Question

At 200 K, the compression factor of oxygen varies with pressure as shown in the table below. Evaluate the fugacity of oxygen at this temperature and 124 atm.

p/atm	1.0000	4.0000	7.0000	10.000	40.00	70.00	100.0
Z	0.9971	0.98769	0.9788	0.9695	0.8734	0.7764	0.6871

Answer 1

Theta = Z – 1/ p ‚ dp   

which is the area under the curve of Z - 1 p vs. p,

where p is the x-value and Z - 1 p is the y-value, in an x, y coordinate system.

The fugacity coefficient f is then the antilog of the area under the curve.

The fugacity of oxygen, in atm = theta p, where p is the pressure in atm.

Make a list of the p and z values given in the problem.

Using the p and z lists, make a list for the Z - 1 p values. Finally, make a list of {p, Z - 1 p } values. Don't forget to transpose.

p = 81.0, 4.0, 7.0, 10.0, 40.0, 70.0, 100.0<;

z = 80.9971, 0.98796, 0.97880, 0.96956, 0.8734, 0.7764, 0.6871<;

yvalue = (z – 1)/ p;

points = [8p, y value]

data = [Transpose[ points]

area =1/2 * sum[ (y value[i+i]) + y value[i]) * ∗(p[][i + 1]] – p[[i]]),{I,1,6]]

The fugacity coefficient φ at 100 atm = 0.73315

−0.310405

Take the anti log of the area to find f:

fugcoeff = Exp[area];

Print["The fugacity coefficient φ at 100 atm = ", fugcoeff]

The fugacity of O2 at 200 K and 100 atm = 73.315 atm.