nitrogen (N₂):
Mass of N₂ / Total mass of mixture = 5600 g / (3200 g + 2200 g + 5600 g) = 0.5500

Mole ratio of Oxygen (O₂):
Moles of O₂ / Total moles of mixture = 100 mol / (100 mol + 50 mol + 200 mol) = 0.3333

Mole ratio of Carbon Dioxide (CO₂):
Moles of CO₂ / Total moles of mixture = 50 mol / (100 mol + 50 mol + 200 mol) = 0.1667

Mole ratio of Nitrogen (N₂):
Moles of N₂ / Total moles of mixture = 200 mol / (100 mol + 50 mol + 200 mol) = 0.6667

(c) To calculate the molar mass of the gas mixture, we need to consider the mass and mole ratios of each component.

Molar mass of Oxygen (O₂) = 32 g/mol
Molar mass of Carbon Dioxide (CO₂) = 44 g/mol
Molar mass of Nitrogen (N₂) = 28 g/mol

Molar mass of the gas mixture:
(0.2667 x 32 g/mol) + (0.1833 x 44 g/mol) + (0.5500 x 28 g/mol) = 33.04 g/mol

(d) The change of enthalpy of the gas mixture can be calculated using the specific heat capacity (Cp) and the temperature change (ΔT). The formula is:

ΔH = Cp * m * ΔT

Given the specific heat capacities:
Cp of O₂ = 0.918 kJ/kg-K
Cp of CO₂ = 0.839 kJ/kg-K
Cp of N₂ = 1.040 kJ/kg-K

The mass of each component can be calculated using the given masses and the molar masses:

Mass of Oxygen (O₂) = 3.2 kg = 3200 g
Mass of Carbon Dioxide (CO₂) = 2.2 kg = 2200 g
Mass of Nitrogen (