Page 15 - Partition & Adsorption of Organic Contaminants in Environmental Systems

6 IMPORTANT THERMODYNAMIC PROPERTIES

heat absorbed by the system to evaporate the liquid (i.e., DH > 0) increases
virtually linearly with the mass of liquid evaporated, whereas the rate of
increase in system entropy (i.e., DS > 0) is relatively large at first but decreases
as the vapor density increases. Here the unfavorable endothermic heat of
evaporation is outbalanced by the more favorable entropy increase until the
system reaches equilibrium, at which point DH = TDS and DG = 0. Conversely,
when a vapor is adsorbing onto a previously evacuated surface, the exother-
mic heat of adsorption (i.e., DH < 0) is relatively large initially but decreases
rapidly when more vapor is adsorbed (because the adsorption sites are usually
energetically heterogeneous, as discussed in Chapter 4). The system entropy
decreases (i.e., DS < 0) in a similar fashion but at a different rate. Thus the
system reaches equilibrium at some point, where DH = TDS and DG = 0. In
this case, the unfavorable entropy loss is outbalanced by the more favorable
decrease in enthalpy before the system reaches equilibrium.

1.4 EXTENSIVE AND INTENSIVE PROPERTIES

Extensive thermodynamic properties are those whose magnitudes are related
to the sizes (or the moles) of the chemical species present. Examples are

G, H, V, E, S or DG, DH, DV, DE, DS

Intensive properties are those whose magnitudes are not a function of their
sizes or masses. Examples are T, P, r (density), and the partial molar quanti-
ties of the extensive properties.
For any extensive property Y at constant T and P in a multiple-component
system, the differential change of the property is thus

)
n dn +∂ (
dY =∂ ( Y ∂ ) 1 Y ∂ n dn +∂ ( Y ∂ ) 3 (1.17)
n dn + ◊◊◊
3
1
2
2
or
dY = Y dn + Y dn + Y dn + ◊◊◊ (1.18)
1
2
2
3
3
1
where the partial molar quantity, Y i , is an intensive thermodynamic property.
1.5 CHEMICAL POTENTIAL
The chemical potential of a substance in a phase serves as a measure of its
escaping tendency. We already know that when two phases in a system are at
equilibrium, they must be at the same T and P. When the transfer of a sub-
stance between two phases is allowed, an additional requirement for equilib-
rium is that the chemical potentials of the substance must be the same in the