AP Chemistry - Free Response Answer 38

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38.	The equations and constants for the dissociation of three different acids are given below. HCO₃^- º H⁺ + CO₃^-2 K_a = 4.2 x 10^-7 H₂PO₄^- º H⁺ + HPO₄^-2 K_a = 6.2 x 10^-8 HSO₄^- º H⁺ + SO₄^-2 K_a = 1.3 x 10^-2
	a.	From the systems above, identify the conjugate pair that is best for preparing a buffer with a pH of 7.2. Explain your choice.
		pK_a = - log K_a pK_{a HCO3 -} = - log 4.2 x 10^-7 = 6.38 pK_{a H2PO4 -} = - log 6.2 x 10^-8 = 7.21 pK_{a HSO4 -} = - log 1.3 x 10^-2 = 1.89 Pick as the acid in the acid-base conjugate pair, the species with the pK_a closest to the desired pH. H₂PO₄^- is the acid and HPO₄^-2 is the conjugate base. The conjugate base will have one less H⁺ than the acid.

	b.	Explain briefly how you would prepare the buffer solution described in (a) with the conjugate pair you have chosen.
		Because the desired pH is the same as the pK_a, the buffer solution should have equal concentrations of H₂PO₄^- and HPO₄^-2 . Higher concentrations create solutions with greater buffer capacities. If the desired pH was not the same as the pK_a, pick a concentration for one of the species, and solve for the other species using the pH to get the [H⁺]. H₂PO₄^- HPO₄^-2 + H⁺ [HPO₄^-2 ]] H⁺ ] K_a = ------------------------ [H₂PO₄^- ] K_a x [H₂PO₄^- ] ] H⁺ ] = ----------------------- equal concentration give pH = pK_a [HPO₄^-2 ]

	c.	If the concentrations of both the acid and the conjugate base you have chosen were doubled, how would the pH be affected? Explain how the capacity of the buffer is affected by this change in concentrations of acid and base.
		H₂PO₄^- HPO₄^-2 + H⁺ [HPO₄^-2 ]] H⁺ ] K_a = ------------------------ [H₂PO₄^- ] K_a x [H₂PO₄^- ] ] H⁺ ] = ----------------------- [HPO₄^-2 ] Doubling both concentrations would not change ratio of concentrations or [H⁺]. The pH would be unchanged. The buffer capacity would be doubled by doubling the concentrations. H₂PO₄^- reacts with any base added to form HPO₄^-2 . When the H₂PO₄^- is used up, the pH begins to change rapidly and the buffer capacity has been exceeded. Doubling the [H₂PO₄^- ] doubles the amount of base that can be added before this occurs. HPO₄^-2 reacts with any acid added to form H₂PO₄^- . When the HPO₄^- is used up, the pH begins to change rapidly and the buffer capacity has been exceeded. Doubling the [HPO₄^- ] doubles the amount of acid that can be added before this occurs.

	d.	Explain briefly how you could prepare the buffer solution in (a) if you had available the solid salt of only one member of the conjugate pair and solutions of a strong acid and a strong base.
		H₂PO₄^- + OH^- --> HPO₄^-2 i 2X X 0 /\ X X X f X 0 X If 2X moles of H₂PO₄^- are added to X moles of OH^- , the solution will end up with equal moles of H₂PO₄^- and HPO₄^-2 . This will create the same buffer solution as starting with equal moles of the two chemicals.