Question

A gravimetric analysis of a mixture of gases used in a manufacturing process has the following proportions: 52 % nitrogen (N2), 27 % oxygen (O2), 11 % hydrogen (H2) and 10 % carbon dioxide (CO2). The mixture of gases has a temperature of 300 K and pressure of 350 kPa.
Determine the following:  
(i) Mass fractions and molar masses for each of the mixture's constituent gases.

(ii) Specific heat capacities at constant pressure for each of the constituent gases and the specific heat capacity at constant pressure for the mixture of gases.   

(iii) Specific gas constants for each of the constituent gases, the specific gas constant for the mixture and the mean molar mass for the mixture of gases.

(iv) Volume fractions for each of the constituent gases.

(v) Specific volume, density, specific heat capacity at constant volume and the ratio of specific heat capacities of the mixture of gases.

Answer 1

(i) Molar mass of N₂ =28 kg/mol

Molar mass of O₂ =32 kg/mol

Molar mass of CO₂ =44 kg/mol

Molar mass of H₂ =2 kg/mol

Consider 100 kmol of mixture, then the mass of each component is,

N (O2)= 27 kmol => m(O2)=27*32= 864 kg

similarly for m(N2)=52*28= 1456 ; m(CO2)=10*44=440 ; m(H2)=2*11=22 kg

total mass= 864+1456+440+22=2782kg

then, mass fraction, mf(N2)=1456/2782= 52.34% ; mf(O2)= 864/2782= 31.05% ; mf(CO2)=440/2782= 15.81% ; mf(H2)=22/2782= 0.80%

(ii) Total mass = 2782/100 = 27.82 kg/mol

For specific heat capacity, for diatomic molecules, C_v=5/2*R and for triatomic C_v=7/2*R ;

C_p=C_v + R

Cv(N2) ; (H2) ; (O2)= 5/2*R=20.785 ; (CO2)= 29.099

Cp (N2) ; (H2) ; (O2) = Cv +R = 29.099 ; Cp (CO2)= Cv +R = 37.413

(iii) Specific gas constant = R/M= 8.314/27.82 = 0.299 kJ/Kg K

(iv)Volume fraction and mole fractions are same; mole fraction = no. of moles of each constituent / total number of moles