In practice, two types of plants are generally used for chemical precipitation hardness removal: One type uses a sludge blanket contact mechanism to facilitate the precipitation reaction. The second type consists of a flash mix, a flocculation basin, and a sedimentation basin. The former is called a solids-contact clarifier. The latter arrangement of flash mix, flocculation, and sedimentation were discussed in previous chapters on unit operations.
A solids-contact clarifier is shown in Figure 10.1. The chemicals are introduced into the primary mixing and reaction zone. Here, the fresh reactants are mixed by the swirling action generated by the rotor impeller and also mixed with a return sludge that are introduced under the hood from the clarification zone. The purpose of the return sludge is to provide nuclei that are important for the initiation of the chemical reaction. The mixture then flows up through the sludge blanket where secondary reaction and mixing occur. The reaction products then overflow into the clarification zone, where the clarified water is separated out by sedimentation of the reaction product solids. The clarified water finally overflows into the effluent discharge. The settled sludge from the clarification is drawn off through the sludge discharge pipe.
10.4 THE EQUIVALENT CaCO3 CONCENTRATION
In the literature, hardness is frequently expressed in terms of CaCO3. Expressing concentrations in terms of CaCO3 can be confusing. For example, when the hardness of water is 60 mg/L as CaCO3, what does this really mean? Related to this question is a second question: Given the concentration of a hardness substance, how is this converted to the equivalent CaCO3 hardness concentration?
To obtain the mass of any substance, the number of equivalents of that substance is multiplied by its equivalent mass. Because the number of equivalents of all substances participating in a given chemical reaction are equal, what differentiates the various species in this chemical reaction are their respective equivalent masses. Thus, to obtain the concentration of 60 mg/L as CaCO3, this equal number of equivalents must have been multiplied by the equivalent mass of calcium carbonate. This section will determine this equivalent mass. This is actually 50 and converting the concentration of any hardness substance to the equivalent CaCO3 hardness concentration is obtained by multiplying the number of equivalents of the substance by 50.
Let [CThard]eq represent the total concentration of hardness in equivalents, where the symbol [ ] is read as "the concentration of" and the subscript eq means that the concentration is expressed in terms of equivalents. If the only hardness ions present are calcium and magnesium,
The number of equivalents of one substance in a given chemical reaction is equal to the same number of equivalents of any other substance in this reaction, so it is entirely correct to arbitrarily express the total concentration of hardness in terms of only one of the ions that participates in the chemical reaction. The concentrations of the other ions must then be subsumed in the concentration of this one ion being chosen. For example, if the total hardness is to be expressed in terms of the magnesium ion only, the previous equation will become
In this equation, the part of the total hardness contained in calcium is subsumed in magnesium, [ Mg2+]eq. Note the prime. The term [ Mg2+]eq means that it is a concentration in terms of magnesium but that the calcium ion concentration is subsumed in it and expressed in terms of magnesium equivalents. Moreover, since an equivalent of one is equal to the equivalent of another, it is really immaterial under what substance the total equivalents of hardness is expressed. Then, in a similar manner, the total concentration of hardness may also be expressed in terms of the calcium ion alone as follows
In this equation, the part of the total hardness contained in magnesium is now subsumed in calcium, [ Ca2+]^. Again, note the prime. Similar to the term [ Mg2+]^, [ Ca2+]^ means that it is a concentration in terms of calcium but the magnesium ion is subsumed in it and expressed in terms of calcium equivalents. If other hardness ions are present as well, then the concentrations of these ions will also be subsumed in the one particular ion chosen to express the hardness.
When any ion participates in a chemical reaction, it will react to the satisfaction of its ionic charge. For example, when the calcium and magnesium ions participate in a softening reaction, they will react to the satisfaction of their ionic charges of two. Thus, if the chemical reaction is written out, the number of reference species for Ca2+ and Mg2+ will be found to be two and the respective equivalent masses are then Ca/2 and Mg/2. In terms of molar concentrations, [Ca2+]eq is then equal to [Ca2+](Ca/Ca/2) = 2[Ca2+ ]. By analogy, [ Ca2+]^ = 2 [ Ca2+]', where [Ca2+]' is now an equivalent molar concentration in terms of the calcium ion that subsumes all concentrations. Also, [Mg ]e? = [Mg ](Mg/Mg/2) = 2[Mg2+] and, again, by analogy, [Mg2+]'e? = 2[Mg]'. [Mg]' is the equivalent molar concentration in terms of the magnesium ion that also subsumes all concentrations. Considering Eqs. (10.2) and (10.3) simultaneously and expressing the molar concentrations of the calcium and magnesium hardness in terms of calcium only,
The term 2[Ca]' can be converted to [CaCO3]'. This is done as follows: In CaCO3, one mole of [Ca2+] is equal to one mole of [CaCO3]. Hence, 2[ Ca2+]' = 2[CaCO3]' and Equation (10.4) becomes
[CjMrdlq = [ Mg2% = [ Ca2% = 2[ Ca2+]' = 2[CaCo3]' or (10.5) [CaCO3]' = [CYlq = [MÖ-q = do.6)
[CaCO3]' is an equivalent molar concentration expressed in terms of moles of CaCO3. Thus, to get the equivalent calcium carbonate mass concentration, it must be multiplied by CaCO3 = 100. Therefore,
[ CTMrd ] asCaC03 = 50^^ = 50 [ Mg2+]^ = 50 [ Ca2+]^ (10.7)
Thus, the concentration of hardness expressed in terms of the mass of CaCO3 is equal to the number of equivalents of hardness ([CT,hard]eq, [Mg , or [ Ca2+Q divided 2 times the molecular mass of calcium carbonate. Or, simply put, the concentration of hardness expressed in terms of the mass of CaCO3 is equal to the number of equivalents of hardness ([Cj;hard]eq, [Mg or [ Ca2+Q times 50.
Note that Equation (10.7) merely states the concentration of hardness in terms of the mass of CaCO3. Although the symbol for calcium carbonate is being used, it does not state anything about the actual concentration of the CaCO3 species present; it is even possible that no species of calcium carbonate exists, but MgCO3 or any other species where the concentrations are simply being expressed in terms of CaC03.
To apply Equation (10.7), suppose that the concentration of Mg2+ in a sample of water is given as 60 mg/L as CaC03. The meq/L of Mg2+ is then equal to [Mg2+]eq = [ Mg2+]^ = 60/50 = 1.2 and the concentration of magnesium in mg/L is 1.2(Mg/2) = 1.2(24.3/2) = 14.58 mg/L.
Take the following reaction and the example of the magnesium ion:
Mg( HC03 )2 + 2Ca( OH) 2 ^ Mg (OH )21 + 2CaC03i + 2H0H
In this reaction, the equivalent mass of CaCO3 is 2(CaCO3)/2 = 100. Again, in any given chemical reaction, the number of equivalents of all the participating species are equal. Thus, if the number of equivalents of the magnesium ion is 1.2 meq/L, the number of equivalents of CaCO3 also must be 1.2 meq/L. Thus, from this reaction, the calcium carbonate concentration corresponding to the 1.2 meq/L of Mg2+ would be 1.2(100) = 120 mg/L as CaCO3. Or, because the species is really calcium carbonate, it is simply 120 mg/L CaCO3—no more "as."
How is the concentration of 120 mg/L CaCO3 related to the concentration of 60 mg/L as CaCO3 for the magnesium ion? The 60 mg/L is not a concentration of calcium carbonate but a concentration of the magnesium expressed as CaCO3. These two are very different. In the "120," there is really calcium carbonate present, while in the "60," there is none.
Again, expressing the magnesium concentration as 60 mg/L CaCO3 does not mean that there are 60 mg/L of the CaCO3 but that there are 60 mg/L of the ion of magnesium expressed as CaCO3. Expressing the concentration of one substance in terms of another is a normalization. This is analogous to expressing other currencies in terms of the dollar. Go to the Philippines and you can make purchases with the dollar, because there is a normalization (conversion) between the dollar and the peso.
Example 10.1 The concentration of total hardness in a given raw water is found to be 300 mg/L as CaCO3. Calculate the concentration in milligram equivalents per liter.
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