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## Hydrogen Ion Concentration

If we express the hydrogen ion concentration of an aqueous solution in relation to its molecular value we derive a scale of 1 (100) via 10-7 to 10-14 mole/litre. This scale is impractical but if written as a function of its negative logarithm a real and simple scale of 0–14 has been created: the pH scale.

 H+ Concentration (mole/litre) OH- Concentration (mole/litre) pH 1 0.00000000000001 0 0.1 0.0000000000001 1 0.01 0.000000000001 2 0.001 0.00000000001 3 0.0001 0.0000000001 4 0.00001 0.000000001 5 0.000001 0.00000001 6 0.0000001 0.0000001 7 0.00000001 0.000001 8 0.000000001 0.00001 9 0.0000000001 0.0001 10 0.00000000001 0.001 11 0.000000000001 0.01 12 0.0000000000001 0.1 13 0.00000000000001 1 14

The pH scale covers the active concentration of the H+ ions and OH- ions and therefore the pH unit of measure is defined as the negative common logarithm of the active hydrogen ion concentration in an aqueous solution.

If the H+ ion concentration changes by a factor of ten, the pH value changes by one unit. This illustrates how important it is to be able to measure the pH value to a tenth of a unit or even a hundredth of a unit in special applications.

Note that this definition of pH refers to the active hydrogen ion concentration and not just to the hydrogen ion concentration. It is important to understand this difference. Only in dilute solutions are all anions and cations so far apart that they are able to produce the maximum of the chemical energy, i.e. the H+ ion concentration and the H+ ion activity are identical. For instance 0.01 mole hydrochloric acid is still classified as a dilute solution which dissociates completely and therefore concentration equals activity.

If the HCl concentration increases, the cation (H+) and the anion (Cl-) increasingly obstruct each other as the space between them gets smaller and smaller. In this case the ion activity is slowed down and does not correspond any longer with the ion concentration. With increasing concentration the ion activity differs to the ion concentration more and more.

It is important to recognize the fact that a pH measurement determines only the concentration of active hydrogen ions in a solution, and not the total concentration of hydrogen ions. It is this factor that is responsible for the observed pH change in pure water with temperature.

## The Effect of Temperature on pH

If the temperature rises in pure water, the dissociation of hydrogen and hydroxyl ions increases. Since pH is related to the concentration of dissociated hydrogen ions alone, the pH value actually decreases although the water is still neutral. Therefore it is very important that we know the relationship between the dissociation constant and temperature, otherwise it is not possible to predict the pH value of a solution at a desired temperature from a known pH reading at some other temperature.

This is best explained if we compare the concentration of 1 mol/l pure hydrochloric acid (HCl) which has a pH value of 0, with a concentration of 1 mol/l pure sodium hydroxide (NaOH) which has a pH value of 14. When both solutions are mixed in same quantities, a neutralization reaction occurs as may be seen by the following equation:

The acidic and alkaline properties of the solutions are lost because of the union of the hydrogen and hydroxyl ions which form water. The newly formed sodium chloride (table salt) does not influence the pH value.

Generally the following can be stated:

• If the concentration of active hydrogen and active hydroxyl ions in a solution is of the same quantity, the solution is neutral (pH value = 7)
• If the solution has a higher concentration of active hydrogen ions than that of hydroxyl ions, the solution is an acid ( pH value below 7)
• If the solution has a higher concentration of active hydroxyl ions than that of hydrogen ions, the solution is a base (pH value above 7)

The graph below provides another way to view the pH scale along with the pH values of some more common liquids.

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