Question

I don't get why fugacity coefficients, ϕ=f/p

, of pure components are usually calculated via integrating an eos over a pressure or volume range. For example, when using a pressure explicit eos (such as the Virial-Eos for example), one can write:
RTlnϕ=∫p0(v−RTp)dp
I was wondering, if we already have the Virial-Coefficients, why not calculate the actual pressure straight away? Isn't the fugacity some kind of real pressure, with ϕ
serving as a conversion factor, f=ϕp
. And isn't the pressure calculated from eos (PR, VdW, Virial etc.) also some kind of real pressure aswell. But why are they not equal?

Answer 1

Fugacity coefficients are calculated via integrating an EOS over a pressure or volume range to account for the non-ideal behavior of the system. The fugacity serves as a conversion factor between the non-ideal behavior and the actual pressure.

Step-by-step explanation:

The fugacity coefficient, ϕ=f/p, is used to calculate the fugacity (f) of a pure component based on the pressure (p) using an equation of state (EOS) like the Virial EOS.

The reason why fugacity coefficients are calculated via integrating an EOS over a pressure or volume range is because it accounts for the non-ideality of the system.

Non-ideal systems, such as gases at high pressures, deviate from ideal behavior and require the use of fugacities to accurately calculate the system's properties.

Although we could directly calculate the actual pressure using the Virial coefficients, it would not account for the non-ideal behavior.

The fugacity (f) serves as a conversion factor between the non-ideal behavior and the actual pressure (p). The pressure calculated from the EOS is a measure of the system's properties, but it is not equal to the fugacity because it does not fully account for the non-ideal effects such as molecular volumes and attractive forces.