2.5.3 Multicomponent systems and chemical potential
The Gibbs energy of a single component will vary with temperature (T),
pressure (P), and the number of moles (n) of the single component. Let’s
focus on how G changes with n while keeping all the other variables
constant. We do this by writing the partial derivative of G with respect
to n. This partial derivative is known as the chemical potential of the
species in question and is the partial molar Gibbs energy of the species.
It’s given the symbol μ and is defined by Equation 2.62:
μ =
∂ G
∂ n
P,T
(2.62)
The concept of chemical potential becomes important when discussing a
multicomponent system (i.e., a system with n A moles of species A, n B
moles of species B, n C moles of species C, and so on). Thus, for a multicomponent system, the total molar Gibbs energy is given by the sum of
their chemical potentials.
The total Gibbs energy of a system containing components A, B, C,... is
given by
G T, P, n A, n B , n C , …
À
Á
= n A μ A + n B μ B + n C μ C + … =
X
n i μ i
(2.63)
where the chemical potential of each component is given by
μ i =
∂ G
∂ n
P,T,n j ≠n i
(2.64)
Chemical potential is a useful concept in thermodynamics in that it helps
us understand how multicomponent systems evolve toward equilibrium.
Chemical potential is analogous to electrical potential, where charge
flows from a region of high electrical potential to a region of low electrical
potential. In the case of chemical potential, transfer of matter always
occurs from a region of high chemical potential to a region of low
chemical potential. As an example, let’s consider a nanofilm in contact
with a solution containing its constituent molecules. This two-phase
system is illustrated in Figure 2.13. The two phases have chemical
potentials μ(bulk) and μ(film). If μ(bulk) > μ(film), then molecules from
the bulk phase will enter the film until μ(bulk) = μ(film), at which point
the two phases are in equilibrium with each other.
We will revisit chemical potential in Section 2.4.3 where we see that its value
depends on the composition of the system according to Equation 2.65:
THE GIBBS ENERGY STATE FUNCTION
49
The Gibbs energy of a single component will vary with temperature (T),
pressure (P), and the number of moles (n) of the single component. Let’s
focus on how G changes with n while keeping all the other variables
constant. We do this by writing the partial derivative of G with respect
to n. This partial derivative is known as the chemical potential of the
species in question and is the partial molar Gibbs energy of the species.
It’s given the symbol μ and is defined by Equation 2.62:
μ =
∂ G
∂ n
P,T
(2.62)
The concept of chemical potential becomes important when discussing a
multicomponent system (i.e., a system with n A moles of species A, n B
moles of species B, n C moles of species C, and so on). Thus, for a multicomponent system, the total molar Gibbs energy is given by the sum of
their chemical potentials.
The total Gibbs energy of a system containing components A, B, C,... is
given by
G T, P, n A, n B , n C , …
À
Á
= n A μ A + n B μ B + n C μ C + … =
X
n i μ i
(2.63)
where the chemical potential of each component is given by
μ i =
∂ G
∂ n
P,T,n j ≠n i
(2.64)
Chemical potential is a useful concept in thermodynamics in that it helps
us understand how multicomponent systems evolve toward equilibrium.
Chemical potential is analogous to electrical potential, where charge
flows from a region of high electrical potential to a region of low electrical
potential. In the case of chemical potential, transfer of matter always
occurs from a region of high chemical potential to a region of low
chemical potential. As an example, let’s consider a nanofilm in contact
with a solution containing its constituent molecules. This two-phase
system is illustrated in Figure 2.13. The two phases have chemical
potentials μ(bulk) and μ(film). If μ(bulk) > μ(film), then molecules from
the bulk phase will enter the film until μ(bulk) = μ(film), at which point
the two phases are in equilibrium with each other.
We will revisit chemical potential in Section 2.4.3 where we see that its value
depends on the composition of the system according to Equation 2.65:
THE GIBBS ENERGY STATE FUNCTION
49