Page 17 - Partition & Adsorption of Organic Contaminants in Environmental Systems

8 IMPORTANT THERMODYNAMIC PROPERTIES

Phase A Phase B
i

Figure 1.1 Distribution of a component (i) between two separate phases, A and B, at
constant temperature and pressure.

At constant T and P, then

dG i = m i,A dn i + m i,B dn i,B (1.25)
,A
When component i is at the state of equilibrium between phases A and B,
dG i = 0. To maintain equilibrium, any infinitesimal increase of component i in
phase A must be accompanied by an equal amount of loss of component i in
phase B, that is,

dn i,A =- dn i,B (1.26)

thus,

m i,A = m i,B (1.27)

Equation (1.27) defines the state of equilibrium for component i between any
two phases at constant temperature and pressure. A similar operation can be
carried out for a component in a multiple-phase system through a series of
steps that allow the transfer of mass between only two phases at a time. This
leads to the conclusion

m i,A = m i,B = m i,C = m i,D ◊◊◊ (1.28)

We shall see later that Eq. (1.27) serves as the criterion for the distribution
(e.g., partition) relations of organic contaminants between water and other
phases of environmental interest (e.g., the soil organic matter in sorption and
the fish lipid in bioconcentration).

1.7 CHANGE IN CHEMICAL POTENTIAL WITH PRESSURE

For 1 mole of a component in a system with no mass change, Eq. (1.15) gives

dm= V dP - S dT (1.29)
i
i
i