Notes On Equivalent Masses

If all the softening reactions were reviewed, it would be observed that the equivalent masses of the hardness "molecules" and their associated ionic species are obtained by dividing the molecular masses by the respective total number of valences of the positive or negative ions of the associated species, irrespective of the coefficients in the reaction. For example, in Equation (10.17), the equivalent mass of the "molecule" MgSO4 is obtained by dividing the molecular mass MgSO4 by 2, the valence of the associated ionic species Mg2+ or SO^-. The equivalent masses of Mg2+ and SO4-would be Mg/2 and SO4/2, respectively. Also, in Equation (10.16), the equivalent mass of Mg(HCO3)2 is obtained by dividing the molecular mass Mg(HCO3)2 by 2, the valence of Mg2+ or the total number of valences of the associated species HCO-; similar calculations will hold for the associated species. The equivalent mass of the hardness and associated species in solution is equal to the molecular mass divided by the total number of valences of the positive or negative ions of the associated ionic species, irrespective of the coefficient.

The previous findings, however, cannot be generalized to the precipitant species or species other than the hardness and its associated ionic species. For example, in Equation (10.16), if the above findings were applied to the precipitant Ca(OH)2, its equivalent mass would be Ca(OH)2/2; however, this is not correct— the equivalent mass of Ca(OH)2 in this equation is 2Ca(OH)2/2. To conclude, the equivalent mass of a precipitant species or species other than the hardness and its associated species cannot be generalized as molecular mass divided by the total number of valences of the species but must be deduced from the chemical reaction.

For emphasis, we make the following summary: For the hardness ions or associated species, the equivalent mass is obtained by dividing the molecular mass by the total number of valences of the positive or negative charges of the species, irrespective of the coefficient; for all other species, the equivalent mass must be deduced from the balanced chemical reaction.

For convenience, the equations for chemical requirements, solids productions, fractional removals, and effluent quality are summarized in Tables 10.1 to 10.4.

Example 10.2 A raw water to be treated by the lime-soda process to the minimum hardness possible has the following characteristics: CO2 = 22.0 mg/L, Ca2+ = 80 mg/L, Mg2+ = 12.0 mg/L, Na+ = 46.0 mg/L, HCO- = 152.5 mg/L, and

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