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11.4 CHAPTER ELEVEN

Magnesium hydroxide does not precipitate quantitatively, as suggested by Equation
(11.5), because the solubility of magnesium hydroxide depends on pH. Generally a pH of
11.0 to 11.3 is necessary to reduce the magnesium ion concentration to low values. Ex-
cess lime must be added to raise the pH for precipitation of magnesium hydroxide. The
resulting excess hydroxide alkalinity must be converted later to carbonate alkalinity to
produce a water of minimum calcium hardness. This process, generally termed reear-
bonation, requires carbon dioxide:
Ca(OH)2 + CO2 = CaCO~ + H20 (11.6)
Once calcium carbonate is formed, its properties are such that resolubilization takes place
only at a very low rate. To remove noncarbonate hardness---calcium or magnesium hard-
ness present in excess of the alkalinity--requires soda ash. Equations (11.7) and (11.8)
illustrate noncarbonate hardness removal.
MgSO4 + Ca(OH)2 = MgfOH)_2 + CaSO4 (11.7)

CaSO4 + Na2CO3 = CaCO3 + Na2SO4 (11.8)
No softening occurs in Equation (11.7), as magnesium hardness is only exchanged for
calcium hardness. Soda ash is used in Equation (11.8) to remove the calcium noncarbon-
ate hardness either originally present or formed as a result of the reactions in Equation
(11.7).

Chemical Requirements. These equations allow reasonably good approximations of the
amounts of lime and soda ash required to soften a water. The lime required to remove
carbonate hardness can be calculated as shown in Equation (11.9):

CaO (lb/mil gal) = 10.6[CO2 (mg/L)] + 4.7[alkalinity (mg/L)
+ magnesium hardness (mg/L) + x] (11.9)

where CaO is 100% pure, CO2 is expressed as CO2, alkalinity and magnesium hardness
are expressed as CaCO3, and x is the required excess hydroxide alkalinity in milligrams
per liter as CaCO3. The magnesium hardness shown is the amount present in the water
to be treated. Desired excess alkalinity can be determined from the magnesium hydrox-
ide solubility relationship; it is typically in the range of 30 to 70 mg/L and can be esti-
mated at 65 mg/L, expressed as CaCO3, for minimum magnesium hardness.
Equation (11.10) shows the calculation for the quantity of soda ash required to remove
noncarbonate hardness
NazCO3 (lb/mil gal) = 8.8[noncarbonate hardness (mg/L) - x] (11.10)
where Na2CO3 is 100% pure, noncarbonate hardness is expressed as CaCO3, and x is the
noncarbonate hardness left in the water.
Because CaO is usually 88% to 95% pure, results from Equation (11.9) must be di-
vided by actual chemical purity. Soda ash is usually essentially pure, so no adjustment to
the calculation is required. If Ca(OH)2 is used instead of CaO, the required amount of
CaO should be calculated by dividing by 56/74, the ratio of the molecular weights.

Use of Caustic Soda. Caustic soda, NaOH, can be used in place of lime or soda ash.
Fewer residuals are produced, and caustic soda is easier to handle, store, and feed. Caus-
tic soda is generally purchased as a 25% or 50% aqueous solution. Softening reactions
with caustic soda are shown in Equations (11.11) through (11.15).