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According to DIN 38409 part 6 (January 1986) “hardness” is defined as the calcium and magnesium ion content of a water sample. In particular cases, barium and strontium ions may also contribute to hardness. Even though the term hardness is not a scientific one and in principle is even legally objectionable since no SI unit exists for it, hardness is still indispensable, as it simplifies the terminology. For this reason, the somewhat dated units are still deemed acceptable alongside the current mg/l, mval/l and mmol/l. The unit “Deutscher Grad” (degrees German hardness), 1 °d (in the past, also known as 1°dH) is equivalent (based on CaO) to 0.3566 mval = 0.179 mmol/l: *)

*) SI units recognized in legal and commercial transactions, whereby °d should be expressed in mmol/l

10.00 mg/l CaO = 7.15 mg/l Ca²⁺ = 0.3566 mval/l

7.19 mg/l MgO = 4.34 mg/l Mg²⁺ = 0.3566 mval/l

For the unit 1 mval/l, the values shown above are higher by a factor of 2.804 (1/10 of the CaO equivalent weight).

28.04 mg/l CaO = 20.04 mg/l Ca²⁺ = 2.804 °d

20.15 mg/l MgO = 12.15 mg/l Mg²⁺ = 2.804 °d

An alkaline earth ion concentration of 1 mg/l corresponds to:

1 mg/l Ca²⁺ = 0.1399 °d = 0.0499 mval/l hardness

1 mg/l Mg²⁺ = 0.2306 °d = 0.0822 mval/l hardness

Calcium and magnesium are the principal alkaline earth metal ions found in natural waters.

For certain applications and/or treatment processes, knowing the total hardness is insufficient, since understanding which alkaline earth metals are responsible for it is important (usually calcium or magnesium ions). These cations are also paired with anions, in which case the ions of carbonic acid play a significant role (carbonate and hydrogen carbonate ions).

The subgroups of hardness can be characterized as follows:

Calcium or lime hardness (Ca-H):

The portion of the water hardness caused by calcium ions.

Magnesium or magnesia hardness (Mg-H):

The portion of the water hardness caused by magnesium ions.

Total hardness (TH):

This term encompasses the sum of the individual types of hardness (Ca-H + Mg-H).

Carbonate hardness (CH):

The carbonate hardness corresponds to the concentration of alkaline earth metal ions equivalent to the hydrogen carbonate and carbonate ions present in the water. These ions are measured in mval/l through determination of the m value. Water that does not require acid for neutralization to reach the m value possesses no carbonate hardness (pH < 4.3). The m value corresponds to the carbonate hardness in mval/l. This is true as long as this value does not exceed the total hardness in mval/l, since by definition the carbonate hardness cannot exceed the total hardness. Water with an m value that exceeds the total hardness in mval/l is called “sodium alkaline” since it contains sodium. In selecting the treatment process, it is advisable to differentiate between calcium and magnesium carbonate hardness (Ca-CH and Mg-CH).

Non-carbonate hardness (NCH):

This is defined as the difference between total hardness and the carbonate hardness and thus, as that portion of calcium and magnesium ions for which no equivalent bicarbonate and carbonate ions are present in the water, but for which an equivalent quantity of other ions exist (e.g., hydroxide, chloride, sulfate, nitrate, phosphate, silicate, humate). Waters, whose m value is ≥ TH (mval/l), do not exhibit non-carbonate hardness.

Required analysis data:

• calcium ion content in mg/l or mval/l

• magnesium ion content in mg/l or mval/l

• acid required to reach the m value in mval/l

The residual alkalinity is calculated using the following parameters: total hardness, calcium hardness and magnesium hardness.

The requirements for boiler feed water are detailed in the analysis methods listed below.

This rapid test for softened water is carried out by means of indicator buffer tablets.

The ions causing hardness can be bound by disodium dihydrogen ethylenediaminetetraacetic acid (EDTA) under formation of complexes through chelation. A mixed indicator is used to form loosely bound complexes, which are red in color, together with the ions that constitute hardness on the basis of Eriochrome Black.

During complexometric titration, the following processes take place:

1.  The ions causing hardness (metal ions) at first form a complex through chelation with the indicator:

     Metal ion + indicator → metal-indicator complex (red)

2.  The metal-indicator complex, however, is less stable than the EDTA complex.

     Therefore, by adding EDTA, the indicator is eliminated from the complex:

     Metal-indicator complex + EDTA → metal-EDTA complex + indicator (green)

In water samples that contain few to no magnesium ions, the color change takes place gradually. Therefore, a substitution titration is performed.

Conventional titrants usually contain a magnesium EDTA complex.

The principle is based on the fact that calcium ions form a more stable chelate with EDTA than magnesium ions do. Thus, the latter are displaced by Ca ions from the EDTA complex:

(Mg-EDTA)^2- + Ca²⁺ → (Ca-EDTA)^2- + Mg²⁺

If a Mg-EDTA complex is added along with the conventional titrant to the solution, the Mg ions present, due to the hardness of the water, in addition to the Mg ions that have been released through substitution with the Ca ions, are both in solution. The sum of Mg ions corresponds to the amount of Mg and Ca in the water and thus its total hardness. The Mg ion content is determined through titration using an EDTA standard solution.

In order to prevent substantial change in the pH during titration due to chelate formation of the released hydronium ions, ammonia and a mixture containing an indicator and a buffer are utilized.

Simple instructions have been created by various suppliers, of which the Titriplex method from Merck, Darmstadt, Germany (www.merck.de) is described below and will serve to represent the instructions for other methods as well (e.g., Riedel de Haën, Hannover, Germany (www.riedeldehaen.de)).