The Electrode Chain
Two electrodes, the pH indicator electrode and the reference electrode, comprise the setup for measuring pH. A combination electrode, which includes the indicator and the reference electrodes built into a single body, is often used for convenience.
A small galvanic cell is produced when the two electrodes are immersed in a solution. The total potential developed is dependent on both electrodes, and is a sum total of several individual potentials. See the diagram below for an explanation of these various potential sources:
E1 = potential difference between the pH glass membrane and the sample being measured.
E2 = potential difference between the electrolyte in the glass electrode and the inner surface of the glass membrane.
E3 = potential difference between the electrode pin and the electrolyte in the glass electrode.
E4 = potential difference between the electrode pin and the electrolyte in the reference electrode.
E5 = potential difference that occurs at the reference junction (the interface which joins the reference electrolyte solution with the sample solution).
The sum total of these potential differences, Et, is expressed as:
Et = E1 + E2 + E3 + E4 + E5
We are only interested in E1 (the potential difference between the pH glass membrane and the sample), so the remaining potentials must be compensated for in such a way as to negate their effect on the true pH measurement. Let us re-examine these potentials:
If the potential difference between the electrolytes and electrode pins in both the pH glass electrode and the reference electrode (respectively) are identical and at the same temperature, the potentials generated by each will be equal but opposite: E3 = -E4, thereby negating each other. We can therefore simplify our equation:
Et = E1 + E2 + E5
With an appropriate selection of reference electrolyte and adequate flowrate through the reference junction, the potential difference, E5 can be neglected, so that
Et = E1 + E2
Because E1 and E2 are of opposite polarities in the pH measuring loop, our equation becomes:
Et = E2 - E1
We can keep the potential difference, E2 constant by filling the glass pH electrode with an electrolyte with excellent buffering properties, leaving us with the only remaining potential difference, E1 (the potential difference between the glass pH membrane and the sample).
Ideal conditions however, rarely exist in actual practice. For various reasons, a small potential difference can develop, and this potential difference is known as the asymmetry potential. The asymmetry potential can be caused by:
- A reference junction potential (E5 not equal to 0).
- The inner and outer surfaces of the pH glass membrane may vary due to differences in glass texture which can occur during the bulb blowing process (E3 + E4 not equal to 0).
Fortunately, Asymmetry potentials are compensated for during the calibration process using appropriate buffer solutions.
Only if the potential of the indicator electrode changes in response to varying pH while the potential of the reference electrode remains constant, do ideal measuring conditions exist.
The Nernst equation expresses the measured voltage:
E = Eind - Eref = E´T - (R · T/F · log aH+)
E = measured voltage ( mV )
E ind = voltage of indicator electrode (mV)
E ref = voltage of reference electrode (mV)
E´T = temperature dependent constant (mV)
R = gas constant ( 8.3144 J/K )
T = absolute temperature ( K )
F = Faraday's constant ( 96485.31 Coulombs )
The formula can be written
E = E´T - (2.303 · R · T/F · log aH+)
By introducing the pH definition as pH = -log aH+, pH can be expressed at the temperature T as follows:
pHT = pHT° - ( E / R' · S · T )
R' = constant = 0.1984 mV/K
S = sensitivity ( since the electrode response may differ from the theoretical response, a correction factor )
pH° = zero pH ( the pH value at which the measured potential is zero; changes with temperature, producing another slope; see Figure 1 )
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