Chemistry Labs

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 pKaK_a values of the three successive dissociations of phosphoric acid at 25 ∘C25\ ^\circ\mathrm{C} are pKa1K_{a1} = 2.12, pKa2K_{a2} = 7.21, pKa3K_{a3} = 12.32. Write down the conjugate base of the dihydrogen phosphate ion and determine its pKbK_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^{-3} contains 0.05 % by weight of HX3POX4\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) 1.00×10−31.00\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 [ZnX2+][\ce{Zn^{2+}}] and [POX4X3−][\ce{PO4^{3-}}]; KspK_{sp} of ZnX3(POX4)X2\ce{Zn3(PO4)2} is 9.1×10−339.1\times10^{-33}.
Step 4 of 4: Solubility with speciation
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Ksp=(3S)3 (2S f3)2=9.1×10−33 ⇒ S=3.0×10−5 M; [ZnX2+]=9×10−5 M, [POX4X3−]=1.1×10−10 MK_{sp} = (3S)^3\,(2S\,f_3)^2 = 9.1\times10^{-33}\ \Rightarrow\ S = 3.0\times10^{-5}\ \text{M};\ [\ce{Zn^{2+}}] = 9\times10^{-5}\ \text{M},\ [\ce{PO4^{3-}}] = 1.1\times10^{-10}\ \text{M}
Analysis

If the molar solubility of ZnX3(POX4)X2\ce{Zn3(PO4)2} is SS, then [ZnX2+]=3S[\ce{Zn^{2+}}] = 3S and the total phosphate is 2S2S, of which only the fraction f3=1.83×10−6f_3 = 1.83\times10^{-6} is free POX4X3−\ce{PO4^{3-}} at pH 7. Solving Ksp=(3S)3(2Sf3)2K_{sp} = (3S)^3(2S f_3)^2 gives S=3.0×10−5S = 3.0\times10^{-5} M, hence [ZnX2+]=9×10−5[\ce{Zn^{2+}}] = 9\times10^{-5} M and [POX4X3−]=1.1×10−10[\ce{PO4^{3-}}] = 1.1\times10^{-10} M.

Common pitfall. Using the total phosphate instead of the free POX4X3−\ce{PO4^{3-}} fraction in KspK_{sp} underestimates the solubility by orders of magnitude.