pH meter principles
What is pH and how is it measured?
by Dr J Floor Anthoni (2005)
This document familiarises you with the potential of hydrogen (pH) and how it is measured, in order to gain most from using a pH meter.
For suggestions and comments, please e-mail the author, Dr J Floor Anthoni
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The history of measuring the acidity of liquids electrically began in 1906 when Max Cremer in his studies of liquid interfaces [1] (interactions between liquids and solids) discovered that the interface between liquids could be studied by blowing a thin bubble of glass and placing one liquid inside it and another outside. It created an electric potential that could be measured.
This idea was taken further by Fritz Haber (who invented the synthesis of ammonia and artificial fertiliser) and Zygmunt Klemsiewicz [2] who discovered that the glass bulb (which he named glass electrode) could be used to measure hydrogen ion activity and that this followed a logarithmic function.

The Danish biochemist Soren Sorensen then invented the pH scale in 1909.

Because the resistance in the wall of the glass is very high, typically between 10 and 100 Mega-Ohm, the glass electrode voltage could not be measured accurately until electron tubes were invented. Later still, the invention of field-effect transistors (FETs) and integrated circuits (ICs) with temperature compensation, made it possible to measure the glass electrode voltage accurately. The voltage produced by one pH unit (say from pH=7.00 to 8.00) is typically about 60 mV (milli Volt). Present pH meters contain microprocessors that make the necessary corrections for temperature and calibration. Even so, modern pH meters still suffer from drift (slow changes), which makes it necessary to calibrate them frequently.

Improvements have also been made in the chemistry of the glass such that pollution by salt and halogen ions could be halted. The reference electrode, which traditionally used silver chloride (AgCl) has been superseded by the kalomel (mercurous chloride, HgCl2) electrode which uses mercuric chloride (HgCl) in a potassium chloride (KCl) solution as a gel (like gelatine). But electrodes do not have eternal life and need to be replaced when they drift unacceptably or take unusually long to settle.

[1] Cremer M (1906): Z. Biol, 47, 562
[2] Haber F and Z Klemensiewicz (1909): Z. Physik. Chem., 67, 385

How a pH meter works
When one metal is brought in contact with another, a voltage difference occurs due to their differences in electron mobility. When a metal is brought in contact with a solution of salts or acids, a similar electric potential is caused, which has led to the invention of batteries. Similarly, an electric potential develops when one liquid is brought in contact with another one, but a membrane is needed to keep such liquids apart. 
A pH meter measures essentially the electro-chemical potential between a known liquid inside the glass electrode (membrane) and an unknown liquid outside. Because the thin glass bulb allows mainly the agile and small hydrogen ions to interact with the glass, the glass electrode measures the electro-chemical potential of hydrogen ions or the potential of hydrogen. To complete the electrical circuit, also a reference electrode is needed. Note that the instrument does not measure a current but only an electrical voltage, yet a small leakage of ions from the reference electrode is needed, forming a conducting bridge to the glass electrode. A pH meter must thus not be used in moving liquids of low conductivity (thus measuring inside small containers is preferable).
schematic pH electrodesThe pH meter measures the electrical potential (follow the drawing clock-wise from the meter) between the  mercuric chloride of the reference electrode and its potassium chloride liquid, the unknown liquid, the solution inside the glass electrode, and the potential between that solution and the silver electrode. But only the potential between the unknown liquid and the solution inside the glass electrode change from sample to sample. So all other potentials can be calibrated out of the equation.
The calomel reference electrode consists of a glass tube with a potassium chloride (KCl) electrolyte which is in intimate contact with a mercuric chloride element at the end of a KCL element. It is a fragile construction, joined by a liquid junction tip made of porous ceramic or similar material. This kind of electrode is not easily 'poisoned' by heavy metals and sodium.
The glass electrode consists of a sturdy glass tube with a thin glass bulb welded to it. Inside is a known solution of potassium chloride (KCl) buffered at a pH of 7.0. A silver electrode with a silver chloride tip makes contact with the inside solution. To minimise electronic interference, the probe is shielded by a foil shield, often found inside the glass electrode.
Most modern pH meters also have a thermistor temperature probe which allows for automatic temperature correction, since pH varies somewhat with temperature.
Water is THE most important and miraculous substance on Earth. Its molecules H-O-H form a boomerang shape with the O- end slightly negative and the H2+ end slightly positively charged. These charged boomerangs are attracted to one another, forming islands of cohesion, such that water forms a liquid at temperatures where life thrives, whereas it should really have been a very volatile gas like hydrogen sulphide (H2S) which has almost twice its molecular weight. At the surface of Earth, water occurs in solid form (ice), liquid (water) and gaseous form (steam or water vapour). In cold areas all three phases co-exist.
Water is also unique in that it is both an acid (with H+ ions) and a lye (with OH- ions). It is thus both acidic and basic (alkaline) at the same time, causing it to be strictly neutral as the number of H+ ions equals that of the OH- ions. Because of its strong cohesion, only few water molecules dissociate (split) in their constituent ions: hydrogen ions (H+) and hydroxyl ions (OH-). Chemists would insist that H+ ions are really H3O+ ions or hydronium ions.

Knowing that one molar of water weighs 18 gram (1+1+16), which equals 18ml, and that this quantity contains a very large number of molecules [1], only 0.1 millionth (10-7) mol are dissociated in one litre of water (pH=7). [2]

The potential difference between the inside of the glass electrode and the outside is caused by the oxides of silicon in side the glass:
Si.O- + H3.O+ = Si.O.H+  + H2.O

Once the ionic equilibrium is established, the potential difference between the glass wall and the solution is given by the equation:
E = R x T / ( F x ln( a ))
Where E= electron potential (Volt), R= molar gas constant 8.314 J/mol/ºK, F= Faraday constant 96485.3 ºC, T= temperature in ºKelvin and a= the activity of the hydrogen ions (hydronium ions). 
ln( a )= the natural logarithm which converts to the decimal logarithm = 2.303 x log( a )
The combination R x T / ( 2.303 x F ) is approximately 0.060 V (60 mV) per tenfold increase in hydrogen ions or one pH unit.
The pH range of 0 to 14 accounts for hydronium activities from 10 to 1E-14 mol/litre. One mol of water weighs 18 gram. A pH=7 corresponds to hydronium activity of 1E-7 mol/litre (1E-7). Because log( 10-7 ) = -7, the pH scale leaves the minus sign out.

Even though modern pH glass electrodes have seen major improvements, they still don't like some substances low in H+ ions, like alkali hydroxides (NaOH and KOH), pure distilled water, etching substances like fluoride, adsorbing substances like heavy metals and proteins.

Most modern pH meters have inbuilt temperature sensors to correct temperature deviation automatically to give values as if these were taken at a standard temperature of 25ºC. The readout is not influenced by temperature at pH=7.00 but outside this by 0.003 per ºC. Thus a pH taken at 5ºC (20º away from 25ºC), showing 4.00 must be corrected downward by 0.003 x 20 x 3.00 = 0.18. Likewise a pH value of 10.00 must be corrected upward by this amount.

Caring for a pH meter depends on the types of electrode in use. Study the manufacturer's recommendations. When used frequently, it is better to keep the electrode moist, since moisturising a dry electrode takes a long time, accompanied by signal drift. However, modern pH meters do not mind their electrodes drying out provided they have been rinsed thoroughly in tap water or potassium chloride. When on expedition, measuring sea water, the pH meter can be left moist with sea water. However for prolonged periods, it is recommended to moist it with a solution of potassium chloride at pH=4 or in the pH=4.01 acidic calibration buffer. pH meters do not like to be left in distilled water.
Note that a pH probe kept moist in an acidic solution, can influence results when not rinsed before inserting it into the test vial. Remember that a liquid of pH=4 has 10,000 more hydrogen ions than a liquid of pH=8. Thus a single drop of pH=4 in a vial measuring 400 drops of pH=8 really upsets measurements! Remember also that the calibration solutions consist of chemical buffers that 'try' to keep pH levels constant, so contamination of your test vial with a buffer is really serious.

[1] Avogadro's constant is 602,213,670,000,000,000,000,000 (602.214 billion trillion) or 6.02E23, named in honour of Amedeo Avogadro. One mole of a chemical substance contains this number of molecules. Amedeo Avogadro (1776-1856) was an Italian physicist.  He proposed in 1811 his famous hypothesis, now known as Avogadro's law.  The law stated that equal volumes of all gases at the same temperature and pressure contain the same number of molecules.  Avogadro also distinguished between an atom and a molecule, and made it possible to determine a correct table of atomic weights.
[2] On the Seafriends web site we frequently use the exponential notation E, such that 2.34E-4 means 2.34 x 10-4.

The pH scale
The values for pH make more sense when compared with that of known substances. Note that the pH scale is logarithmic and that each next value contains ten times less hydrogen ions. A pH=0 contains the most, and is highly acidic.
0 5% Sulphuric acid, H2SO4, battery acid.
1 0.1 N HCl, hydrochloric acid (1.1)
2 Lemon juice. Vinegar (2.4-3.4)
3 wine (3.5-3.7)
4 Orange juice. Apple juice (3.8). Beer. Tomatoes.
5 Cottage cheese. Black coffee. Rain water 5.6.
6 Milk. Fish (6.7-7). chicken (6.4-6.6). 
7 Neutral: equal numbers of hydrogen and hydroxyl ions. Blood (7.3-7.4). Distilled water without CO2, after boiling.
8 Sea water (8.1). Egg white.
9 Borax. baking soda.
10 Milk of magnesia, Magnesium hydroxide Mg (OH)2.
11 Household ammonia
12 Photographic developer, household bleach
13 Oven cleaner
14 Sodium lye NaOH, 1 mol/litre.