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An indicator of the efficiency of removal is that the concentration of phosphorus in solution must be the minimum. To find this phosphorus in solution, it is necessary to perform a phosphate (PO4) molar mass balance in solution using the above reactions. AlPO4(s) is a solid; thus, not in solution and will not participate in the balance. The other species, however, are in solution and contain the PO4 radical. They are [PO4-], [HPO4-], [H2PO-], and [H3PO4]. Note the PO4 embedded in the respective formulas; thus, the formulas are said to contain the PO4 radical. Because they contain this PO4 radical, they will participate in the molar mass balance. Let [spPO Al]

represent the total molar concentration of the phospate radical contained in all the species. Then, the molar mass balance on PO4 becomes

[ sPpo4AI ] = [ PO3-] + [ HPO2-] + [ H2PO-] + [ H3PO4 ]

The symbol Al] needs to be explained further, since this mode of subscripting is used in the unit processes part of this book. First, [ ] is read as "the concentration of." The symbol sp stands for species and its first subscript, PO4, stands for the type of species, which is the PO4 radical. The second subscript, Al, stands for the "reason" for the existence of the type of species. In other words, the use of alum (the Al) is the reason for the existence of the phosphate radical, the type of species.

Example 7 In removing the phosphorus using a ferric salt, the following series of reactions occurs:

Fe3+ + PO3- ^ FePO41 FePO4i ^ Fe3+ + PO3— PO4-+ H+ ^ HPO2-

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