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Practical pH: Theory and Use TEXT SIZE: A A A    PRINT THIS PAGE   EMAIL THIS PAGE

This article will discuss the principles and theory behind the pH measurement and relate these to the actual pH measurement done in the field / laboratory.

Introduction

Since the Danish chemist S.P.L. Sorensen defined pH in 1909, an enormous development of the theory and practical application of the pH concept has taken place. Today, the pH value is an important determining factor in a majority of chemical processes and the pH meter has, consequently, become the most widely used analytical laboratory instrument. Measurement of pH by means of electronic instrumentation and electrodes holds a key position in the modern laboratory.

Reliable pH measurement requires more than a well functioning pH meter. The electrodes should be selected in accordance with the actual sample(s) and should be in a proper working condition, that is, should be fast and reproducible. Furthermore, the calibration buffers and the calibration procedure are cornerstones if accurate results are to be obtained. The buffers applied should be precision solutions without contamination ( CO2 or microbiological ) and the calibration procedure should be correctly performed.

Microprocessor controlled pH meters simplify calibration and operation so that pH measurements can be obtained quickly. Advanced instruments inform the operator about electrode failures or possible operator mistakes. The meter itself is able to check for a properly functioning electrode and correctly perform calibration procedures. A self-check program allows the pH meter to check itself for operational errors. Using NIST buffer solutions rounds out the necessary ingredients for proper and accurate pH measurement.

What is pH?

The Danish scientist S.P.L. Sorensen first proposed the term pH as an abbreviation of "pondus hydrogenii" in 1909 to express very small concentrations of hydrogen ions.

The original definition of pH, is the negative base 10 logarithm of the hydrogen ion concentration, or:
 

pH = - log10[H+]

 

However, since most chemical and biological reactions are governed by the hydrogen ion activity, the definition was changed to:
 

pH = - log10aH+

 

The operational pH definition, which is currently defined using a standard hydrogen electrode setup and buffers standardized in accordance with IUPAC recommendations, is closely related to the definition of pH given above, using the hydrogen ion activity.

In any collection of water molecules, a small number of water molecules will dissociate to form [H+] and [OH-] ions:
 

H2O = H+ + OH-

 

At 25°C (standard temperature), pure water contains 1 x 10-7 moles per liter of hydrogen ions and 1 x 10-7 moles per liter of hydroxide ions.

In any aqueous solution, the concentration of hydrogen ions multiplied by the concentration of hydroxide ions is constant, allowing us to define the dissociation constant for water, Kw:
 

Kw = [H+] [OH-] = 10-14

where the brackets signify molar concentrations.

The value of Kw (and therefor pH) is temperature dependent:

pH of pure water vs. Temperature pKw vs. Temperature
Kw Chart
0°C pKw = 14.94 pH = 7.47
18°C pKw = 14.22 pH = 7.11
25°C pKw = 14.00 pH = 7.00
50°C pKw = 13.22 pH = 6.61
100°C pKw = 12.24 pH = 6.12

The pH scale was established to provide a convenient and standardized method of quantifying the acidity or basicity of a particular solution. The range of the pH scale is based on the dissociation constant of water, Kw, defined above.

Since most samples we care about measuring will have less than 1 Molar H+ or OH- concentrations, the extremes of the pH scale are established at pH 0 to pH 14. With strong acids or bases, pH values below pH 0 and above pH 14 are possible, but such samples are rarely measured.

When acids and bases are dissolved in water, they alter the relative amounts of H+ and OH- ions in solution. If an acid is dissolved in water, it increases the H+ ion concentration. Because the product [H+] [OH-] must remain constant, the OH- ion concentration must therefor decrease. If a base is dissolved in water, the converse happens.

Thus, pH can also be viewed as a simultaneous measurement of both acidity and basicity, since by knowing the concentration of either the H+ or the OH- ion, one can determine the other.

pH is a logarithmic function. A change in one pH unit is equal to a ten-fold change in H+ ion concentration. The table below illustrates the relationship between the H+ and OH- ions at different pH values:

HYDROGEN AND HYDROXIDE ION CONCENTRATIONS
IN MOLES/LITER AT 25°C
pH [H+] [OH-]
0 (100) 1 0.00000000000001 (10-14)
1 (10-1) 0.1 0.0000000000001 (10-13)
2 (10-2) 0.01 0.000000000001 (10-12)
3 (10-3) 0.001 0.00000000001 (10-11)
4 (10-4) 0.0001 0.0000000001 (10-10)
5 (10-5) 0.00001 0.000000001 (10-9)
6 (10-6) 0.000001 0.00000001 (10-8)
7 (10-7) 0.0000001 0.0000001 (10-7)
8 (10-8) 0.00000001 0.000001 (10-6)
9 (10-9) 0.000000001 0.00001 (10-5)
10 (10-10) 0.0000000001 0.0001 (10-4)
11 (10-11) 0.00000000001 0.001 (10-3)
12 (10-12) 0.000000000001 0.01 (10-2)
13 (10-13) 0.0000000000001 0.1 (10-1)
14 (10-14) 0.00000000000001 1 (100)

 

The principle of the potentiometric pH measurement is rooted in Nernst's Law.
Nernst found that when a metal object is immersed into a solution containing ions of the same metal, a potential difference occurs.
Nernst defined this potential difference, E, generated by the exchange of metal ions between the metal and liquid, as:

E = E0 + ((RT) / (nF)) · ln [M+]


Where:
R = gas constant (R=8.314J/mole·K)
F = Faraday number (F = 96493 C/mole)
n = valency of the metal
[M+] = metal ion concentration
T = absolute temperature in Kelvin
E0 = normal potential

The "normal potential" is the potential difference arising between the metal and solution when the solution contains 1 mole M+/liter.

Because the hydrogen ion has similar properties to metal ions (both have a positive charge), Nernst's law can also be applied to a "Hydrogen Electrode" immersed into a solution containing hydrogen ions.

Nernst's original equation can be rewritten as:
 

E = E0 + ((RT) / (nF)) · ln [H+]


By definition, the normal potential, E, of the metal "hydrogen" in a 1 normal H+ solution is 0 volt at all temperatures. So, we can rewrite the formula as:
 

E = ((RT)/F)) · ln [H+]

The Standard Hydrogen Electrode


The Standard Hydrogen Electrode
A "Hydrogen Electrode" can be made by coating a platinum electrode with a layer of platinum-black and passing a flow of hydrogen gas over it. The platinum-black coating allows the adsorption of hydrogen gas onto the electrode, resulting in a "Hydrogen Electrode".

In 1906, Max Cremer discovered that some types of glass generated a potential difference dependent on the acidic value of the liquid it was immersed in. Together with Fritz Haber, they proved that this potential difference, within a fixed pH range, followed Nernst's law in the same manner as did the "Hydrogen Electrode". They discovered that what made their glass sensors sensitive to changes in pH levels was the formation of what is known in the pH industry as the "gel-layer", or "hydration-layer" of the glass.

pH Glass Structure

As shown in the figure to the left, the structure of pH glass is a network of oxygen atoms held together in irregular chains by silicon atoms. Each silicon atom is associated with four oxygen atoms, and each oxygen is shared by two SiO4 groups to form a three-dimensional network. The "holes" in this three-dimensional network are occupied by cations (the particular metal cations and their concentrations are typically proprietary formulas), held in place more or less strongly by the electrostatic field of neighboring oxygen ions.
When immersed in an aqueous solution, the surface layers of the pH glass undergo an ion-exchange process, whereby alkali metal ions from the glass go into solution and are replaced by hydrogen ions. This results in both the development of an electrical potential and the buildup of a thin layer containing numerous hydroxyl groups: =Si-O-Na + H2O --> =Si-OH + Na+ + OH- on the surface of the glass membrane. This "gel-layer" or "hydration layer" is the equivalent of the metal in Nernst's theory and is essential for the proper functioning of the pH glass electrode. The formation of this gel-layer continues until the ion exchange equilibria is reached and the electrochemical potential remains constant.

With the equilibrium having been reached, the hydrogen ion concentration/activity outside the glass and inside the gel-layer are equal and no further transport of hydrogen ions occurs. The voltage across the glass membrane is now zero. If the hydrogen ion concentration outside the glass and inside the gel-layer differs from the hydrogen ion concentration in the solution being measured, a transport of hydrogen ions takes place. This movement of ions affects the neutrality of the gel-layer and, consequently, a voltage will develop to prevent further transport of hydrogen ions. The value of this voltage is dependent upon the hydrogen ion concentration in the solution being measured. Because this voltage cannot be measured directly, it is necessary to add a pH independent reference potential to the measuring circuit. The addition of this reference potential allows us to measure the potenital differences that arise across the glass membrane.

 

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