PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 156

Note:Since these relations are derivatives at constant natural variables and not at constant

temperature and pressure, they are not partial molar quantities.

• The dependence of the chemical potential on temperature is expressed by the equation

μi(T 2 ) =μi(T 1 ) +

∫T 2

T 1

(

∂μi

∂T

)

p,n

dT , (6.67)

with (∂μi/∂T)p,nobtained by differentiating equation (3.41) with respect toni.

(

∂μi

∂T

)

p,n

=

(

∂Gi

∂T

)

p,n

=−Si. (6.68)

• The dependence of the chemical potential on pressure is expressed by the equation

μi(p 2 ) =μi(p 1 ) +

∫p 2

p 1

(

∂μi

∂p

)

T,n

dp , (6.69)

where (

∂μi

∂p

)

p,n

=

(

∂Gi

∂p

)

T,n

=Vi. (6.70)

S Symbols: The subscriptnemphasizes that this is a change at constant amounts of sub-

stance of all components, i.e. also at constant composition.

• Dependence of the chemical potential on composition
  The chemical potential is written as a sum of two terms

μi=μsti +RTlnai, (6.71)

of which the first, μsti, the standard chemical potential^1 of a component [see 6.5.4]

does not depend on composition. Dependent on composition is the activity of theith

component in the mixture,ai[see6.5.4] in the second term of the equation.

(^1) According to the new IUPAC recommendations, a general (unspecified) standard state is denoted asμ◦i.