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.
 
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