Page 53 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch05 Elementary Physical Chemistry

38 Elementary Physical Chemistry

of species, i, is defined as

o
G i = G + n i RT ln a i (5.21)
i
Note that the activity is defined in terms of G, which is a true value of
the system. However, to obtain the exact value of a i ,one must know the
value of G i, which is generally not known exactly. What is done often is to
approximate the activity as follows:
For an (ideal) gas a i = P i /P o (5.22a)
For a pure liquid or solid a i = 1 (5.22b)
For a solution a i = c i /c o (5.22c)

The symbol P o stands for standard pressure (760 Torr or 1 atm or
o
101.2325kPa); c i denotes the concentration of species i,and c represents
the standard concentration (1 mol dm −3 or 1kgm −3 ).

5.5. Partial Molar, Molal Quantities

Suppose we have a mixture of n A moles of pure A and n B moles of pure B.
∗
Denoting the molar volumes of A and B respectively as V ,and V ,thenin
∗
A B
general, the total volume will not be the sum of the individual values, i.e.
∗
∗
V = V ,+ V . [This applies also to the other thermodynamic functions,
A B
such as H, S, G, etc.] The reason why this is so is that molecules attract
or repel each other, causing deviations from the sum rule. In general, the
volume of a mixture depends on temperature, pressure, mole fractions, etc.
It can be shown that if a system is homogeneous, the total volume is
V =Σ i n i V i,m (5.23a)

and, in particular, in a two-component system,

V = n AV A,m + n B V B,m (5.23b)
The subscript m refers to molar quantity.
The Gibbs free energy can be written conveniently as
G = G(T, P, n 1 ,n 2 ,...) (5.24)

The partial molar volume of species i is defined as the derivative of V with
respect to n i holding constant P, T, and all n j not equal to n i .Denoting