Problem 2

Phosphoric acid is of great importance in the fertilizer industry; it and its salts are also used in metal treatment, food, detergent and toothpaste industries. (2.1) The p

K_a

values of the three successive dissociations of phosphoric acid at

25\ ^\circ\mathrm{C}

are p

K_{a1}

= 2.12, p

K_{a2}

= 7.21, p

K_{a3}

= 12.32. Write down the conjugate base of the dihydrogen phosphate ion and determine its p

K_b

value. (2.2) Small quantities of phosphoric acid impart the sour taste of soft drinks. A cola of density 1.00 g cm

^{-3}

contains 0.05 % by weight of

\ce{H3PO4}

. Determine the pH of the cola, ignoring the second and third dissociation steps and assuming the acidity arises only from phosphoric acid. (2.3)

1.00\times10^{-3}

M phosphoric acid is added to an aqueous soil suspension and the pH is found to be 7.00. Determine the fractional concentrations of all phosphate species present, assuming no soil component interacts with any phosphate species. (2.4) Zinc is an essential micronutrient absorbed only in water-soluble form. In soil water of pH 7.0, zinc phosphate is the only source of zinc and phosphate. Calculate

[\ce{Zn^{2+}}]

and

[\ce{PO4^{3-}}]

;

K_{sp}

\ce{Zn3(PO4)2}

9.1\times10^{-33}

Step 1 of 4: Conjugate base and its pKb

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\ce{H2PO4- + H2O <=> HPO4^{2-} + H3O+};\quad pK_b(\ce{HPO4^{2-}}) = 14 - pK_{a2} \;\text{but for}\ \ce{H2PO4-}\ \text{as acid: }\ pK_b\ \text{of conjugate base} = 14 - 7.21 = 6.79

Analysis

The conjugate base of $\ce{H2PO4-}$ is $\ce{HPO4^{2-}}$ . For the pair $\ce{H2PO4-/HPO4^{2-}}$ , $pK_{a2} + pK_b = pK_w = 14$ , hence $pK_b = 14 - 7.21 = 6.79$ .