Page 153 - Science at the nanoscale

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June 5, 2009
7.1. Some Basic Thermodynamic Definitions
1
in the system. The molar Gibbs energy is known as the chemical
potential (µ) and defined as the partial derivative of G with respect
to the number of particles n at constant T and P:
∂G

(7.2)
µ =
∂n
T,P
For a system of binary mixture with substances X and Y at con-
stant T and P, each substance has its own chemical potential (i.e.
µ x and µ y ) and we can express the change in Gibbs energy in terms
of the compositional changes of ∆n x and ∆n y respectively:
(7.3)
∆G = µ X ∆n X + µ Y ∆n Y
It follows that if a one-component system is at equilibrium
between two phases, e.g. liquid X and its vapour, the chemical
potentials of the two phases must be equal:
(7.4)
µ x (liquid) = µ x (gas)
The chemical potential may be viewed as a measure of the driving
force that a substance has for bringing about a change in the sys-
tem. Transformation occurs spontaneously from a region of high
µ to a region of low µ, until µ is uniform throughout the system.
7.1.3
Equilibrium in Solution
If a solid A is placed in a solvent B, it will dissolve until the sol-
vent has become saturated with the solute A. Equilibrium is now
established between the solid A and the solvated A, i.e. the chem-
ical potential of the solid is equal to the chemical potential of the 143 ch07
∗
solute in the saturated solution (Fig. 7.2). If we now define µ A (l)
as the chemical potential of the pure liquid A, the chemical poten-
tial of the solute µ A (l) may be expressed in term of the activity A
in the solution (a A ):
∗
µ A (l) = µ (l) + RT ln a A (l) (7.5)
A
Activity is a dimensionless quantity and may be viewed as the
“effective concentration” of the species in solution. Activity of
1 One molar quantity of a substance consists of 6.02214 × 10 23 (Avogadro’s num-
ber) constituent units of that substance; e.g. 1 mole of N 2 molecules consists of
6.02214 × 10 23 N 2 molecules.