Biomedical Engineering Reference
In-Depth Information
=
[A
−
]resp.a
HA
=
=
[H
+
]
a
A
−
f
A
−
·
f
HA
·
[HA] resp. a
H
+
f
H
+
·
The factor f depends on the analytical concentration of a reactant
and becomes 1 at infinite dilution. Factor f is significantly lower
than 1, too, if a reactant is dissolved in the presence of a neutral
salt,suchasNaClorKCl.
Transformation of the equilibrium equation gives an expression
of the H
+
-concentration in solution (Henderson-Hasselbalch
equation):
pK +
a
A
−
a
HA
“p” symbolizes the negative common logarithm of the respective
quantity. The value of K
D
of pure water at 20
◦
C is 10
−14
; therefore,
a neutral solution, i.e., [A
−
]=[H
+
]haspH
=
pH
=
7.
Sincethefactorsfareknownforonlyacoupleofsubstances,
only more or less rough empirical calculations are possible
1
.To
illustrate the concentration dependency of the activity factor f,
Table 7.1 lists it for some substances.
The increase of f during dilution explains the observation that
a buffer solution alters its pH when diluted.
The pH of a buffered solution also changes when temperature
is increased or decreased. Table 7.2 gives K
a
, molar mass M
r
as well
as dpK
a
/dT data for some substances often used in buffer solutions.
“−
∆
pH/grd” means that pH increases when temperature decreases.
For example, Tris buffer adjusted to pH 7.8 at 22
◦
C has pH 8.4 at
4
◦
C, or during a PCR cycle the pH can differ up to 1.5 units.
The change of pH at different temperature is illustrated for
some buffer substances in Fig. 7.1.
Table 7.1.
Dependence of activity coefficients on concentration
Ion
Activity coefficient f
Concentration:
0.001 M 0.01 M 0.1 M
H
+
0.98
0.93
0.86
OH
−
0.98
0.93
0.81
Acetate
−
0.98
0.93
0.82
H
2
PO
4
0.98
0.93
0.74
HPO
2
4
0.90
0.74
0.45
PO
3
4
0.80
0.51
0.16
Citrate
−
0.98
0.93
0.81
Citrate
2−
0.90
0.74
0.45
Citrate
3−
0.80
0.51
0.18
1
Buffer formulations and calculations at
www.liv.ac.uk/buffers/buffercalc.html; software at
http://www.liv.ac.uk/
∼
jse/software.html
