PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 158

6.5 Fugacity and activity

6.5.1 Fugacity

The fugacity of a pure substance was defined in section3.2.6. For mixtures, the fugacity of a

component is defined by the relation

fi=pstexp

(

Gi−G◦m,i

RT

)

=pst exp

(

μi−G◦m,i

RT

)

. (6.74)

U Main unit:Pa.

• The dependence of fugacity on temperature is expressed by the relation

lnfi(T 2 ) = lnfi(T 1 ) +

∫T 2

T 1

(

∂lnfi

∂T

)

p,n

dT , (6.75)

where (

∂lnfi

∂T

)

p,n

=−

Hi−Hm◦,i

RT^2

. (6.76)

• The dependence of fugacity on pressure is expressed by the relation

lnfi(p 2 ) = lnfi(p 1 ) +

∫p 2

p 1

(

∂lnfi

∂p

)

T,n

dp , (6.77)

where (

∂lnfi

∂p

)

T,n

=

Vi

RT

. (6.78)

• For an ideal mixture of ideal gases [see6.1.2] we have

fi=pi=xip. (6.79)

In this case the fugacity of theithcomponent in a mixture equals its partial pressure.

• For an ideal mixture of real fluids [see6.1] we write
  fi=xifi•. (6.80)

The fugacity of theithcomponent in a mixture can be calculated from the fugacity of

the pureithcomponent. Relation (6.80) is termed theLewis-Randall rule.