Question

Estimate the fugacity for each species in the following gases at 290 K and 800 bar:

(a) Pure oxygen;

(b) Pure nitrogen;

(c) Oxygen and nitrogen in a 30% mol O2 and 70% mol N2 mixture using the Lewis-Randall rule

(d) Oxygen and nitrogen mixture in part (c) using van der Waals equation of state.

Answer 1

Solution:

a) we will calculate fugacity by van dar waals fugacity,

ln(f/p) = (b - a/RT)(p/RT)

Wherre, f - fugacity unit will be pressure unit

p - pressure

R - gas constant

T - Temp

a, b, c - Van dar waals constant

for O2 van dar waals constant are, a = ln(f/p) = 1.382 bar l2/mol2, b = 0.03186 l/mol

R = 0.08314 bar l/K mol

ln(f/800) = (0.03186 - 1.382/(0.08314* 290))(800/0.08314 * 290)

= (0.03186 - 0.05734) * (33.18)

lnf - ln800 = -0.02548 * 33.18

lnf = ln800 - 0.8454

lnf = 6.68460 - 0.8454

lnf = 5.840

f = 343.5 bar

b. Pure N2

Use the same fotmula with van dar waals constantof a = 1.37bar l2/mol2, b= 0.0387 l/mol

ln(f/p) = (0.0387 - 1.37/(0.08314 * 290)) * (800/0.08314 * 290)

= (0.0387 - 0.05682) * 33.18

= -0.01812 * 33.18

lnf = ln800 - 0.60122

f = 438.51 bar

C. We know the Lewis Randall relation,

f_i^g = x_i * f

Here,f_i^g is fugacity of ideal solution and f - that of pure component

f_i^g = 0.3 * 343.5 = 103.05

from vander waals equation of state: