Page 108 - Instant notes

Physical chemistry 94

Partial molar quantities can be calculated for many variables, including thermodynamic
variables. The most important thermodynamic variable for a closed system, which can
exchange energy with its surroundings, is the Gibbs free energy (see Topic B6). The
partial molar Gibbs free energy or chemical potential, µ i, of a species is the Gibbs free
energy per mole of the species in the mixture. Therefore, the total Gibbs free energy, G,
of a mixture of species of n A moles of A, n B moles of B and n C moles of C is given by
G=n Aµ A+n Bµ B+n Cµ C or, more generally, G=Σ in iµ i for all the species, i, in the system. As
with all other partial molar quantities, the chemical potential of a pure substance is
generally not the same as the chemical potential of that substance in a mixture. This is
due to differences in the molecular arrangement, which produce differences in the
molecular interactions, in the two systems.
Generally, these differences in chemical potential for any species i at any temperature,
T, are given by its activity, a i, as:

where is the standard chemical potential of the species, or the chemical potential
when the activity is unity. For a perfect gas (see Topic A1), the activity is given by
where p i is the partial pressure of the gas, i, (see Topic A1) and is the
standard pressure of 1 atmosphere. Essentially, the more chemical potential the molecules
in a perfect gas have (the more Gibbs free energy) the faster they move and the more
pressure they exert. This is a relatively simple expression, which is a consequence of the
fact there are no intermolecular interactions in perfect gases. Generally, in all systems,
the activity expression allows the change in the chemical potential (the partial molar
Gibbs free energy) of any species to be calculated when its molecular environment is
changed from standard conditions. However, for more complicated systems which have
significant intermolecular interactions, such as ions in solution (see Topics E1 and E2) or
non-ideal mixtures of liquids (see Topic D2), the activity relationship is more
complicated, reflecting the greater complexity introduced by these interactions.
At equilibrium, the change in Gibbs free energy for the reaction is zero (see Topic C1)
and hence the Gibbs free energy of reactants and products are equal. For a physical
transition, for example vaporization:

this means that the chemical potentials of A in the gas phase and A in the liquid phase
must be equal or µ (1)=µ (g).
Also, away from equilibrium, the overall Gibbs free energy of any reaction
aA+bB→cC+dD

can be calculated from the individual chemical potentials as
∆G=(cµ C+dµ D)−(aµ A+bµ B).