Question

A gaseous mixture has the following composition: C₂H₄, 57% mol; Ar, 40 mol%; and He, 3% mol. Calculate the volume occupied by 100 mol of this mixture at 120 atm and 25 ° C, using:  The ideal gas equation. (Answer: 20.4 L)  The generalized compressibility factor and Kay's rule. (Answer: 14.3 L)

Answer 1

Given: Mole fraction of ethylene (C₂H₄), y_C2H4=57 mol%=0.57

Mole fraction of argon, y_Ar=40 mol%=0.40

Mole fraction of helium, y_He=3 mol%=0.03

Total moles of the gas mixture, n=100 mol

Pressure, P=120 atm

Temperature, T=25⁰C=298.15 K

i) Volume of the gas mixture, V, using ideal gas law is

where n is the Number of moles of gas mixture

R is the Gas constant, R=0.0821 atm L/mol K

T is the Temperature

P is the Pressure

Thus the volume of the gas mixture obtained using ideal gas law is V=20.4 L

ii) Volume of the gas mixture, V, using the compressibility factor is

where Z is the Compressibility factor

Obtain the critical properties of the components from the Physical Property Table.

For C₂H₄, critical temperature, T_c=283.1 K and critical pressure, P_c=50.5 atm

For helium, T_c=5.26 K and P_c=2.26 atm.

For argon, T_c=150.86 K and P_c=48 atm.

In case of helium, Newton's correction is included for critical temperature and critical pressure

Adjusted critical temperature for He, T^a_c=T_c+8 K=5.26 K+8 K=13.26 K

Adjusted critical pressure for He, P^a_c=P_c+8 atm=2.26 atm+8 atm=10.26 atm

Pseudocritical temperature, T'_c, is obtained using the Kay's rule

where y_C2H4, y_Ar and y_He is the Mole fraction of ethylene, argon and helium respectively

T_c is the Critical temperature

T^a_c is the Adjusted critical temperature for He

Pseudocritical pressure, P'_c, is obtained using the Kay's rule

where P_c is the Critical pressure

P^a_c is the Adjusted critical pressure for He

Pseudoreduced temperature, T'_r, is

where T is the Temperature of the gas mixture

Pseudoreduced pressure, P'_r, is

where P is the Pressure of the gas mixture

From the Generalized Compressibility Chart for medium pressures, obtain the compressibility factor.

For T'_r=1.34 and P'_r=2.43, compressibility factor, Z=0.70

Thus the volume of the gas mixture is

Therefore, the volume of gas mixture obtained using generalized compressibility factor and Kay's rule is V=14.28 L