A vessel contains a mixture consisting of polystyrene (2) (molar mass: 158 kg/mol) and CO2 (1). The liquid mole fraction is x1 = 0.02 and the liquid density is 1007 kg/m3. Which pressure will be built up in the vessel at 393.15 K?
References: http://www.th.bci.tu-dortmund.de/de/forschung/pc-saft/theory/equations
J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 2001, 40, 1244 - 1260
All references to equations are to the textbook from which this example was taken.
Like other more conventional equations of state, the PC-SAFT equation in itself is only capable of describing the behaviour of pure fluids. Therefore in order to extend the equation to mixtures, appropriate mixing rules need to be employed in place of pure component parameters, and combining rules are needed to account for the cross-interactions of these same parameters. In this regards, the van der Waals one-fluid mixing rules an the Berthelot-Lorentz combining rules are often sufficiently accurate:
The binary interaction parameter, kij, is introduced to correct the segment-segment interactions of unlike chains.
The PC-SAFT Equation
The PC-SAFT equations are based on the reduced Helmholtz energy contributions relative to the ideal gas. Contributions for the residual Helmholtz energy from chain of hard-spheres and dispersion are added to the ideal gas value. The complete equation of state is therefore an additive combination of
- the ideal gas contribution (id)
- a hard-chain contribution (hc) which includes ,
- a dispersive contribution (disp),
- an association contribution (assoc)
- an polar contribution (polar)
In order to calculate the pressure from the reduced Helmholtz energy, the following thermodynamic relation is employed: