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# Introduction to pH measurement

pH is a unit of measure which describes the degree of acidity or alkalinity of a solution. It is measured on a scale of 0 to 14. The term pH is derived from "p", the mathematical symbol of the negative logarithm, and "H", the chemical symbol of Hydrogen. The formal definition of pH is the negative logarithm of the Hydrogen ion activity.

pH = -log[H+]

Why is pH control a problem?
Why is pH control a problem? After all, you've got an odd but simple scale of measurement from 0 to 14 dimensionless units, measuring electrodes that have been around long enough to be well understood and readily applied, and instrument vendors who must have seen every possible application by now.

pH provides the needed quantitative information by expressing the degree of the activity of an acid or base in terms of hydrogen ion activity. The pH value of a substance is directly related to the ratio of the hydrogen ion [H+] and the hydroxyl ion [OH-] concentrations. If the H+ concentration is greater than OH-, the material is acidic; i.e., the pH value is less than 7. If the OH- concentration is greater than H+, the material is basic, with a pH value greater than 7. If equal amounts of H+ and OH- ions are present, the material is neutral, with a pH of 7. Acids and bases have free hydrogen and hydroxyl ions, respectively. Since the relationship between hydrogen ions and hydroxyl ions in a given solution is constant for a given set of conditions, either one can be determined by knowing the other. Thus, pH is a measurement of both acidity and alkalinity, even though by definition it is a selective measurement of hydrogen ion activity. Since pH is a logarithmic function, a change of one pH unit represents a ten-fold change in hydrogen ion concentration. Table 1 shows the concentration of both the hydrogen ion and the hydroxyl ion at different pH values.

The Molar Concept
A mole of a compound is defined as Avogadro's number of molecules (6.02 x 1023 molecules), which has a mass approximately equal to the molecular weight, expressed in grams. For example, sodium hydroxide, NaOH, which has a molecular weight of 23+16+1=40, would have 40 grams in a mole. Since the atomic weight of the hydrogen ion (H+) is one (1), there is one gram of hydrogen ions in a mole of hydrogen. A solution with a pH of 10 has 1 x 10-10 moles of hydrogen ions, or 10-10 grams in a one liter solution.

Ionization
An ion is a charged particle, created by an atom or molecule which has either gained or lost electron(s). The presence of ions in solution allows electrical energy to be passed through the solution as a conductor. Different compounds form ions in solution in different amounts, depending on the ability of the atoms to gain or lose electrons. They will dissociate (or ionize) in solution to form hydrogen (H+) or hydroxyl (OH-) ions in the solution.

Molecules that dissociate easily will form strong acids or bases when in aqueous solution (water solvent). Examples of these are hydrochloric acid (HCI) or sodium hydroxide (NaOH):

HCI + H2O -> H3O+ + Cl-
NaOH -> Na+ + OH-

In an aqueous solution, hydrogen ions normally combine with the water solvent to form the hydronium ion (H3O+). pH measurements of these solutions are therefore measurements of the hydronium ion concentration. Normally, the terms "hydronium ion" and "hydrogen ion" are used interchangeably in pH measurement applications.

Some compounds form weak acids or bases; only a very small percentage of the compounds dissociates into its constituent ions, so very few hydrogen or hydroxyl ions are formed. An example of this is acetic acid, which forms less than one hydrogen ion for every one hundred molecules:

H2O + CH3COOH -> H3O+ + CH3COO-

Pure water also dissociates weakly, with 10-7 hydrogen and 10-7 hydroxyl ions formed for every water molecule at 25°C: 2H2O ' H3O+ + OH- The addition of acid to water increases the concentration of hydrogen ions and reduces the concentration of hydroxyl ions. A base added to water has the opposite effect, increasing the concentration of hydroxyl ions and reducing the concentration of hydrogen ions:

H2O + HCl -> H3O+ + Cl- H2O + NaOH -> Na+ + H2O + OH-

There is a wide variety of applications for pH measurement. For example, pH measurement and control is the key to the successful purification of drinking water, the manufacture of sugar, sewage treatment, food processing, electroplating, and the effectiveness and safety of medicines, cosmetics, etc. Plants require the soil to be within a certain pH range in order to grow properly, and animals can sicken or die if their blood pH level is not within the correct limits. Figure 1 gives pH values for some common industrial and household products.

pH Measurement
A rough indication of pH can be obtained using pH papers or indicators, which change color as the pH level varies. These indicators have limitations on their accuracy, and can be difficult to interpret correctly in colored or murky samples.

More accurate pH measurements are obtained with a pH meter. A pH measurement system consists of three parts: a pH measuring electrode, a reference electrode, and a high input impedance meter. The pH electrode can be thought of as a battery, with a voltage that varies with the pH of the measured solution. The pH measuring electrode is a hydrogen ion sensitive glass bulb, with a millivolt output that varies with the changes in the relative hydrogen ion concentration inside and outside of the bulb. The reference electrode output does not vary with the activity of the hydrogen ion. The pH electrode has very high internal resistance, making the voltage change with pH difficult to measure. The input impedance of the pH meter and leakage resistances are therefore important factors. The pH meter is basically a high impedance amplifier that accurately measures the minute electrode voltages and displays the results directly in pH units on either an analog or digital display. In some cases, voltages can also be read for special applications or for use with ion-selective or Oxidation-Reduction Potential (ORP) electrodes.

Temperature Compensation
Temperature compensation is contained within the instrument, because pH electrodes and measurements are temperature sensitive. The temperature compensation may be either manual or automatic. With manual compensation, a separate temperature measurement is required, and the pH meter manual compensation control can be set with the approximate temperature value. With automatic temperature compensation (ATC), the signal from a separate temperature probe is fed into the pH meter, so that it can accurately determine pH value of the sample at that temperature.

Buffer Solutions
Buffers are solutions that have constant pH values and the ability to resist changes in that pH level. They are used to calibrate the pH measurement system (electrode and meter). There can be small differences between the output of one electrode and another, as well as changes in the output of electrodes over time. Therefore, the system must be periodically calibrated. Buffers are available with a wide range of pH values, and they come in both premixed liquid form or as convenient dry powder capsules. Most pH meters require calibration at several specific pH values. One calibration is usually performed near the isopotential point (the signal produced by an electrode at pH 7 is 0 mV at 25°C), and a second is typically performed at either pH 4 or pH 10. It is best to select a buffer as close as possible to the actual pH value of the sample to be measured.

Temperature Effects
As previously stated, the pH electrode is temperature dependent, and may be compensated for in the pH meter circuitry. The circuitry of the pH meter utilizes the Nernst equation, which is a general mathematical description of electrode behavior.

E=Ex + 2.3RTK log (ai)/nF
where:
Ex = constant depending upon reference electrode
R= constant
TK = absolute temperature (Kelvin)
n = charge of the ion (including sign)
F = constant
ai = activity of the ion
For pH measurement, we are interested in the hydrogen ion for
H+: 2.3RTK/nF = 59.16 mV
where: n = 1 and T = 25°C. This term is commonly known as the Nernst coefficient. Since pH is defined as the negative logarithm of the hydrogen ion activity, the general equation at any temperature can be expressed as:

E = Ex- 1.98 TKpH

Changes in temperature of a solution will vary the millivolt output of the glass pH electrode in accordance with the Nernst equation. Its variation in the electrode sensitivity versus temperature is a linear function, and most pH meters have circuitry designed to compensate for this effect (refer to Temperature Compensation). Figure 2 shows the effect on the glass pH electrode signal at various temperatures. In figure 2, all three slopes intersect at the point of 0 mV and pH 7.0; this implies no millivolt change with temperature at this, the isopotential point. Also, it can be seen that when working near 7.0 pH, temperature compensation is not a significant factor. However, when working at pH levels of 3.0 or 11.0, a temperature change of 15°C can result in an error of 0.2pH. Since the temperature effect on the electrode has been shown to be linear, the temperature dependence of pH can then be expressed as: 0.03 pH error/pH unit/10°C

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 does not correct for this, and is not desirable, because an accurate pH measurement is desired at that particular temperature. Temperature compensation only corrects for the change in the output of the electrode, not for the change in the actual solution pH. Temperature will also affect the glass membrane's impedance. For each 8° below 25°C, the specified impedance approximately doubles. Depending on the original impedance of the glass membrane, the meter will have to handle a higher impedance at a lower temperature.

 Hydrogen Ion Concentration in MOLES/LITER at 25° C pH H+ OH+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 (100)1 (10-1)0.1 (10-2)0.01 (10-3)0.001 (10-4)0.0001 (10-5)0.00001 (10-6)0.000001 (10-7)0.0000001 (10-8)0.00000001 (10-9)0.000000001 (10-10)0.000000001 (10-11)0.0000000001 (10-12)0.00000000001 (10-13)0.000000000001 (10-14)0.0000000000001 0.00000000000001(10-14) 0.000000000001(10-13) 0.00000000001(10-12) 0.0000000001(10-11) 0.000000001(10-10) 0.00000001(10-9) 0.0000001(10-8) 0.000001(10-7) 0.00001(10-6) 0.0001(10-5) 0.0001(10-4) 0.001(10-3) 0.01(10-2) 0.1(10-1) 1(100)