Theoretical Review

In pH measurement systems, a pH responsive glass takes up hydrogen ions and establishes a potential at the glass surface with respect to the solution. This potential is related to the hydrogen ion activity of the solution by the Nernst relationship as follows:

logi,

where:

Eg = the sum of reference potentials and liquid junction potentials, which are constants (in millivolts)

EO = the potential when a = 1 a = hydrogen ion activity

T = absolute temperature degrees Kelvin (°C + 273) R = 1.986 calories per mol degree F = Faraday (coulombs per mol) 2.303 = logarithm conversion factor

The process variable pH is the negative logarithm of the hydrogen ion (i.e., proton) activity as follows:

If both sides of the equation are multiplied by — 1 and the definition of an antilogarithm is used, the result shows that the hydrogen ion activity is equal to 10 raised to the negative power of the pH. The lowercase p designates the mathematical relationship between the ion and the variable as a power function; the H denotes the ion is hydrogen as follows:

For dilute aqueous (water) solutions, the activity coefficient is approximately unity, and the hydrogen ion concentration is essentially equal to the hydrogen ion activity. As the concentrations of acids, bases, and salts increase, the crowding effect of the ions reduces hydrogen ion activity. Thus, an increase in salt concentration can increase the pH reading even though the hydrogen ion concentration is constant.

An acid is a proton donor, and a base is a proton acceptor. When an acid dissociates (breaks apart into its component ions), it yields a hydrogen ion and a negative acid ion. When a base dissociates, it gives a positive base ion and a hydroxyl ion that is a proton acceptor. When water dissociates, the result is both a hydrogen ion (proton) and hydroxyl ion (proton acceptor). Thus, water acts as both an acid and a base. Neutralization is the association of hydrogen ions from acids and hydroxyl ions from bases to form water.

pH measurement can track fourteen decades of hydrogen ion concentration and detect changes as small as 10—14 (at 14 pH). The concentration changes of strong acids and bases also follow the decade change per pH unit within this range. No other concentration measurement has such rangeability and sensitivity. These characteristics have profound implications for pH control.

Concentrated strong acids and bases have a pH that lies outside this range. For example, concentrated sulfuric acid has a pH of —10, and concentrated sodium hydroxide has a pH of19 as measured by a hydrogen electrode. However, the set point of a pH loop is usually well within the 0 to 14 range. Some feedforward pH loops can require measurements outside this range, but the shortened life expectancy and increased error from the electrode at range extremes make such measurements impractical.

The neutral point is where the hydrogen ion concentration equals the hydroxyl ion concentration. At 25°C, this point occurs at 7 pH (see Table 7.7.3).

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