## Po4 H hpo2

Let sp p^ Al represent the species in solution containing the PO4 species of the orthophosphates, using alum as the precipitant. Therefore,

[ spPOAl ] = [ PO3-] + [ HPO2-] + [ H2PO-] + [ H3PO4 ] (14.5)

Express Equation (14.5) in terms of [ PO33-] using Eqs. (14.2) through (14.4). This will enable [ spP^Al ] to be expressed in terms of [Al3+] using Equation (14.1) and Kjp,AlPO . Proceed as follows:

7hpo4 7hpo4k hpo4 7hpo4k hpo4

m pn-1 = {H2PO-} = {HPO4-}{H+} = rPo4yH[POU[H+f [ h2po4 ] = — - — k = Y K K ( )

{ h2po-}{ H+} 7po47^[p03-][h+]3 [ H3PO4 ] = {H3PO4} = 1 2„4J1 j = k-4-h---- (14.8)

— H.PO. — hpo — hpo — HPO, n3 rw4 — n3 rw4— n2 4— nrw4

Equations (14.6) through (14.8) may now be substituted into Equation (14.5) to produce n r™3-n YPO Yh[P°31 [H+] Yp°4Yh[P°31 [H+]2 [SPPOM] = [PO4 ] + '

7hpo4—hpo4 Yh2po4kh2po4khpo4

KHPO K HPO K H

But, from Equation (14.1), [ PO4"] = { PO3-}/Ypo4 = -Sp,aipo4/Ypo4 { Al3+} = KspMpo4 / Ypo,YAl[Al3+]. Substituting,

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