fugacity 
 isotherms 
pressure (MPa)
10
volume (cm3/mol)
100
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Details
About
The fugacity f and the fugacity coefficient φ are calculated for water using the Peng–Robinson equation of state (EOS). Select “fugacity” and change pressure and volume with sliders; the corresponding state is indicated by the black dot on the log pressure versus log volume diagram. The fugacity coefficient indicates how much the fluid deviates from ideal-gas behavior (φ = 1 for an ideal gas). Select “isotherms” to display isotherms on the log P– log V diagram and change temperature with a slider; the horizontal blue line represents vapor-liquid equilibrium. The yellow areas between the isotherm and the horizontal blue line are equal when viewed on a linear scale.
The Peng–Robinson EOS is used to calculate pressure:
P = R TV − b − aV2 + 2b V − b2 ,
where P is pressure (MPa), R is the ideal gas constant ([cm3 MPa] / [mol K]), T is temperature (K), V is volume (cm3) and a and b are constants:
a = 0.457 (1 + κ (1 − √T / Tc))2 R2 Tc2Pc ,
b = 0.0778 R TcPc ,
κ = 0.375 + 1.542 ω − 0.270 ω2 .
Here κ is a constant associated with the acentric factor ω = 0.344, Tc is the critical temperature (K) and Pc is the critical pressure (MPa).
The following equation is solved in order to obtain the compressibility factor Z:
Z3 + a2 Z2 + a1 Z + a0 = 0 ,
where a2, a1, a0, A and B are all constants:
a2 = B − 1 ,
a1 = A − 3B2 − 2B ,
a0 = −A B + B2 + B3 ,
A = a PR2 T2 ,
B = b PR T .
The fugacity f and activity coefficient φ are calculated by:
f = φ P ,
ln φ = (Z − 1) − ln (Z − B) − A2√2 B ln  Z + (√2 + 1)BZ − (√2 − 1)B .
When the EOS has three roots, the correct solution is the one that has the lowest fugacity.
This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Rachael L. Baumann, John L. Falconer, and Nick Bongiardina. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.