Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev

Thermodynamics

Civil Engineering (CE) : Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev

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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: 

Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev

Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev

Thus, on using eqn. 6.80:  Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev

Hence,  Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev                     ...(6.98)

  

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

Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev                 ...(6.99)

Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev                 ...(6.100)

Using Eqn. 6.100 in 6.99: 

Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev
 

On simplifying: 

Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev                 ...(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: 

Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev                 ...(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: 

Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev               ...(6.104)

RK-EOS:

Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev               ...(6.105)

SRK EOS:

Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev               ...(6.106)

PR-EOS:

Fugacity Expressions for Pure Gases Civil Engineering (CE) Notes | EduRev              ...(6.107)

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