Polyprotic Acid Titrations * Chemistry 102 Summary July 24 th Question: Sketch a generic curve for a diprotic acid titration with a strong base. Answer: Question: Consider the titration curve of 50.0 ml of 0.10 M carbonic acid (H2CO3) titrated by 0.10 M NaOH. Answer: H2CO3 is a diprotic acid since it has two acidic protons and the titration curve is basically two titration curves in one. Triprotic acids have three titration curves in one. We will only worry about calculating the ph at specific points: 1. The initial point (point A). 2. The halfway points to equivalence (points B and D) 3. The equivalence points (C and E) In order to calculate the ph at these points, we must be able to identify the major species present as the titration progresses. For the H2CO3 curve, lets first identify the major species present at the points AE and then discuss how to calculate the ph at each point. Question: Write out the stepwise Ka expressions for H2CO3. Answer: * Courtesy of Tom Hummel s Chemistry 102 Handouts
Point A: H2CO3 is the major species (no OH has been added). To calculate the ph we perform a weak acid problem. We assume that H2CO3 is the major contributor to the H + concentration. We ignore the H + contribution from Ka2 because the Ka s differ by at least 1000. We solve for ph using only the Ka1 reaction. Point B: As soon as some OH has been added to solution, some H2CO3 is neutralized into its conjugate base HCO3. A buffer solution containing a weak acid (H2CO3) and its conjugate base (HCO3 ) exists. At point B we have added enough OH to neutralize exactly one half of the original amount of H2CO3 present. At point B, [H2CO3] = [HCO3 ] so ph = pka1. Point C: As we add more OH, more H2CO3 is converted into HCO3 until we finally reach point C, where all the H2CO3 present initially is converted into its conjugate base HCO3. The major species present is HCO3. HCO3 can act as a weak acid and it can act like a weak base. HCO3 is an amphoteric species. It can act as an acid through the Ka2 reaction: (aq) CO 3 2 (aq) + H + (aq) K a2 = 5.6 x 10 11 HCO3 is also the conjugate base of a weak acid H2CO3. Thus, HCO3 is also a weak base. The weak base reaction is: (aq) + H 2 O H 2 CO 3 (aq) + OH (aq) K b = K W = 2.3 x 10 8 K a1 We have never seen this before. We will not derive this expression but to calculate the ph of an amphoteric species, we use the following equation: ph = pk a1 + pk a2 Point D: After the first equivalence point, the Ka2 reaction is used to determine ph. (aq) CO 3 2 (aq) + H + (aq) K a2 = 5.6 x 10 11 2
As more OH is added from point C, it reacts with the next best acid present, HCO3 (all of the H2CO3 has reacted). The neutralization reaction from point C is: (aq) + OH (aq) CO 3 2 (aq) + H 2 O (l) As OH is added past point C, it converts HCO3 into its conjugate base CO3 2. A buffer solution containing HCO3 and CO3 2 exists. At point D, exactly onehalf of the HCO3 present at point C has been converted into CO3 2. At point D, [HCO3 ] = [CO3 2 ]. Here, ph = pka2. Point E: At point E, we have reached the second equivalence point. We have added just enough OH past point C to convert all the HCO3 present into its conjugate base, CO3 2. CO3 2 is the major species present. To calculate the ph of a CO3 2 solution, we treat it as a typical weak base problem where we only worry about the following reaction: CO 3 2 (aq) + H 2 O (l) (aq) + OH (aq) K b = K W = 1.8 x 10 4 K a2 We ignore the OH contribution from the Kb reaction resulting from HCO3 because it has a value of 2.3 x 10 8 which is much less than that of CO3 2. (aq) + H 2 O H 2 CO 3 (aq) + OH (aq) K b = K W = 2.3 x 10 8 K a1 To calculate the ph at point E, we calculate the concentration of CO3 2 present, then perform a weak base calculation. Past point E in the titration curve, the ph is determined by the excess OH added. We will not concern ourselves with this calculation for polyprotic acid titrations.
Triprotic Acid Titration Question: Consider the titration of 100.0 ml of 0.10 M H3AsO4 by 0.10 M NaOH. For arsenic acid, Ka1 = 5.6 x 10 3, Ka2 = 1.7 x 10 7 and Ka3 = 4.0 x 10 12. Calculate the ph at the following volumes of OH added: (a) 0.0 ml (d) 150.0 ml (g) 300.0 ml (b) 50.0 ml (e) 200.0 ml (c) 100.0 ml (f) 250.0 ml First sketch the titration curve for a triprotic acid H3A, titrated by strong base.