Yokogawa PH72 Personal pH/ORP Meter - Manual (Page 69)

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
؋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
In the equation, pH
i
is the pH buffer solution filled in the glass electrode so the pH
should be constant. Using a solution (pH standard solution) with known pH as pH
S
at a
certain temperature, the relationship between millivolt and pH can be determined,
thereby the pH can be directly derived from the membrane potential difference, as shown
in Figure 9.3.