Environmental Engineering Reference
In-Depth Information
μ
i
varies nonlinearly with
P
i
for gases and with
x
i
for solutions (Section 2.5.2). For
real, nonideal gases and solutions, the expressions for chemical potentials have to
be modified and the concept of fugacity as corrected pressure was introduced. As
will be shown later the fugacity is directly related to equilibrium and can be obtained
experimentally.
3.2.1 F
UGACITY OF
G
ASES
Fugacity is defined as an idealized pressure,
f
g
i
, for a real gas such that the expression
for chemical potential can be written as
RT
ln
f
i
f
g0
i
.
g
i
= μ
g0
i
μ
+
(3.5)
The standard state fugacity is
f
g0
i
=
1 atm. For an ideal gas mixture, fugacity is the
same as partial pressure, and
f
g
i
=
P
i
.
Fugacity coefficient
,
χ
i
=
f
g
i
/P
i
, indicates the degree of nonideality of the gas
mixture. Note that
P
i
=
y
i
P
T
, where
y
i
denotes the mole fraction of
i
in the gas phase
and
P
T
is the total pressure (1 atm for most environmental calculations). Fugacity has
dimensions of pressure and is linearly related to pressure. The ratio
f
i
/f
g0
is termed
i
activity
,
a
i
.
3.2.2 F
UGACITY OF
C
ONDENSED
P
HASES
(L
IQUIDS AND
S
OLIDS
)
The concept of fugacity can be extended to condensed phases such as liquids and
solids. Both liquids and solids exert vapor pressure, and hence their escaping tendency
(fugacity) can be evaluated similar to that of a gas. If the fugacity of the saturated
vapor at temperature
T
and its saturated vapor pressure
P
i
is denoted by
f
i
and the
fugacityofthecondensedphase(liquid
l
orsolid
s)
isdenotedby
f
i
,thenthefollowing
equation can be derived (Prausnitz, Lichtenthaler, and de Azevedo, 1999):
P
i
χ
i
exp
P
P
i
RT
d
P
,
V
i
f
i
=
(3.6)
f
i
/P
i
.
The fugacity coefficient corrects for the departure from ideal gas behavior.The second
correction, which is the exponential factor, is called the
Poynting correction
and
indicates that the pressure
P
of the condensed phase (liquid or solid) is different from
the condensed-phase saturation pressure
P
i
.The Poynting correction is nearly 1 under
the low-pressure conditions of a few atmospheres encountered in most environmental
engineering calculations. Thus we have for both pure solids and liquids,
where
V
i
is the partial molar volume of
i
in the condensed phase
c
, and
χ
i
=
f
i
P
i
.
≈
(3.7)
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