How to Measure pH
The principle of pH measurement is founded in Nernst's Law which was developed by nobel prize winner Walther Nernst.
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+]
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+ / litre.
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. When dealing exclusively with hydrogen ions, we rewrite Nernst' equation as:-
E = E0 +((RT) / (nF)) · ln [H+]
Further to this - the 'metal' Hydrogen's standard electrode potential (E0) is declared to be zero volts at all temperatures - so the formula can be rewritten as:-
E = ((RT) / (nF)) · ln [H+]
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.
The pH glass is specifically formulated glass, combining oxygen atoms held together with chains of silicon atoms. Each silicon atom is shown as being bonded to three oxygen atoms in the plane of the paper. In addition, each is bonded to another oxygen above or below the plane. Therefore, the glass consists of an infinite three-dimensional network of SiO groups, in which each silicon is bonded to four oxygens and each oxygen is shared by two silicons.
Within the interstices of this structure are sufficient cations to balance the negative charge of the silicate groups. Cations such as sodium and lithium are singly charged, making them mobile in the lattice and are responsible for electrical conduction within the membrane , however, the precise nature and concentrations of the cations are proprietary formulas. Adjusting the concentrations allows us to produce pH electrodes that will outperform many others on the market. Specific formula's are also used to produce pH electrodes for specific applications, such as those that eliminate sodium ion error in solutions, with a very high pH - such as our 9037-10B pH electrode.
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 potential differences that arise across the glass membrane.
A modern pH electrode actually comprises of two electrodes. The pH indicator electrode and the reference electrode. Modern pH electrodes are manufactured as a combination type pH electrode, where both the indicator electrode and reference electrode are integrated into the same assembly.
For the purposes of simplicity, we'll begin by looking at the traditional pH measurement setup, which uses a separate indicator and reference electrode.
A small galvanic cell is produced when the two electrodes are immersed in a solution. The total potential developed is dependent on both electrodes, and is a sum total of several individual potentials.
E1 = potential difference between the pH glass membrane and the sample being measured.
E2 = potential difference between the electrolyte in the glass electrode and the inner surface of the glass membrane.
E3 = potential difference between the electrode pin and the electrolyte in the glass electrode.
E4 = potential difference between the electrode pin and the electrolyte in the reference electrode.
E5 = potential difference that occurs at the reference junction (the interface which joins the reference electrolyte solution with the sample solution).
The sum total of all the potential difference is ET which can be expressed as:-
ET = E1 + E2 + E3 + E4 + E5
Our principle measurement is E1 which is the potential difference between the pH glass membrane and the sample we're measuring. As ET comprises of the sum of the potentials, we need to compensate for the other constituent parts in our equation.
Firstly E3 is the potential difference between the electrode pin and the electrolyte in the glass electrode, and E4 the potential difference between the electrode pin and the electrolyte in the reference junction. As these are identical and subject to the same solution temperature as one another, we can deduce that E3 = - E4 which cancels one another out.
Secondly, with an adequate flow rate through the reference junction and using an appropriate reference junction solution, we can negate the effects of E5.
This leaves us with the equation of:-
ET = E1 + E2
The polarity E2 will be the inverse polarity of E1 so we can express our equation as ET = E2 - E1
As E2 is the potential difference between the electrolyte and the inner surface of the glass electrode, we can ensure that E2 is a constant by using a high quality electrolyte with excellent buffering properties.
This leaves us with the only potential difference lying as the difference between the pH glass membrane and the sample being measured.
By measuring a change at this point, we can then determine the pH of the measured solution by expressing the measured voltage of the solution using the Nernst equation:-
E = Eind - Eref
Eind can be expressed as:- Eind = E ́T and Eref can be expressed as:- Eref = R·T/F·ln aH+
E = measured voltage ( mV )
Eind = voltage of indicator electrode (mV)
E ́T = temperature dependent constant (mV)
Eref = voltage of reference electrode (mV)
R = gas constant ( 8.3144 J/K )
T = absolute temperature ( K )
F = Faraday's constant ( 96485.31 Coulombs )
This gives us a constant and final formula of:-
E = E ́T - (2.303 · R · T/F · log aH+)
As the temperature has an effect on the measured pH, we can express the pH at temperature using the following equation:-
pHT = pHT° - (E / R' · S · T)
R' = constant = 0.1984 mV/K
S = sensitivity (since the electrode response may differ from the theoretical response, a correction factor)
pH° = zero pH (the pH value at which the measured potential is zero; changes with temperature, producing another slope)
pH Theory and Practice - The Need For pH Buffering
Understanding the theory of pH is a great starting point for making pH measurements in professional environments, including laboratories and within industry. Unfortunately, the ideal situation reflected in the theoretical equations listed above rarely, if ever, exists.
For various reasons, a small potential difference can develop, and this is known as the asymmetry potential. The asymmetry potential can be caused by a number of different issues. The reference junction potential can be greater than or not equal to zero, and during the manufacturing process the inner and outer surfaces of the pH glass membrane may vary.
The electrolyte solution is often a polymerised version of a proprietary blend, normally specified for a specific application, such as high temperature, or low conductivity. This is gradually consumed as the electrode is used, all of which results in a real world adjustment to the potential developed by the electrode, ensuring that the signal we receive is not always the signal that we expect.
A lot of these errors can be removed from our measurement by conductivity and periodic electrode buffering and preventive maintenance.
Calibration matches the pH meter to the characteristics of the pH electrodes being used and continued calibration of the electrode on a regular basis, corrects for continually changing characteristics during the lifetime of the electrodes.
The most accurate calibration is performed using two different buffer solutions. This enables both pH° ( zero pH ) and the slope ( sensitivity ) to be determined. There is more information on buffering pH electrodes here.
We've been supplying pH instruments since 1982, and our pH electrodes are often the secret to making accurate and reliable pH measurements in a wide range of processes, while outperforming those from other manufactures. If we can assist you with any specific pH measurement or control applications, then please don't hesitate to get in touch.