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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

Osmolality is defined as the number of particles of osmotically active substances per kilogram of a solvent (usually water). The size or type of particles is irrelevant for the osmotic pressure, only the number of particles (cations, anions, sugars, organic acids, amino acids, proteins, ethanol, etc.) is of importance. The presence of substances dissolved in an aqueous solution lowers the freezing point, as compared with pure water. The freezing point is lowered in proportion to the amount of dissolved particles or molecules. For this reason, measuring the freezing point of a solution provides a means for calculating the concentration of dissolved particles. The more dissolved particles there are in a solution, the greater the drop in freezing point.

Dissolved nitrogen in a liquid medium is measured using the same procedure as the CO₂ determination, i.e., using heat conductivity.

CO₂ is employed as a purge gas in the beverage industry. Therefore, in order to measure nitrogen, the change in thermal activity and CO₂ and N₂ is used. The thermal conductivity is determined in a small measurement chamber, which in turn is separated from the material being measured by a semipermeable membrane. Diffusion through the membrane changes the thermal conductivity in the measurement chamber.

The gas volume in the measurement chamber is fully replaced in cycles of 10–20 s. The changes in thermal conductivity over time are a measure of the diffusion of N₂ through the membrane, which allows the concentration in the medium to be calculated, taking temperature into account.

The calculation for the concentration of N₂ is achieved using the change in thermal conductivity in the measurement chamber, also taking the temperature into account.

Since the thermal conductivity of oxygen is similar to that of nitrogen, a second channel may need to be used to compensate for any oxygen in the medium [1].

The analytical determination of oxygen using amperometric electrodes is achieved through measurement of the electrical current. The electrodes consist of a cathode and an anode, which are connected conductively through an electrolyte solution (KCl/KOH). Precious metals, such as platinum and gold are chosen for the cathode, and silver, for the anode. The gas-permeable membrane separates the two electrodes from the solution being measured. An appropriate polarization voltage causes diffusion of the oxygen across the membrane into the measurement cell, where it reaches the surface of the cathode and is reduced, producing hydroxide ions.

Reaction at the cathode:     O₂ + 4e^– + 2 H₂O      → 4 OH⁻

Reaction at the anode:        4 Ag + 4 Cl⁻               → 4 AgCI + 4e⁻

This chemical reaction creates an electrical current that is proportional to the partial pressure p_O2 of the oxygen. Oxygen must be steadily liberated from the solution being measured for the oxygen electrode to receive a constant supply. The concentration of oxygen in the medium can be determined using HENRY’s law and the solubility coefficient of oxygen [1]. Three different variations on the types of the equipment required for performing this analysis are present below.