Biology Reference
In-Depth Information
where T is in
C. Thus, there is some intrinsic temperature dependence in the ionic
strength adjustment itself (see
Fig. 4
A, broken line). These corrections provide a
reasonably good description of the influence of ionic strength on the K
0
Ca
in
Figs. 3-5
.
a. Activity Coe
Y
cient for Protons
The association constants as usually reported (e.g., in
Martell and Smith, 1974,
1977
) are often called stoichiometric (or concentration) constants. These terms are
sensible because they imply (correctly) that they are to be used with concentrations
or stoichiometric amounts in chemical equilibria (e.g., as in
Eq. (1)
). While we
routinely talk about ion concentrations in ''concentration'' or ''stoichiometric''
terms, the usual exception is pH (where pH
¼
log Hydrogen ion activity or
10
pH
¼
a
H
¼g
H
[H
þ
]).
Thus, one can simply convert pH to [H
þ
] and go ahead using the ''stoichiomet-
ric'' constants at face value. That is, then everything is in concentration terms and
not activity. This is the way we have done it in our programs.
The alternative is to change the stoichiometric constants to ''mixed'' constants
(for proton interactions, or K
H1
-K
H4
only). Then you can still use pH (or 10
pH
rather than 10
pH
/
g
H
) in your calculations. Thus, acid association constants (K
H1
-
K
H4
) should be divided by the value of
g
H
. Then you can multiply the constant by
the proton activity (since they are always of the same order in the equations (see
Eq. (5)
)). That is to say that [H
þ
]K
H1
¼
([H
þ
]
g
H
)(K
H1
/
g
H
), where [H
þ
]
g
H
¼
10
pH
.
This method seems a bit more awkward, but the result is the same.
The proton activity coe
cient,
g
H
varies with both temperature and ionic
strength. The empirical relationship we devised to describe this relationship is the
following
Y
g
H
¼
:
ð
B I
e
Þ þ
:
ð
:
I
e
Þ þ
:
0
145045
exp
0
063546
exp
43
97704
0
695634
ð15Þ
where B
¼
4.015942 and I
e
is ionic strength and T
is temperature (in
C). This gives very good estimates of
g
H
from 0 to 40
C and
from 0 to 0.5 M ionic strength. This expression was sent to Alex Fabiato for use in
his computer program (
Fabiato, 1991
). While there is a typographical error in text
(the first coe
0.522932
exp(0.0327016
T)
þ
cient was erroneously 1.45045), the correct expression is in the
program as it was distributed.
Y
IV. Materials
A. [Ca
2
þ
] Measurement and Calibration Solutions
1. Measuring [Ca
2
þ
]
While we can calculate the free [Ca
2
þ
] or [Ca
t
] for our solutions with the
computer programs to be described below, there are still many potential
sources of error (e.g., contaminant Ca
2
þ
, systematic errors in pH, impurities in
