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Acid-Base
Syllabus: Protolysis of water, pH, acid-base neutralization curves, Buffer action: Henderson-Hasselbalch equation. Regulation of pH by blood buffers. Determination of pH – Basic concept of indicators, principle of pH meter- hydrogen electrode and glass electrode.
Protolysis of Water Although many of the solvent properties of water can be explained in terms of the uncharged H 2O molecule, the small degree of ionization of water to hydrogen ions (H+^ ) and hydroxide ions (OH−) must also be taken into account. Like all reversible reactions, the ionization of water can be described by an equilibrium constant. When weak acids are dissolved in water, they contribute H+^ by ionizing; weak bases consume H+^ by becoming protonated. These processes are also governed by equilibrium constants. The total hydrogen ion concentration from all sources is experimentally measurable and is expressed as the pH of the solution. The degree of ionization of water at equilibrium is small; at 25 °C only about two of every 10 9 molecules in pure water are ionized at any instant. The equilibrium constant for the reversible ionization of water is [H+^ ] [OH−^ ] Keq = --------------- [H2O] In pure water at 25 0 C, the concentration of water is 55.5 M (grams of H2O in 1 L divided by its gram molecular weight: (1,000 g/L)/(18.015 g/mol)) and is essentially constant in relation to the very low concentrations of H+^ and OH−, namely, 1 X 10 −^7 M. Accordingly, we can substitute 55.5 M in the equilibrium constant expression to yield
[H+^ ] [OH−^ ] Keq = --------------- 55.5M which, on rearranging, becomes (55.5 M)( K eq) = [H +] [OH −] = K (^) w where K (^) w designates the product (55.5 M)( K eq), the ion product of water at 25 °C.
The value for K eq, determined by electrical-conductivity measurements of pure water, is 1.8 X 10 − (^16) M at 25 0 C. Substituting this value for K eq in the above equation gives the value of the ion product of
water: K (^) w = [H+] [OH −] = (55.5 M)( 1.8 X 10−^16 M) = 1.0 X 10 −^14 M^2 Thus the product [H+] [OH −] in aqueous solutions at 25 °C always equals 1.0 X 10 −^14 M^2. When there are exactly equal concentrations of H +^ and OH −, as in pure water, the solution is said to be at neutral pH. At
this pH, the concentration of H+^ and OH^ −^ can be calculated from the ion product of water as follows:
K (^) w = [H+^ ] [OH−] = [H +] 2
Solving for [H +] gives PS/ Physiology (H)/ Part I/ Paper I/Unit I- Biophysics/ Acid-Base Page
[H +] = √ K (^) w = √1.0 X 10 −^14 M^2
[H+^ ] = [OH−^ ] = 10−^7 M
As the ion product of water is constant, whenever [H+^ ] is greater than 1 X 10 −^7 M, [OH −] must become less than 1 X 10−^7 M, and vice versa. When [H +] is very high, as in a solution of hydrochloric acid, [OH−^ ] must be very low. From the ion product of water we can calculate [H +] if we know [OH −], and
vice versa. The pH Scale Designates the H +^ and OH^ −^ Concentrations The ion product of water, K w, is the basis for the pH scale. It is a convenient means of designating the concentration of H+^ (and thus of OH −) in any aqueous solution in the range between 1.0 M H +^ and 1. M OH −. The term pH is defined by the expression 1 pH= log-------- = − log [H +] [H +] The symbol p denotes “negative logarithm of.” For a precisely neutral solution at 25^0 C, in which the concentration of hydrogen ions is 1.0 X 10−^7 M, the pH can be calculated as follows:
1 pH= log--------------- = − log [1.0 X 10^7 ] 1.0 X 10 −^7
= log 1.0 + log 10^7
= 0+7 = 7 Solutions having a pH greater than 7 are alkaline or basic; the concentration of OH −^ is greater than that of H+^. Conversely, solutions having a pH less than 7 are acidic. Note that the pH scale is logarithmic, not arithmetic. To say that two solutions differ in pH by 1 pH unit means that one solution has ten times the H+^ concentration of the other, but it does not tell us the absolute magnitude of the difference.
pK (^) a of weak acids and bases Hydrochloric, sulfuric, and nitric acids, commonly called strong acids, are completely ionized in dilute aqueous solutions; the strong bases NaOH and KOH are also completely ionized. Of more interest to biochemists is the behavior of weak acids and bases—those not completely ionized when dissolved in water. These are common in biological systems and play important roles in metabolism and its regulation. The behavior of aqueous solutions of weak acids and bases is best understood if we first define some terms. Acids may be defined as proton donors and bases as proton acceptors. A proton donor and its corresponding proton acceptor make up a conjugate acid-base pair. Acetic acid (CH (^) 3COOH), a proton donor, and the acetate anion (CH3COO −), the corresponding proton acceptor, constitute a conjugate acid base pair, related by the reversible reaction
CH (^) 3COOH^ ⇌^ H+^ + CH3COO−
PS/ Physiology (H)/ Part I/ Paper I/Unit I- Biophysics/ Acid-Base Page
Fig 1. The titration curve of acetic acid. Fig 2. Comparison of the titration curves of three weak acids.
Fig 2 compares the titration curves of three weak acids with very different dissociation constants: acetic acid (p K a = 4.76); dihydrogen phosphate, H (^) 2PO 4 −^ (p K a = 6.86); and ammonium ion, NH^4 −^ (p K a = 9.25). Although the titration curves of these acids have the same shape, they are displaced along the pH axis because the three acids have different strengths. Acetic acid, with the highest K a (lowest p K a) of the three, is the strongest (loses its proton most readily); it is already half dissociated at pH 4.76. Dihydrogen phosphate loses a proton less readily, being half dissociated at pH 6.86. Ammonium ion is the weakest acid of the three and does not become half dissociated until pH 9.25. The most important point about the titration curve of a weak acid is that it shows graphically that a weak acid and its anion—a conjugate acid- base pair—can act as a buffer.
Buffers in the Biological system Cells and organisms maintain a specific and constant cytosolic pH, keeping biomolecules in their optimal ionic state, usually near pH 7. In multicellular organisms, the pH of extracellular fluids is also tightly regulated. Constancy of pH is achieved primarily by biological buffers: mixtures of weak acids and their conjugate bases. Buffers Are Mixtures of Weak Acids and Their Conjugate Bases: Buffers are aqueous systems that tend to resist changes in pH when small amounts of acid (H +) or base (OH −) are added. A buffer system consists of a weak acid (the proton donor) and its conjugate base (the proton acceptor). As an example, a mixture of equal concentrations of acetic acid and acetate ion is a buffer system. The pH of the acetate buffer system does change slightly when a small amount of H+^ or OH−^ is added, but this change is very small compared with the pH change that would result if the same amount of H +^ or OH −^ were added to pure water or to a solution of the salt of a strong acid and strong base, such as NaCl, which has no buffering power PS/ Physiology (H)/ Part I/ Paper I/Unit I- Biophysics/ Acid-Base Page
Whenever H +^ or OH−^ is added to a buffer, the result is a small change in the ratio of the relative concentrations of the weak acid and its anion and thus a small change in pH. The decrease in concentration of one component of the system is balanced exactly by an increase in the other. The sum of the buffer components does not change, only their ratio. Each conjugate acid-base pair has a characteristic pH zone in which it is an effective buffer. The H2PO 4 −^ / HPO 4 2 −^ pair has a p K a of 6.86 and thus can serve as an effective buffer system between
approximately pH 5.9 and pH 7.9; the NH 4 −^ /NH 3 pair, with a p K a of 9.25, can act as a buffer between approximately pH 8.3 and pH 10.3.
Relation between pH, pKa, and Buffer Concentration: The shape of the titration curve of any weak acid is described by the Henderson-Hasselbalch equation, which is important for understanding buffer action and acid-base balance in the blood and tissues of vertebrates. This equation is simply a useful way of restating the expression for the dissociation constant of an acid. For the dissociation of a weak acid HA into H+^ and A −, the Henderson-Hasselbalch equation can be derived as follows: [H +^ ] [A−^ ] K (^) a = ------------- [HA]
[HA] Or, [H+^ ] =^ K^ a ------------- [A−^ ]
Taking the negative logarithm of both sides [HA] −log [H+^ ] = −log Ka – log -------- [A −]
[HA] Or, pH = p K a – log -------- [A −]
[A −] Or, pH = p K a + log -------- [HA]
The above Henderson-Hasselbalch equation can be stated more generally: [proton acceptor] pH = p K a + log -------------------------- [proton donor]
Weak Acids or Bases Buffer Cells and Tissues against pH Changes: The intracellular and extracellular fluids of multicellular organisms have a characteristic and nearly constant pH. The organism’s first line of defense against changes in internal pH is provided by buffer systems. Principal buffers of extracellular and intracellular fluids are listed below.
PS/ Physiology (H)/ Part I/ Paper I/Unit I- Biophysics/ Acid-Base Page
[HA]
Or, pH = 6.8 + log [HPO 4 2 −^ ]/ [H^2 PO 4 −^ ] Or, pH = 6.8 + log 4 Or, pH = 7. The phosphate buffer has a far higher concentration in ICF than in ECF. Moreover, the pH of ICF (6.0-6.9) is closure to the pKa of the phosphate buffer, making it more effective buffering system in ICF.
Protein buffers: These are of considerable importance in the plasma and ICF. Many of these plasma proteins are acidic proteins with acidic isoelectric pH. So, at the blood pH of 7.4, these exist as anions, serve as conjugate bases (Pr−^ ) and may accept H+^ ions to form the corresponding conjugate acids (HPr). The cytoplasm of most cells contains high concentrations of proteins, which contain many amino acids with functional groups that are weak acids or weak bases. For example, the side chain of histidine has a p K a of 6.0; proteins containing histidine residues therefore buffer effectively near neutral pH. Nucleotides such as ATP, as well as many low molecular weight metabolites, contain ionizable groups that can contribute buffering power to the cytoplasm.
Fig 3. The amino acid histidine, a component of proteins, is a weak acid. The p K a of the protonated nitrogen of the side chain is 6.0.
Hemoglobin buffer: Deoxyhemoglobin (Hb−^ ) (hemoglobin not bound to oxygen) is a weaker acid (pK (^) a
8.18) and consequently possesses a much higher capacity than oxyhemoglobin (HbO 2 −) (pK (^) a 6.62) for accepting H+^ ion. On entering RBC, CO (^) 2, in presence of enzyme carbonic anhydrase, combines with water to form H (^) 2CO3. Most of this H (^) 2CO 3 dissociate into H +^ and HCO 3 –. H+^ ions liberated need
immediate buffering. Deoxyhemoglobinn (Hb −) acting as a buffer accepts the H +^ ion forming HHb.
PS/ Physiology (H)/ Part I/ Paper I/Unit I- Biophysics/ Acid-Base Page
Fig 4. The buffering action of hemoglobin.
Subsequently in lungs, HHb combines with O 2 to form HHbO (^) 2. As oxyhemoglobin is stronger acid with pKa 6.62, HHbO 2 dissociates into H+^ and HbO 2 −^. H+^ ion thus released is promptly neutralized by
HCO 3 –^ inside RBC to form H2O and CO 2 in presence of carbonic anhydrase. The latter diffuses out of the RBC and escape in alveolar air. In tissue level inside RBC: Carbonic anhydrase H2O + CO 2 H +^ + HCO 3 – Hb−^ + H+^ HHb (Carried to the lungs by venous blood)
In lungs inside RBC
HHb + O 2 HHbO (^2)
` H+^ + HbO 2 −^ (Carried to the tissue as arterial blood) HCO 3 – Carbonic anhydrase
`Alveolar air CO2+H (^) 2O
Glass electrode pH meter
Most often used pH electrodes are glass electrodes. Typical model is made of glass tube ended with small glass bubble. Inside of the electrode is usually filled with buffered solution of chlorides in which silver wire covered with silver chloride is immersed. pH of internal solution varies - for example it can be 1.0 (0.1M HCl) or 7.0 (different buffers used by different producers). PS/ Physiology (H)/ Part I/ Paper I/Unit I- Biophysics/ Acid-Base Page
