Chapter 15

Complex Acid/Base Systems

Polyfunctional acids and bases play important roles in many chemical and biological systems. The human body contains a complicated system of buffers within cells and within bodily fluids, such as human blood. Shown here is a scanning electron micrograph of red blood cells traveling through an artery. The pH of human blood is controlled to be within the range of 7.35 to 7.45, primarily by the carbonic acid-bicarbonate buffer system:

This chapter describes polyfunctional acid and base systems including buffer solutions. Calculations of pH and of titration curves are also described.

15A Mixtures of Strong and Weak Acids or Strong and Weak Bases • 산혼합물 또는 염기혼합물 조성 결정

① 강산 + 약산 혼합물 ② 강염기 + 약염기 혼합물

• 농도가 비슷하거나, Ka 또는 Kb가 <10-4 일 경우 각 혼합물 조성 결정

• 적정 초기: HCl이 약산의 해리를 억제시킴 → [A-] ≪ cHCl →[H3O+] = cHCl

• Ex. 15-1에서 사용된 approximation은 염산이 중화될 때 까지만 사용 →이 영역의 적정곡선은 0.1200M 강산만이 있을 때의 적정곡선과 같음

• First end point에 접근하면, Ex. 15-2에서와 같이 HA도 고려해야 함

• 첨가한 염기의 양과 처음 존재하는 HCl의 양이 같을 때 → 용액의 조성은 약산(HA)과 염(NaCl)이 녹아있는 용액과 동일 함 → NaCl은 pH에 영향을 미치지 않음 → 이후의 적정곡선은 HA의 적정곡선과 동일

Fig. 15-1

• 약산과 강산 혼합물의 적정곡선을 나타냄

• 적정곡선의 모양은 약산의 세기에 크게 영향 받음

• Ka가 상대적으로 클 경우(Curve A, B) →첫 번째 당량점에서의 pH 증가가 없거나 작음

• Ka가 매우 작을 경우 → 강산의 농도만 구함

• Ka가 중간크기(10-4<Ka<10-8) →두 개의 유용한 end point 가짐

15B Polyfunctional Acids and Bases

15B-1 The Phosphoric acid system

15B-2 The Carbon Dioxide Carbonic acid System

• Polyfunctional system의 pH는 Ch. 11의 systematic approach로 부터 계산 가능

• 연속되는 Ka 또는 Kb 값이 103배 이상 차이가 나면 단순화하는 가정 사용 가능

15C Buffer Solutions Involving Polyprotic Acids

Two buffer systems can be prepared from a weak dibasic acid and its salts. The first consists of free acid H2A and its conjugate base NaHA, and the second makes use of the acid NaHA and its conjugate base Na2A. The pH of the NaHA/Na2A system is higher than that of the H2A/NaHA system because the acid dissociation constant for HA2 is always less than that for H2A. Thus, for a buffer prepared from H2A and NaHA, the dissociation of HA─ to yield A2─ can usually be neglected so that the calculation is based only on the first dissociation.

• NaHA/Na2A 완충계

→2번째 해리가 주된 반응임

→HA- + H2O H2A + OH- 반응은 무시

→[H3O+]는 두 번째 해리상수로부터 단순한 완충용액에서 사용한 방법으로 구함

• Polybasic acid 혼합물로 구성된 대부분의 완충용액 pH → 주된 하나의 평형만이 존재한다고 가정하여 pH 계산

• 산 또는 염의 농도가 매우 낮거나 두 해리상수가 비슷할 경우→ 상당한 error발생

15D Calculation of the pH of Solutions of NaHA We have not yet considered how to calculate the pH of solutions of salts that have both acidic and basic properties, that is, salts that are amphiprotic. Such salts are formed during neutralization titrations of polyfunctional acids and bases. For example, when 1 mol of NaOH is added to a solution containing 1 mol of the acid H2A,1 mol of NaHA is formed. The pH of this solution is determined by two equilibria established between HA─ and water:

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15E Titration Curves for Polyfunctional Acids Compounds with two or more acidic functional groups yield multiple end points in a titration if the functional groups differ sufficiently in strength as acids. The computational techniques described in Chapter 14 permit construction of reasonably accurate theoretical titration curves for polyprotic acids if the ratio Ka1/Ka2 is somewhat greater than 103. If this ratio is smaller, the error becomes excessive, particularly in the region of the first equivalence point, and a more rigorous treatment of the equilibrium relationships is required. Figure 15-2 shows the titration curve for a diprotic acid H2A with dissociation constants of Ka1 = 1.00 x 10─3 and Ka2 = 1.00 x10─7. Because the Ka1/Ka2 ratio is significantly greater than 103, we can calculate this curve (except for the first equivalence point) using the techniques developed in Chapter 14 for simple monoprotic weak acids. Thus, to calculate the initial pH (point A), we treat the system as if it contained a single monoprotic acid with a dissociation constant of Ka1 = 1.00 x 10─3. 24

• H2A (Ka1=1.00ⅹ10-3, Ka2=1.00ⅹ10-7) 적정곡선

• Ka1/Ka2 > 103임 → simple monoprotic weak acid에 대해 적용한 Ch. 14 방법으로 curve를 계산 (first equivalence point는 제외)

• 각 point에서의 pH 계산

Point A: Ka1=1.00ⅹ10-3인 simple monoprotic weak acid

Point B: H2A/NaHA simple buffer solution

Point C: acidic salt of NaHA

Point D: HA-/Na2A buffer solution(Ka2 사용)

Point E: Na2A (Ka2=1.00ⅹ10-7인 약산의 짝염기)

Point F: excess NaOH만 고려

Molecular models of maleic acid, or (Z)-butenedioic acid (top), and fumaric acid, or (E)-butenedioic acid (bottom). These geometric isomers exhibit striking differences in both their physical and their chemical properties. Because the cis isomer (maleic acid) has both carboxyl groups on the same side of the molecule, the compound eliminates water to form cyclic maleic anhydride, which is a very reactive precursor widely used in plastics, dyes, pharmaceuticals, and agrichemicals. Fumaric acid, which is essential to animal and vegetable respiration, is used industrially as an antioxidant to synthesize resins and to fix colors in dyeing. It is interesting to compare the pKa values for the two acids; for fumaric acid, pKa1 = 3.05, and pKa2 = 4.49; for maleic acid, pKa1 = 1.89, and pKa2 = 6.23.