# pH Electrode Theory

## pH Electrode Theory

The degree of acidity (or alkalinity) of aqueous solutions may be expressed as pH, which is defined by the equation:

pH = -log aH+ (1)

where aH+ equals the hydrogen ion (H+) activity, which is defined by the thermodynamic equation:

aH+ = γH+ • MH+ (2)

where:
γH+ = activity coefficient of H+
MH+ = molarity of H+ in mols/liter

The hydrogen ions are produced with an equal number of hydroxyl ions (OH-) when pure water dissociates according to the chemical equation:

H2O = H+ + OH- (3)

The equilibrium constant (K) for this reaction is given by the thermodynamic equation:

K = (aH+ • aH-) / aH2O (4)

Since the degree of dissociation is quite small, the activity of H2O (aH2O) is essentially constant, so that Equation 4 may be written as:

Kw = K • aH2O = aH+ • aOH- (5)

At 25°C, the experimental value of Kw is very close to 10-14. The number of hydrogen ions is equal to that of the hydroxyl ions:

aH+ = aOH- = 10-7

so that Kw = 10-14.

Now Equation 5 may be written in logarithmic form:

pKw = pH + pOH = 14 (at 25°C) (6)

where: pKw = -log Kw = 14

and for the neutral solution:

pOH = -log aOH = pH = 7

If additional H+ is added to pure water in the form of an acid, then its activity is increased, and in accordance with Equation 1, the pH is decreased from the neutral value of 7. For example, in a 0.01 molar solution of HCl (which is sufficiently dilute for γH+ = 1), aH+ = MH+ = 0.01 and:

pH = -log 0.01= 2

Similarly, if additional OH- is added to pure water in the form of a base (alkali), then the pH is increased from the neutral value of 7 in accordance with Equation 6. Thus, in a 0.01 molar solution of NaOH (which is sufficiently dilute for γOH- = 1),
aOH- = MOH- = 0.01 and:

pH = 14 - pOH = 14 + log 0.01 = 12

pH Measurement

The simplest device for measuring pH is a strip of paper impregnated with a dye whose color changes with pH. It is nothing more than an elaboration of the Litmus paper of the early days of chemistry. Besides the old time dyes such as phenolphthalein and methyl orange, there are about 100 organic dyes suitable for this application. Thus, wide range pH papers are available covering the useful ranges of 0 to 14 with a sensitivity of 1 pH unit. Narrow range papers are also available for pH changes of about 2 units, and are sensitive to 0.2 to 0.4 of a pH unit depending on the range. Using a half dozen narrow ranges, the complete range (0 to 14) can be covered.

For a more precise measurement of pH (to 0.01 of a unit), the reversible electromotive force (emf) cell is used. It is essentially a battery consisting of two electrodes, each immersed in its respective solution, joined by a salt bridge (a fine capillary tube containing a suitable electrolytic solution). For a reversible emf cell consisting of two hydrogen electrodes, one having a solution with unknown activity (aH+), and the other with a standard activity (a+), the voltage as measured by a precision potentiometer is a function of the free energy change for the overall reaction in the cell [ΔG = -nF (E - E°), so that the following form of the Nernst electrode equation (Equation 1) applies:

E - E° = 2.303 [(RT) / (nF)] log (a+ / aH+)

where:

E = voltage of the hydrogen electrode with unknown activity aH+
E° = voltage of the standard hydrogen electrode with activity a+
2.303 = conversion of common to natural logs
R = ideal gas constant = 8.314 volt-coulombs / °K mol.
T = absolute temperature = 298.1°K at 25° C
n = valence (number of charges on ion) = 1 for H+
F = Faraday constant = 96,490 coulombs / mol

At 25° C:

2.303 (RT) / (nF) = (2.303 • 8.314 • 298.1) / (1 • 96,490) = 0.05915 volts

Since there is no workable electrode that has an absolute potential of zero, all electrode potentials (voltages) are referred to the standard hydrogen electrode with an activity of a+ = 1, assumed to have a zero potentiali.e., E° = 0.

Equation 1 may now be written as follows:

pH = E / 0.05915 (at 25°C)

which is a measure of the pH of the unknown solution from the voltage of the above cell at 25°C, which may be written as:

 PlatinizedH2 gas (1 atm) Saturated KCl bridge PlatinizedH2 gas (1 atm)H+STD Unknown solutionaH+ StandardaH°+ = 11.20M HCl

Electrode Reactions:

On the left, H+ + e = 1/2 H2
On the right, 1/2 H2 - e = H+STD
Overall Reaction: H+ = H+STD1, K = (aH°+ / aH+)

The two hydrogen electrodes consist of freshly platinized platinum surfaces in an open glass tube immersed in the respective solutions with a constant supply of pure hydrogen bubbling at 1 atmosphere (atm) pressure. When freshly prepared, this cell is the most accurate and is used for calibration and research work. However, it is quite cumbersome and not practical for ordinary laboratory measurements. For laboratory work, a more convenient reference electrode is the half cell calomel electrode, namely:

Hg (liq), HgCl (solid) / KCl solution II

 Figure 1 Cable Cap Fill hole Body-glass or epoxy Outer reference chamber filled with internal fill solution Ag/AgCl wire Annular reference junction allows reference solution to leak Inner reference chamber Outer reference chamber pH sensing bulb
Three concentrations of KCl are used: 0.1 M, 1.0 M, and saturated. The saturated is mostly used because it has a very small liquid junction potential correction; but for more precise work, the 0.1 M solution is used, even though it has a larger correction. When measured against the standard hydrogen electrode, the voltages at 25°C are as follows:

 Concentration Voltage 0.1 M 0.3334 1.0 M 0.2805 Saturated 0.2479

Prior to the introduction of the glass electrode, other more convenient types such as the quinhydrone and antimony electrodes were used with the calomel electrode to complete the emf cell. The quinhydrone electrode is a piece of platinum or gold, not platinized, with a very small amount of quinhydrone [a equimolecular mixture of quinone (0 = C6H4 = 0) and hydroquinone (HO - C6H4 - OH)] added to the solution. It has a useful range of 0 to 9 pH, but above 9, the electrode accuracy breaks down because the quinhydrone becomes too soluble and easily oxidized. The antimony electrode consists of a block of specially prepared antimony metal with one surface in full contact with the solution. Its range is 4 to 11.5 pH and, although quite rugged, is subject to error.

The glass electrode, which consists of a thin wall glass bulb (sometimes as little as 1 micron thick) and is made of a critically composed glass, has an extremely high resistance (2 to 6 megohms) so that galvanometers of comparable sensitivity are required. In the early 1940s, suitable electronic devices were developed with sufficient sensitivity to make the glass electrode practical. Today, there are an abundance of glass electrodes of almost every conceivable type to measure the concentration of ions other than hydrogen. The anatomy of an electrode is shown in Figure 1. More advanced electrodes contain a third element to measure the temperature and automatically give the corrected pH on the meter. These are known as automatic temperature compensation (ATC) electrodes. This correction is needed to give the correct pH (whether manual or automatic) as seen from Equation 1, where the voltage is a function of temperature.

Today, most pH meters are minicomputers that measure the voltage and translate them into pH values at the correct temperature under the most adverse conditions. These meters with glass electrodes are now calibrated with buffer solutions (resistant to changes in pH) that can be traced to standards at the NIST.

Typical standard buffers include:

• 0.05 M potassium hydrogen phthalate (pH = 4.008)
• 0.025 M disodium hydrogen phosphate + 0.025 M potassium dihydrogen phosphate (pH = 6.865)
• 0.01 M borax (pH = 9.180)

The pH values are at 25°C and accurate to ±0.002. These and many more buffer solutions are available from ® at 1-800-323-4340 or under the pH Buffers of of our online catalog.