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**Fugacity expressions for pure gases**

Fugacity coefficient (and hence fugacity) of pure gases may be conveniently evaluated by applying eqn. 6.80 to a volume-explicit equation of state. The truncated virial EOS is an example of the latter type, for which the compressibility factor of pure species (i) is given by:

Thus, on using eqn. 6.80:

Hence, ...(6.98)

**Derivation of fugacity coefficient expression for cubic EOS: Starting from eqn. 5.38: **

...(6.99)

...(6.100)

Using Eqn. 6.100 in 6.99:

**On simplifying: **

...(6.101)

Here: V_{∞} = molar volume at P → 0, orV_{∞} = ideal gas volume

Therefore: V / V_{∞} = Z ...(6.102)

Using eqn. 6.102 in 6.101 one arrives at:

...(6.103)

Equation 6.103 is a generalized expression for obtaining pure component fugacity from a pressure explicit EOS. We show below the expressions for fugacity coefficients that derive on application of the above equation to various cubic EOSs. (The reader may refer to section 2.3.3 for various forms of cubic

EOS).

VdW EOS:

...(6.104)

RK-EOS:

...(6.105)

SRK EOS:

...(6.106)

PR-EOS:

...(6.107)

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