Selected Geochemical Processes - Contaminant Geochemistry - page 33

the composition of the mixture changes and consequently l i changes as a function
of the amount in moles (n)ofi:
l i ¼ o G
on i

: ð 2 : 8 Þ

T ; P ; n j 6 ¼1

Because l i = G i = H i - TS i , the chemical potential can be used to assess the
tendency of components i to be transferred to another system or transformed
within a system; in other words, matter flows spontaneously from a region of high
chemical potential to a region of low chemical potential, just as mass flows from a
position of high gravitational potential to a position of low gravitational potential.
The chemical potential, therefore, can be used to determine whether or not a
system is in equilibrium: at equilibrium, the chemical potential of each substance
is the same in all phases appearing in the system.
An ideal solution can be defined as a solution in which the chemical potential of
each species is given by the expression

l i ¼ l i ð P ; T Þþ RT ln x i ;

ð 2 : 9 Þ

where R is the gas constant (=0.001987 kcal/mol/K), T is the temperature, and x i is
the mole fraction of species i. The chemical potential of a pure species i, l i P ; ð Þ ,
is a measure of the activity of compound i in its standard state, that is, pure organic
liquid at the same pressure (P) and temperature (T). The term l i P ; ð Þ is referred
to as the standard state chemical potential. From Eq. ( 2.9 ), it is seen that the
chemical potential of a species in an ideal solution is lower than the chemical
potential of the pure component.
Usually, only very dilute solutions can be considered ideal. In most aqueous
solutions, ions are stabilized because they are solvated by water molecules. As the
ionic strength is increased, ions interact with each other. Thus, when calculating
the chemical potential of species i, a term that takes into account the deviation
from ideal conditions is added. This term is called an excess term and can be either
positive or negative. The term usually is written as RT ln c i , where c i is the activity
coefficient of component i. The complete expression for the chemical potential of
species i then becomes

l i ¼ l i ð P ; T Þþ RT ln x i þ RT ln c i ¼ l i ð P ; T Þþ RT ln ð x i c i Þ: ð 2 : 10 Þ

As mentioned previously, in this expression, l i P ; ð Þ is the chemical potential of
a pure species i. For a pure species i, x i = 1, and consequently, from Eq. ( 2.10 ),
c i = 1, too.
The expression x i c i is referred to as the activity of the species, a i , and is a
measure of how active a compound is in a given state compared to its standard
state (e.g., the pure liquid at the same T and P).
For aqueous solutions of salts, l i P ; ð Þ represents the chemical potential of
pure ions. This chemical potential cannot be measured experimentally. Instead