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.