Biomedical Engineering Reference
In-Depth Information
TABLE 3.2 Species Activity Based on Different Choices of Standard-State Activity
State at (
T
,
P
)
Standard state at (
T
,
P[
1 bar)
At low and moderate pressures
Pure gas G j
P
Pure gas
a j z
1
bar
p j
Pure gas G j
Species in a gaseous mixture
a j z
1
bar
Pure liquid G j
Pure liquid
a j z
1
C j
C g j ;
as C j
Pure liquid G j
Species in a liquid mixture
a j z
g j / 1
C / 1
C j g j
1
G j
¼
G j ð
T
;
P
¼ 1
bar
;
C j ¼ 1
M
Þ
a j z
M ;
g j / 1
as C j / 0
G j T
C j
C ¼ 1
C j
C g j ;
G j
¼
;
P
¼ 1
bar
;
a j z
g j / 1
as C j / 0
Pure solid G j
Pure solid
a j z
1
Pure solid G j
Species in a solid mixture
a j z
1
C n þ
j
C n
j
G j
Dissolved electrolyte in solution
A j ¼ n þ A þ n A j
¼ n þ G ð
T
;
P
¼ 1
bar
;
C ¼ 1
M
Þ
þ
Þ n þ þn ðg Þ n þ þn
a j z
ð1
M
þ n G j ð
T
;
P
¼ 1
bar
;
C j ¼ 1
M
Þ
We define the standard state of a liquid as a j ¼
1 and for gases as an ideal gas pressure of l
bar, p j ¼
1. For ideal liquid solutions (activity coefficients of unity), we write
C j
C j
a j ¼
(3.76)
0
j
where C
is either the total concentration or 1 mol/L (as shown in Table 3-1 ). At chemical
equilibrium
!
C j
C j
! n j
Y
N S
D G R
RT
K eq ¼ exp
¼
(3.77)
j
¼1
and for gases
!
Y
N S
DG R
RT
p n j
j
K eq ¼ exp
¼
(3.78)
j
¼1
In these expressions, K eq is dimensionless, while p j has dimensions; this equation is
still correct because we implicitly write each partial pressure as p j /1 bar which is
dimensionless.
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