| The Langelier Saturation Index is based on the study of the carbonate equilibrium in water. For the Langelier Saturation Index click here The elements that are important for the carbonate equilibrium are gaseous carbon dioxide CO2, aqueous carbon dioxide (CO2)aq, carbonic acid H2CO3, bicarbonate HCO3-, carbonate CO32- and solids containing carbonate like calcium carbonate CaCO3 or magnesium carbonate MgCO3. Below you can see all the equations that matters for the carbonate equilibrium. These are all equilibrium reactions symbolized by double arrows. |
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| | | | | | (A) | ||||||||||||||
| | | | | | (B) |
Figure 1
| Figure 1 can give you the filling that you have to start with gaseous CO2 in your water to obtain at the end calcium carbonate CaCO3. This is not the right interpretation. You can have water that naturally contains bicarbonate ions HCO3-. So equilibrium equation (A) may occur without the earlier equilibrium reactions with carbon dioxide. The formula to calculate the Langelier Saturation Index is:
where:
The pH of a solution is usually known. Equations (A), (B) and (C) are used to compute the saturation pH (pHs). Equation (C) is a result of the combination of equations (A) and (B).
The equilibrium constant Ka of equation (A) can be calculated with the following formula:
The equilibrium constant Ksp of equation (B) can be calculated with the following formula:
The equilibrium constant K of equation (C) can be calculated with the following formula:
From this point untill the formula of pHs you only have to use mathematics.
Simplify
If X=Y then log(X) = log(Y) So:
log (X * Y) = log(X) + log(Y) and log(X/Y) = log (X)-log(Y) so:
The formula for pHs is then:
If you have a water analysis de calcium and bicarbonate concentration are known so you have to calculate the activity coefficients. These coefficients are approximately equal to one but it is better for the accuracy of pHs to calculate them. The activity coefficient can be calculated by the following formula:
The ionic strength can be calculated with the following formula:
All the parameters are now known and the Langelier Saturation Index can be calculated:
The equilibrium constants Ka and Ksp change with temperature. The following values for the equilibrium constants are given in [1]:
The relation between the constant solubility product Ksp of calcium carbonate and temperature is as follows
This equation is found by adding an exponential trendline in the graph of the solubility product constant as a function of the temperature in degree Celsius. The relation between the equilibrium constant Ka of carbonate/bicarbonate (CO32-/HCO3-) and temperature is as follows:
Go to the Langelier Index Calculator References: [1] :Metcalf & Eddy, Inc. Wastewater Engineering Treatment and Reuse, Fourth Edition | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||













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