IM 12B03D02-01E
9-2
9
.
Technical Information
9.2 Relationship between EMF of Glass Membrane and
pH Value
The relationship between the potential difference (electromotive force) developed
across the glass membrane and the pH value had been studied and the theoretical
values were determined. Actual values, however, do not match the theoretical values
due to manufacturing variations or deterioration with time. Therefore, a pH meter must
be calibrated using standard solutions.
The emf of a glass electrode is affected by temperature. To compensate for this
temperature effect is called “temperature compensation” which is essential for pH
measurement.
Figure 9.2 shows the diagram of glass electrode membrane. Both membrane
surfaces in contact with solutions are hydrated and the hydrogen ion activity in these
hydrated layers is constant. A boundary potential develops depending on the ratio of
the hydrogen ion activities of the hydrated layer and of the solution. This boundary
potential, e, is expressed from the Nernst equation as follows.
R : gas constant, 8.3145 [J/(mol·K)]
T : absolute temperature (t [°C]+273.15) [K]
F : Faraday constant, 9.6485 x 10 [C/mol]
C : potential at interface between glass and internal solution
C : potential at interface between glass and sample solution
e = -
Where:
pH + C (internal solution side)
2.3026 R T
F
(9.1)
i
i
i
e = -
pH + C (sample solution side)
2.3026 R T
F
(9.2)
S
4
i
S
S
S
Given the potential at internal solution side is reference, the difference across the
membrane e
g
is:
e = e −e =
(pH −pH ) + (C −C )
2.3026 R T
F
(9.3)
g
i
i
i
S
S
S
To determine the difference of membrane potentials, two inner electrodes are
incorporated in a glass electrode and a reference electrode and the difference in
potential at two electrodes is measured by a pH converter with high input impedance.
This potential difference Eg is expressed as follows when the difference of single
electrode potential of the two inner electrodes and C
S
– C
i
in equation 9.3 are
collectively represented by E
AS
.
E =
(pH −pH )
+ E
2.3026 R T
F
(9.4)
g
i
S
AS
E = (54.20 +
0.1984 t)×(pH −pH )
+ E
(9.5)
g
i
S
AS
