Question

The gravimetric analysis of a gas mixture is 50% N2, 40% CO2 and 10% CH4 with a temperature of 40°C and pressure of 1 bar. Calculate, 1.1 the partial pressure of each component, in bar. 1.2 the molar mass for the gas mixture, in kg/kmol. 1.3 the mass by 4 m? of mixture, in kg.

Thermodynamics

Answer 1

Gravimetric analysis means percentage is wrt mass

lets assume total mass is 100gm

So N2 is 50gm

CO2 is 40gm

CH4 is 10 gm

Now finding the number of moles of each gas

X_N = 50/ Molar mass of N2 =50/ 28= 1.78 moles of N2

X_C= 40/ Molar mass of CO2 =40/ 44= 0.91 moles of Co2

X_Ch = 10/ Molar mass of CH4 =10/ 16= 0.625 moles of CH4

Now fraction of moles

Xnn=1.78/ total moles = 1.78/ 3.315=  0.54

Xcc = 0.91 / total moles =0.91/ 3.315=  0.27

Xc4 = 0.625 / total moles = 0.625/ 3.315=  0.19

Now partial pressue

P(N2) = Xnn * Ptotal = 0.54 * 1 Bar = 0.54 Bar

P(CO2) = Xcc * Ptotal =0.27 bar

P(N2CH4) = Xc4 * Ptotal = 0.19 Bar

2) Molar masses of gas mixture

$MM =\sum mole fraction of that gas * Molar mass of that gas$

MM= 0.54 * 28 + 0.27 * 44 + 0.19 * 16

MM = 30.04 gm per mole = 30kg/kmol

3)

PV=(m/MM)RT

1* 10 ⁵ * 4= (m/MM) * 8.31 * 313 ( 1 bar = 10⁵ Pa, Pa is SI unit)

m/MM= 153.63

m = 153.63 * 30.04 =4615 gm

m = 4.62 kg