27-Acid-Base Buffers and Titrations

27-Acid-Base Buffers and Titrations - 5.111 Lecture 27...

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Unformatted text preview: 5.111 Lecture # 27. ACID-BASE BUFFERS AND TITRATIONS [Pages 445-466 from the “Chemical Principles” textbook, 4th edition, by Peter Atkins & Loretta Jones, Freeman, New York, 2008] Controlling pH is critical for all living organisms (and in many other areas). What’s the chemical mechanism of doing that? Buffer: An aqueous solution containing both a weak acid and its conjugate base that can resist a change in pH by neutralizing an added acid or an added base. Let’s add a drop of a strong acid (e.g., 1 M HCl) or a strong base (e.g., 1 M NaOH) to pure water. What will happen to the pH? Now let’s replace pure water in the foregoing scenario with an aqueous solution containing a mixture of a weak acid, CH3COOH, and its conjugate base, CH3COO'. What will happen to the pH in this case? Consider the following proton-transfer reactions: H3O+ (aq) + CH3COO' (aq) <—> CH3COOH (aq) + H20 (1) (1) and CH3COOH (aq) + OH' (aq) <—> CH3COO‘ (aq) + H20 (1) (2) These equations are the reverse of the dissociation of the acid CH3COOH and the base CH3COO‘. Therefore, the equilibrium constants for reactions (1) and (2) are (Kay1 = (1.8 x 10‘5 M)"1 = 0.56 x 105 M'1 and (Kb)'1 = (5.8 x 10'10 M)‘1 = 0.17 x 1010 M'l, respectively. Consequences of such large equilibrium constants — [Slide 27 .1]. Stabilization of the pH by providing both a sink and a source of protons — [Slide 27.2]. How does one select a suitable buffer? Consider an equimolar mixture of a weak acid HA and its conjugate base A‘ dissolved in water: HA (21(1) + H20 (1) H I130+ (m) + A" (N) (3) Since Ka =4 [H30+] [A']/ [HA], when [HA] = [A'] then Ka = [H3O+] and hence pKa = pH. Analogous reasoning for a base buffer (as opposed to an acid buffer, as above) in selecting a suitable weak base (B) and its conjugate acid (HB+). In general, the pH of a buffer solution (roughly) equals the pKa 0f the weak acid component when the acid and base have the same concentrations. Importance of buffered solutions. How to quickly estimate their pH values even when the acid and conjugate base concentrations are not the same? Rearrange Ka = [H3O+][A]/[HA] into [H3O+] = Ka[HA]/[A']. Hence PH = pKa + 10g([A']/[HAD Note that the values of [A'] and [HA] in equation (4) are the equilibrium molarities, not the initial ones. However, since HA is a weak acid and A' is a weak base, [HA]equilibrium 3 [HA] initial = [HAlo and [Ajequilibrium z [A-linitial = [A10 As a result of this approximation, we obtain the Henderson-Hasselbalch equation: 23 302 I 8.3 .822 pH = pKa + log([base]0/[acid]o) (4) Note that the Henderson-Hasselbalch equation is valid only when (i) the Ka value for the acid in the conjugate acid-base pair is small (i.e., < 10'3 M), and (ii) the [baseL/[acid]0 ratio is between ~0.l and ~10. In addition to resisting changes in the pH upon strong acid or base additions, buffers also do that upon dilutions with solvent (water). Why? The pH of human blood is 7.35 to 7.45. The body uses primarily the H2CO3/ HCOg' buffer system. Buffer capacity — The maximum amount of acid or base than can be added before the bufi’er loses its ability to resist large changes in pH. The capacity of a buffer is determined by its (a) concentration and (b) pH versus the pKa of the buffer’s weak acid. Acid—B ase Titrations Analfles and titrants. Volumetric analysis. pH curves. Strong acid—strong base titrations (i) Strong acid (e. g., HCl) is added to a strong base (e. g., NaOH) — [Slide 27.3]. Stoichiometric (or equivalence) point S in the graph (pH = 7). Sudden drop in the pH at point S. 3.5 .833 22.. B we:_o> on 8 2 o S 1 J O u 6 e D. P O What’s point A in the graph? How to calculate other points (e. g., B, C, D, and E) in the graph? (ii) Strong base is added to a strong acid — [Slide 27.4]. The pH curve is the mirror image of that in (i). Weak acid—strong base titrations For example, let’s titrate CH3COOH (aq) with NaOH (aq) —— [Slide 27.5]. Note that the stoichiometric point S is _n_o_t at pH = 7. Why? Consider the titration reaction: CHgCOOH (aq) + NaOH (aq) <—-> CH3COONa (aq) + H20 (1) Since Na+ has no effect on the pH and CH3COO' is a base, the pH at point S will be > 7. Another usefial feature of this titration curve is that it can be used to experimentally determine the pKa value — [Slide 27.6] ~— as the pH half way to the stoichiometric point. Similar analysis reveals that when a weak base is titrated with a strong acid —— [Slide 27 .7] —- (i) the pH at the stoichiometric point is < 7, and (ii) the pr value can be determined (from pr = pKW — pKa). Polyprotic acid titrations For example, H3PO4 — [Slide 27.8]. Distinctive feature of such titrations compared to those of monoprotic acids (as above): there are as many stoichiometric points as there are acidic hydrogen atoms. Estimating the pH at any point in the titration curve by 3.5 vat—um gas “.0 wE:_o> om ON 0—. o S 1.. J 0 u 6 a- D. s a O 0—. NF .1. 3:: guns wann— wc wE:_o> on 2 - 2 o S 1 J O u 6 q a s a «.035 mass h3 wE:_o> All Eva gum; *o cows—cm *0 In ......... All Run :33 *0 aka saugod agnaluogqagms . All FEES—Om u-Mm *0 In. aseq Buons 5 Mod amawogqfims o; Rem JIEH ................... ,. .................. Allfimmn mcobmvucmhzuuo In 3.5 .328 .2: .o 8.3.5 on ON 0 —. o n o 6—. ppe Buons NF 3. 36.3 9.8. *0 082.5 mam Nn—m Pam - 0.3.: 0%. 2.. 2. N -Neonirwonm : We . - on.N : nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn considering the main species in solution and the proton transfer equilibrium that determines the pH. Acid—Base 19H) Indicators A water-soluble organic dye whose color depends on the pH. The sudden change in the pH that occurs at the stoichiometric of a titration is signaled by a sharp change in color of the dye as it responds to the pH. An acid—base indicator (In) is a weak acid Whose acid form (HIn) has one color and conjugate base (In') another. Therefore, HIn (aq) + H20 (1) e» H30+ (aq) + In' (aq) (5) and , Kin = [H30+][1n']/[H1n] At the end point of an indicator, [1n] = [HIn] and hence, substituting this equality into equation (5), one obtains that the color change occurs when pH PKIn In reality, the color starts changing noticeably ~l pH unit before pKIn and is essentially complete ~l pH unit after pKIn. Common acid—base indicators and their pKIn values — [Slide 27.9]. An acid-base indicator should be chosen so that its end point is close to the stoichiometric point of the titration — [Slide 27 .10]. .3200 RES 2: :0 020808330 0:038? w 3:0 20 Emfl 0:0 00 030% £50: 33 :00 20“ 0:0 :0 30:00 22; I I 28% m: v.2 8 0.: we 53% l D we a: OS 9 2: 32:; m 26:“; 33% D D 0103 Tm 0:: 00 N.m 30:00:00 5305:3000an I _III_ 33 3w 0d 8 3 as? 33 65% I D :00 m. \1 0.x 00 Wm 30:0» :00 300:: I D 033 H.\. Wm. 00 06 30:0» 053 38350803 I I 2.3 3 3w 9 ca 02 2:5: D I 30:03 o.w ed 00 m6 :2 :8 TESS I D 053 5+ Tm 00 Wm 30:0» 59% 38.80805 I D 03: QM 0+ 00 o.m 30:03 003 30230805 D I 30:03 «am TV 00 N.m :8 umcwuo TEES _III_ I 30:0» \14 Wm 00 NA :8 0:3 :08?“ 8.8: 83 :0 0200 EM“ owuanu 00:00 :0 0952 In 800m 300 :0 00—00 088%:— +.8m§:U 00—00 088%:— n.— — HES. tut—gm mama .5 Sun *0 oE=_o> o mac—20 .3qu 3&2. mach: utquoExcum A 522.2222: {.33 mrobm Eum ocbm ...
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