In 1936 Professor W.F. Langelier published his work related to the conditions at which water is in equilibrium with calcium carbonate (the primary compound responsible for scale). Professor Langelier developed an equation (Langelier Saturation Index) that predicts the likelihood of calcium carbonate to either precipitate out, or to dissolve, under different conditions. The Langelier equation expresses the relationship of pH, calcium, total alkalinity, dissolved solids, and temperature as they relate to the solubility of calcium carbonate in waters with a pH of 6.5-9.5. Following is the equation:
pHs = (pK2 – pKs) + pCa2+ + pAlk
pHs = the pH at which water with a given calcium content and alkalinity is in equilibrium with calcium carbonate
K2 = the second dissociation constant for carbonic acid
Ks = the solubility product constant for calcium carbonate
These terms are functions of temperature and total mineral content. Values for a given condition can be computed from known thermodynamic constants. Both the calcium ion and the alkalinity terms are the negative logarithms of their respective concentrations. The calcium content is molar. The alkalinity is the titratable equivalent of base per liter.
The Langelier Saturation Index (LSI) is calculated as LSI = pHa – pHs, where pHa is the actual pH, and pHs is the pH of the sample water. The result is an index of the tendency of calcium carbonate to deposit or dissolve. If the LSI is positive, calcium carbonate has a tendancy to deposit. If the LSI is negative, then the calcium carbonate will tend to dissolve. If the LSI is zero, then the water is at equilibrium. Because the LSI is only a directional tendency, it is not effective as a quantitative measure.