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Work done by Professor Langelier, published in 1936, deals with the conditions at which a given water is in equilibrium with calcium carbonate.
The equation developed by Langelier makes it possible to predict the tendency of water either to precipitate or to dissolve calcium carbonate.
The equation expresses the effects of pH, calcium, total alkalinity, dissolved solids and temperature as they relate to the solubility of calcium carbonate for waters in the 6.5 - 9.5 pH range.
The equation is written:
The left side of the equation represents the pH at which water with a given calcium content and alkalinity is in equilibrium with calcium carbonate.
The terms K2 and Ks symbolize the second dissociation constant and the solubility product constant for calcium carbonate, respectively.
These terms are functions of temperature and total mineral content. Their values for any given condition can be computed from the known thermodynamic constants. Both the calcium and the alkalinity terms are the negative logarithms of their respective concentrations.
The algebraic difference between the actual pH of a sample of water and its computed pHs is called the Calcium Carbonate Saturation Index.
Hence, Saturation Index equals pH minus pHs.
Langelier Index = pH - pHs
This index is a qualitative indication of the tendency of calcium carbonate to deposit or dissolve. If the index is positive, calcium carbonate tends to deposit. If it is negative, calcium carbonate tends to dissolve. If it is zero, the water is at equilibrium.
The calculation of pHs has been simplified by the preparation of various nomographs.
A suitable one can be downloaded by clicking the image on the right.
A spreadsheet for computer calculation is listed below.
Drawbacks of the use of Indexes
The Saturation Index, however, measures only the directional tendency or driving force of a water. It cannot be used as a quantitative measure.
Two different waters, one of low hardness and thus corrosive, and the other of high hardness and thus scale forming, can have the same Saturation Index.
The most important drawback related to the Langelier (and all other indexes) is that it calculates the current situation of the specific sample.
So, if it was originally a matter of a scaling forming water, and deposition has already took place, calcium, alkalinity and total solids are missing from the sample, while pH has been modified.
So the sample is not any more scale forming, but balanced.
Modifications also occur in an originally corrosive water, after corrosion is taking place.
If we calculate the index under such conditions, we will conclude erroneously.
Water Services Ltd has developed an extremely accurate recalculation method, based upon the Langelier Index and computer analysis, available to its customers.
By this procedure, the user can define not only the current situation, but also the history of the water into the system (p.e. if deposition or corrosion has already take place, and in which level).
Please contact us for more details, or click on the image below to enlarge parts of a sample report.
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