Question

Consider a gas mixture that consists of 3 kg of O2

, 5 kg of N2

, and 12 kg of CH4

,

as shown in Figure. Determine (a) the mass fraction of each component, (b) the

mole fraction of each component, and (c) the average molar mass and gas

constant of the mixture.

​

Answer 1

Answer:

a) Mass fraction of O2 = 0.15

   Mass fraction of N2 = 0.25

   Mass fraction of CH4 = 0.6

b)Mole fraction of O2 = 0.0917

  Mole fraction of N2 = 0.1746

  Mole fraction of CH4 = 0.7336

c) Average molar mass =  428kg

  Gas constant of mixture = 0.42437

Explanation:

Mass fraction of each component = Mass of component/Total mass of mixture

Total mass of mixture = 20kg

Mass fraction of O2 = 3/20 = 0.15

Mass fraction of N2  = 5/20 = 0.25

Mass fraction of CH4 = 12/20 = 0.6

Mole fraction of component = No of moles of component/Total no of moles of components

Mole fraction of O2 =93.75/1022.32 = 0.0917

Mole fraction of N2 = 178.57/1022.32 = 0.1746

Mole fraction of CH4 = 750/1022.32 =  0.7336

Average molar mass = sum of (fraction of i'th component x molecular weight of i'th component)

= (3×32)+(5×28)+(12×16) = 428kg

Characteristic gas constant of O2= 8.314/32 = 0.2598

Characteristic gas constant of  N2 = 8.314/28 = 0.296

Characteristic gas constant of CH4 = 8.314/16 = 0.519

Gas constant of mixture = 3x0.2598 + 5x0.296 + 12x0.519/(3+5+12)

= 8.4874/20 = 0.42437

Answer 2

Answer:

And (C) The Average Molar Mass And Gas Constant Of The Mixture.

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Consider a gas mixture that consists of 3 kg of O2, 5 kg of N2, and 12 kg of CH4. Determine (a) the mass fraction of each component, (b) the mole fraction of each component, and (c) the average molar mass and gas constant of the mixture.