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Appendix A General pH Information
A.1 pH Measurement Theory
pH is the negative logarithm of the hydrogen ion activity and a measure of the acidity or
alkalinity of a solution.
pH = –log A[H+]
pH is normally measured using a glass electrode and a reference electrode.
The glass electrode acts as a transducer, converting chemical energy (the hydrogen ion
activity) into an electrical energy (measured in millivolts). The reaction is balanced and the
electrical circuit is completed by the flow of ions from the reference solution to the solution
under test.
The electrode and reference solution together develop a voltage (emf) whose magnitude
depends on the type of reference electrode, the internal construction of the glass
electrode, the pH of the solution and the temperature of the solution. This voltage is
expressed by the Nernst Equation:
E = E
o
– (2.3 RT/F) x log A[H+]
E = E
o
– (slope) x log A[H+]
where:
E = the emf of the cell
E
o
= the zero potential (isopotential) of the system. It depends on the internal
construction of the glass and reference electrodes.
R = gas constant
T = temperature in Kelvin
A[H+] = activity of the hydrogen ion (assumed to be equivalent to the concentration of
hydrogen ions)
F = Faraday constant
For every unit change in pH (or decade change in ion concentration) the emf of the
electrode pair changes by 59.16 mV at 25 °C. This value is known as the Nernstian Slope
of the electrode.
The pH electrode pair is calibrated using solutions of known and constant hydrogen ion
concentration, called buffer solutions. The buffer solutions are used to calibrate both the
electrode isopotential and slope.
A.2 PID Controller Basics
A pH control loop operates as follows: The pH meter measures the value of the pH in the
effluent, and, if the pH is different from the setpoint, the controller actuates the reagent
pump (or valve) that adds reagent to a mixing tank. The added reagent adjusts the pH
value of the process.
The physical layout of the loop, the sizing of the pump (valve), type of mixing tank, and
location of the pH electrodes all have a major impact on the ultimate performance of the
loop, after the controller is tuned for optimal performance. The largest single performance
factor is the delay time around the loop. This includes the response time of the
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