What is the connection between the 1920 Noble Prize Winner (Dr Hermann Nernst) for Chemistry, the 1921 Noble Prize Winner (Dr Albert Einstein) for Physics, the development of microware radar and the Manhattan Project? pH measurements are based on the Nernst Equation. The later Nernst-Einstein Equation describes ion diffusion and mobility. The control knob of the original pH meters designed by Dr Beckman evolved into the Helipot (for ˇ§helical potentiometerˇ¨), which was used by the Massachusetts Institute of Technology (MIT) to develop microware radar for military use. The principle of signal amplification has helped the development of micro-microammeter (later into dosimeter) to measure the amount of radiation produced during the Manhattan Project.

What is pH?
Understanding the definition of the measurement unit and how it is practically measured will help us understand and interpret the results we obtain. pH meters operate based on the famous Nernst Equation produced in 1888 [2] by the German physical chemist Dr Hermann Walther Nernst (1864-1941). The equation is as follows:



where
Em = Measured galvanic potential of the electrode in equilibrium with the solution
E0 = Standard potential of the electrode at pH 7
R = Universal gas constant = 8.314 J/mol*K
T = Absolute temperature in degrees Kelvin = 298.15 K
z = charge number of the electrode reaction (number of moles of electrons involved in the reaction)
F = Faraday's constant (96,500 C/mol)
Ared = Chemical activities on the reduced side of the electrode reaction
Aox = Chemical activities on the oxidized side of the electrode reaction

With z = 1 for valency of hydrogen ion the expression becomes 0.02569

In 1909, the Danish biochemist S P L Sorensen defined pH [1] as the negative logarithmic of the concentration of hydrogen ions. Therefore we have to further convert the Nernst Equation as follows:





Therefore the pH slope at 25 deg C is 59.15 mV.

The original Nernst Equation was a mathematical model to describe the chemical activities of an electrode system for any species [11]. pH measurement for aqueous solution is a particular application of the Nernst Equation involving hydrogen ions or hydroxide ions. The theoretical model was based on electrodes using hydrogen gas bubbled at a pressure of 101 kPa and a platinum electrode. Practical pH measuremenst in the real world rely on ion-selective membranes which are normally glass.

How does it work?
pH electrodes measure the pH of a solution potentiometrically. When the electrode comes into contact with an aqueous sample an electrical potential develops across the sensing membrane surface. To complete the electrical circuit a reference with constant potential is required. A reference electrode (salt bridge) containing a reference electrolyte provides this function.



The relationship of mV against pH is sometimes known as the Nernstian slope.

The pH meter was invented by Dr Arnold O Beckman [12] when he was asked by an old friend who worked for the California Fruit Growers Exchange to device a sturdy and reliable method for testing the fruits' acidity. The first design was submitted to the Patent Office in October 1934 as an ˇ§acidimeterˇ¨ and no major innovation with respect to the working principle of pH measurement came about until 1970.

Is it a traceable unit?
The IUPAC Recommendations [3] published in 2002 deals with the question of whether pH, as a conventional quantity, can be incorporated into the internationally accepted system of measurement, the International System of Units (SI, Systeme International dˇ¦Unites).

Section 3.1 of the recommendations reads: ˇ§Since pH, a single ion quantity, is not determinable in terms of a fundamental (or base) unit of any measurement system, there was some difficulty previously in providing a proper basis for the traceability of pH measurement.ˇ¨

The recommendations indicate that primary pH standard values can be determined from electrochemical data from the cell without transference using the ˇ§Harned cellˇ¨. This is considered to be a primary standard having good reproducibility and low uncertainty.

The Recommendations also indicate that, for non-traceable secondary standards, the pH uncertainty will be 0.02; that is, the practical pH measurement will have at least this error incorporated. Below are extracts from the recommendations for various random and systematic effects for practical pH measurements:
1. The response of the glass electrode may vary with time, history of use, and memory effects.
2. The potential of the glass electrode is strongly temperature-dependent. Calibrations and measurements should, therefore, be carried out under temperature-controlled conditions.
3. Liquid junction devices, particularly some commercial designs, may suffer from memory and clogging effects,
4. Liquid Junction Potential may be subject to hydrodynamic effects such as stirring

Practical pH measurement in the real world
Unless a water science laboratory can afford a ˇ§Harned Cellˇ¨ [7] as a primary method for the absolute measurement of pH (Section 4 of reference [3]), one should understand more about errors and uncertainties inevitably introduced to the practical measurement of the unit in the real world, both in an ordinary laboratory using handheld instrument and on the field using inline instrument, for better understanding of the reading obtained from commercially available devices.

What are the sources of error in practical measurements? From the author's practical experiences and various reference articles the sources can be summarised as follows.

Problem with Reference Junction
The reference junction (sometimes called the Salt Bridge or Liquid Reference Junction) is an electrically conductive bridge between the reference electrolyte and the sample being measured. This junction must allow free movement of electrons but at the same time isolate the reference electrolyte from the sample. Normally this junction is made of porous material (for example, porous ceramic, Telflon and annular sleeve) which may introduce a significant error by absorbing the sample and eventually become clogged due to insufficient care.

Errors introduced by bad buffer solutions used for calibrations
Buffer solutions are not always stable, their pH value changes under different temperature, they soak up CO2 from the atmosphere and air trapped in near empty tanks. Even worse, volume loss through evaporation also affects pH [4]. Note also that some buffers, such as pH 10, do not last nearly as long as other buffers do. Some pH 10 buffers can drop as much as 0.1 pH per day when exposed to the air [16].

Temperature
As can be seen from the Nernst Equation, pH is temperature-sensitive. Uncertainty could be introduced between the sample being measured in the field and the grab sample taken to the laboratory due to temperature difference. Furthermore, the actual pH of the sample can change with temperature due to a change in the hydrogen ion activity in the solution, because ionization of compounds and hydrogen ion activity in the solution may be temperature-dependent. Temperature compensation on the handheld device does not correct this [9][16][17].

High electrode impedance
Most pH electrode is made of glass. pH glass electrodes have resistance measured from 100 M to more than 1,000 M . As the resistance of the glass increases, electrical noise picked up from the environment via the cable acting like an antenna will affect the signal to the analysers.

Sample contamination
Strict protocols for taking grab sample and in washing, rinsing and drying sampling bottles are important to avoid sample contamination. Standard Methods [17] recommends non-glass labware of polyethylene or Teflon beakers and Teflon-coated magnetic stirrer, which is sometimes overlooked by laboratory practitioners.

Hydrodynamic effects
Stirring the electrode in the sample beaker in the laboratory may initially speed upthe response, but it could be a source of trouble in taking the pH measurement of the grab sample in the laboratory. Stirring can adversely affect any junction potential that may exist, especially in porous junctions and annular-ring sleeve type junctions. [4]

Output stabilisation
Reference electrodes take time to stabilise before reaching thermal and ionic equilibrium. It is also a known fact that the more the inline electrodes are taken out for calibration, the more they need to be calibrated. The recommended practice would be inspection and calibration only if error drift is consistently greater than 0.25 pH. For triple validated installation, raise the alarm if the absolute value of the difference between the middle reading and the individual reading exceeds 0.5 pH continuously for minutes. Remove the installation for thorough checking only if the analyser displays error or the value is consistently greater than 1.0 pH [5].

Sodium error
The presence of sodium ion is known to be a problem when the pH is above 10 because a pH electrode does not easily discriminate between the sodium ion and the hydrogen ion at these elevated pH values. Beware of buffer solution based on sodium compounds if this is used for pH 10 calibration as this will suppress the mV slope at this pH by up to 7%, leading to high pH readings when put online [8].

Grounding potential
This is caused by two or more electrically grounded points at different potentials causing electrical noise that may affect the readings of inline instruments. Manufacturerˇ¦s troubleshooting guide should be strictly followed for this to be eliminated.

Advances in electrode design
In 1970 there was a breakthrough in pH sensor construction with the development of non-glass pH measurement. The development was in response to the need of industries which cannot tolerate glass breakage. ISFET (Ion-Selective Field Effect Transistor) was developed to serve industries which require robust and glass-free electrodes. Nowadays there are over a dozen brands in the market offering ISFET handheld laboratory pH instruments.

Other electrochemical pH electrode systems available commercially are metal/metal oxide and liquid membrane electrodes. Other new possibilities are fibre optic and electro-conductive polymers as pH sensors [18].

Whether you are using a traditional glass pH electrode or an ISFET probe, the result is always relative to a calibrated value when the instrument was last calibrated to an aqueous pH buffer solution. No matter what technology you are using, there is no absolute measure of the hydrogen ion concentration or activity in an aqueous sample. That is to say, there could only be a relative accuracy and reproducibility that one could achieve.

References
[1] S P L Sorensen and K L Linderstrom-Lang. C R Trav Lab Calsberg (1924)
[2] Walther Nernst Memorial, http://www.nernst.de
[3] IUPAC Recommendations 2002, Measurement of pH. Definition, Standards, and Procedures R P Buck et al Pure Appl Che, Vol 74, No 11
[4] Presley, Hach Co, Reprint from American Laboratory News June 1999
[5] Method of Controlling pH, Gregory K McMillan, Monsanto Co
[6] Operating Manual, LCP and Ryton Encapsulated pH Sensors, GLI International, Inc Rev 8-302
[7] H S Harned and B B Owen. The Physical Cheistry of Electrolytic Solutions, Chap 14, Reinhold, New York (1958)
[8] Discrepancies between On-line and Laboratory Grab Sample Results ABB Automation, Technical Guide.
[9] http://www.omega.com/techref/ph.html
[10] http://www.thermorussell.com/techph.htm
[11] James A Pambeck, http://www.pasigate.ac.uk
[12] http://www.chemheritage.org
[13] Nikolai Pitchforth, Research Analyst, 2001 WaterWorld ˇV Water and Wastewater Technology, http://www.pennnet.com
[14] Rosemount Product Data Sheet Model TF396, August 2002
[15] Eric Pfannenstiel, October 2003, Process pH measurement continues evolution, ISA Print?
[16] pH Measurements in a Power Plant, 60th International Water Conference, Pittsburgh, PA (October 1999), Paper #IWC-99-75
[17] Standard Methods, APHA-AWWA-WPCF, 21st Edition, Page 4-88, Section 4500.
[18] Norman F Sheppard, Jr and Anthony Guiseppi-Elie. ˇ§pH Measurementˇ¨ in the Measurement, Instrumentation and Sensors Handbook; John Webster, Editor-in-Chief; CRC Press and IEEE Press, Florida, 1999.

About the author: Ir Stanley Fong is a project manager of Chevalier (Envirotech) Ltd. He has been involved in various water and sewage treatment projects since 1981 and is currently working on the Tai Po Treatment Works and Pumping Station project.