Environmental Engineering Reference
In-Depth Information
Activity Coefficient (
γ
i
)
Mole Fraction of Chloroform (
x
i
)
Convention I
Convention II
0.40
1.25
0.70
Solution
: The standard state chemical potential is not given. Hence we can only
determine the difference in chemical potentials,
Δμ
i
=
RT
ln
(
γ
i
·
x
i
).
Convention I:
Δμ
i
=
(
8.314 J/mol K
)(
323 K
)
ln
(
1.25
·
0.4
)
=
240 J/mol.
Convention II:
Δμ
i
=
(
8.314 J/mol K
)(
323 K
)
ln
(
0.7
·
0.4
)
=−
383 J/mol.
E
XAMPLE
3.3 C
ALCULATION OF THE
A
CTIVITY OF
W
ATER IN
S
EAWATER
Problem statement
: If the vapor pressure of a sample of seawater is 19.02 kPa at 291 K,
calculate the activity of water in the solution.
Solution
: The vapor pressure of pure water at 291 K is 19.38 kPa (
CRC Handbook of
Chemistry and Physics
). Hence,
a
water
=
19.02
/
19.38
=
0.9814.
TABLE 3.2
Standard States, Fugacity, and Activity Coefficients for Real Gas
Mixtures and Solutions
Fugacity Coefficient or
Activity Coefficient
Standard States
f
i
P
i
=
f
i
y
i
P
T
f
i
→
P
i
as
P
T
→
0
χ
i
→
1as
P
T
→
0
Real gas mixture
χ
i
=
f
i
f
l
0
i
Real solutions
a
i
= γ
i
x
i
=
γ
i
→
1as
x
i
→
0
(
convention I
)
γ
i
→
1as
x
i
→
1
(
convention II
)
f
i
f
i
0
f
l
0
i
=
P
i
Solid mixture
a
i
= γ
i
x
i
=
f
s0
i
=
P
i
+
RT
ln
f
i
/f
g
i
, where
f
g
0
g
i
= μ
g0
i
Notes:
(1) For gases
μ
=
1 atm, and for solu-
i
l
i
+
RT
ln
f
i
/f
l
i
.
(2)
P
i
denotes saturated vapor pressure and
P
T
is the total pressure.
(3) For a gaseous mixture
f
g
i
l
i
= μ
tions
μ
=
y
i
f
g,pure
i
and is called the
Lewis-Randall rule
,
that is, the fugacity of
i
in a mixture is the product of its mole fraction in the gas
mixture and the fugacity of pure gaseous component at the same temperature
and pressure.
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen500.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen501.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen502.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen503.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen504.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen505.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen506.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen507.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen508.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen509.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen510.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen511.png)
![](Elements-of-Environmental-Engineering-Thermodynamics-and-Kinetics_images/img-gen512.png)
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