Principles of Buffering
A buffer is a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. The two forms of the buffer are called the buffer pair. In Brønsted-Lowry nomenclature, for a weak acid, the acid form is called HA and is defined as the H+ donor. The base form is called A− and is defined as the H+ acceptor. Likewise, for a weak base, the H+ donor is called BH+ and the H+ acceptor is called B.
A buffered solution resists a change in pH. Thus, H+ can be added to or removed from a buffered solution, but the pH of that solution will change only minimally. For example, when H+ is added to a buffered solution containing a weak acid, it combines with the A− form of the buffer and converts it to the HA form. Conversely, when H+ is removed from a buffered solution (or OH− is added), H+ is released from the HA form of the buffer, converting it to the A− form.
The body fluids contain a large variety of buffers, which constitute an important first defense against changes in pH. Robert Pitts demonstrated this buffering capacity experimentally by injecting 150 mEq of H+ (as hydrochloric acid, HCl) into a dog whose total body water was 11.4 L. In a parallel experiment, Pitts added 150 mEq of H+ to 11.4 L of distilled water. In the dog, the addition of H+ caused the blood pH to decrease from 7.44 to 7.14—the dog was acidemic but alive. In the distilled water, addition of the same amount of H+ caused the pH to drop precipitously to 1.84, a value that would have been instantly fatal to the dog. Pitts concluded that the dog’s body fluids contained buffers that protected his pH from the addition of large amounts of H+. The added H+ combined with the A− form of these buffers, and a strong acid was converted to a weak acid. The change in the dog’s body fluid pH was minimized, although not totally prevented. The distilled water contained no buffers and had no such protective mechanisms.
The Henderson-Hasselbalch equation is used to calculate the pH of a buffered solution. This equation is derived from the behavior of weak acids (and bases) in solution, which is described by the kinetics of reversible reactions:
The forward reaction, the dissociation of HA into H+ and A−, is characterized by a rate constant, K1, and the reverse reaction is characterized by a rate constant, K2. When the rates of the forward and reverse reactions are exactly equal, there is a state of chemical equilibrium, in which there is no further net change in the concentration of HA or A−. As shown here, the law of mass action states that at chemical equilibrium,
The ratio of rate constants can be combined into a single constant, K, called the equilibrium constant, as follows:
Rearranging again to solve for [H+]:
To express [H+] as pH, take the negative log10 of both sides of the previous equation. Then,
Recall that −log [H+] equals pH, that −log K equals pK, and that minus log HA/A− equals plus log A−/HA. Thus, the final form of the Henderson-Hasselbalch equation is as follows:
= −log10 [H+] (pH units)
= −log10 K (pH units)
= Concentration of base form of buffer (mEq/L)
= Concentration of acid form of buffer (mEq/L)
Therefore, the pH of a buffered solution can be calculated with the following information: the pK of the buffer, the concentration of the base form of the buffer ([A−]), and the concentration of the acid form of the buffer ([HA]). Conversely, if the pH of the solution and the pK of the buffer are known, it is possible to calculate the relative concentrations of the A− and HA forms.
pK is a characteristic value for a buffer pair. What factor, or factors, determine its value? In the previous derivation, note that the equilibrium constant (K) is the ratio of the rate constant of the forward reaction divided by the rate constant of the reverse reaction. Therefore, strong acids such as HCl are more dissociated into H+ and A−, and they have high equilibrium constants (K) and low pKs (because pK is minus log10 of the equilibrium constant). On the other hand, weak acids such as H2CO3 are less dissociated and have low equilibrium constants and high pKs.
SAMPLE PROBLEM. The pK of the HPO4−2/H2PO4− buffer pair is 6.8. Answer two questions about this buffer: (1) At a blood pH of 7.4, what are the relative concentrations of the acid form and the base form of this buffer pair? (2) At what pH would the concentrations of the acid and base forms be equal?
SOLUTION. The acid form of this buffer is H2PO4−, and the base form is HPO4−2. The relative concentrations of the acid and base forms are set by the pH of the solution and the characteristic pK.
(1) Answering the first question: The relative concentrations of acid and base forms at pH 7.4 are calculated with the Henderson-Hasselbalch equation. (Hint: In the last step of the solution, take the antilog of both sides of the equation!)
Therefore, at pH 7.4, the concentration of the base form (HPO4−2) is approximately fourfold that of the acid form (H2PO4−).
(2) Answering the second question: The pH at which there would be equal concentrations of the acid and base forms can also be calculated from the Henderson-Hasselbalch equation. When the acid and base forms are in equal concentrations, HPO4−2/H2PO4− = 1.0.
The calculated pH equals the pK of the buffer. This important calculation demonstrates that when the pH of a solution equals the pK, the concentrations of the acid and base forms of the buffer are equal. As discussed later in the chapter, a buffer functions best when the pH of the solution is equal (or nearly equal) to the pK, precisely because the concentrations of the acid and base forms are equal, or nearly equal.
Titration curves are graphic representations of the Henderson-Hasselbalch equation. Figure 7-2 shows the titration curve of a hypothetical weak acid (HA) and its conjugate base (A−) in solution. As H+ is added or removed, the pH of the solution is measured.
Figure 7–2 Titration curve of a weak acid (HA) and its conjugate base (A−). When pH equals pK, there are equal concentrations of HA and A−.
As previously shown by the Henderson-Hasselbalch equation, the relative concentrations of HA and A− depend on the pH of the solution and the pK of the buffer. The pK of this hypothetical buffer is 6.5. At low (acidic) pH, the buffer exists primarily in the HA form. At high (alkaline) pH, the buffer exists primarily in the A− form. When the pH equals the pK, there are equal concentrations of HA and A−: Half of the buffer is in the HA form and half in the A− form.
A striking feature of the titration curve is its sigmoidal shape. In the linear portion of the curve, only small changes in pH occur when H+ is added or removed; the most effective buffering occurs in this range. The linear range of the curve extends 1.0 pH unit above and below the pK (pK ± 1.0). Therefore, the most effective physiologic buffers will have a pK within 1.0 pH unit of 7.4 (7.4 ± 1.0). Outside the effective buffering range, pH changes drastically when small amounts of H+ are added or removed. For this buffer, when the pH is lower than 5.5, the addition of H+ causes a large decrease in pH; when the pH is higher than 7.5, the removal of H+ causes a large increase in pH.
Extracellular Fluid Buffers
The major buffers of the ECF are bicarbonate and phosphate. For bicarbonate, the A− form is HCO3− and the HA form is CO2 (in equilibrium with H2CO3). For phosphate, the A− form is HPO4−2 and the HA form is H2PO4−. The titration curves of these buffers are shown in Figure 7-3.
Figure 7–3 Comparison of titration curves for H2PO4−/HPO4−2 and CO2/HCO3−. ECF, Extracellular fluid.
The most important extracellular buffer is HCO3−/CO2. It is utilized as the first line of defense when H+ is gained or lost from the body. The following characteristics account for the preeminence of HCO3−/CO2 as an ECF buffer: (1) The concentration of the A− form, HCO3−, is high at 24 mEq/L. (2) The pK of the HCO3−/CO2 buffer is 6.1, which is fairly close to the pH of ECF. (3) CO2, the acid form of the buffer, is volatile and can be expired by the lungs (see Fig. 7-3).
The function of the HCO3−/CO2 buffer is illustrated in the previous example of HCl injection into a dog. To understand this example, assume that ECF is a simple solution of NaHCO3, ignoring its other constituents. When HCl is added to ECF, H+ combines with some of the HCO3− to form H2CO3. Thus, a strong acid (HCl) is converted to a weak acid (H2CO3). H2CO3 then dissociates into CO2 and H2O, both of which are expired by the lungs. The pH of the dog’s blood decreases, but not as dramatically as if no buffer were available. The reactions are as follows:
The Henderson-Hasselbalch equation can be applied to the HCO3−/CO2 buffer. The base form (A−) is HCO3− and the acid form (HA) is H2CO3, which is in equilibrium with CO2. In the presence of carbonic anhydrase, most of the H2CO3 is present in the CO2 form (i.e., 400 CO2:1 H2CO3); thus, the H2CO3 concentration usually is so low that it is ignored.
The pH of arterial blood can be calculated with the Henderson-Hasselbalch equation by substituting the normal concentrations of HCO3− and CO2 and by knowing the pK. Note that because values of CO2usually are reported as partial pressures, PCO2 must be converted to CO2 concentration by multiplying by the solubility of CO2 in blood (0.03 mmol/L/mm Hg). The final form of the equation is as follows:
Substituting the following normal values, the pH of arterial blood can be calculated as follows:
The Henderson-Hasselbalch equation also can be represented on an acid-base map, which shows the relationships between PCO2, HCO3− concentration, and pH (Fig. 7-4). The lines radiating from the origin on the map are called the isohydric lines (meaning same H+ concentration or same pH); each isohydric line gives all of the combinations of PCO2 and HCO3− that yield the same value of pH. The ellipse in the center shows the normal values for arterial blood. Any point on the graph can be calculated by substituting the appropriate values into the Henderson-Hasselbalch equation. For example, the previous calculations show that a PCO2 of 40 mm Hg and an HCO3− concentration of 24 mEq/L yields a pH of 7.4. The acid-base map confirms that when the PCO2 is 40 mm Hg and the HCO3− concentration is 24 mEq/L, the pH is 7.4.
Figure 7–4 Acid-base map. The relationships shown are between arterial blood PCO2, [HCO3−], and pH. The ellipse in the center gives the range of normal values. (Modified from Cohen JJ, Kassirer JP: Acid/Base. Boston, Little, Brown, 1982.)
It is important to note that abnormal combinations of PCO2 and HCO3−concentration can yield normal (or nearly normal) values of pH. For example, the combination of a PCO2 of 60 mm Hg and an HCO3−concentration of 36 mEq/L also corresponds to a pH of 7.4, although both the HCO3− concentration and the PCO2 clearly are higher than normal. For another example, the combination of a PCO2 of 20 mm Hg and an HCO3− concentration of 12 mEq/L also corresponds to a pH of 7.4, although both the HCO3− concentration and the PCO2 are lower than normal. (This important principle underlies the processes of respiratory and renal compensation that attempt to normalize the pH when there is an acid-base disorder.)
The importance of the HCO3−/CO2 buffer system in protecting the pH can be illustrated by imagining that 12 mmol/L of HCl is added to ECF. The initial HCO3− concentration of ECF is 24 mmol/L. Then, 12 mmol/L of added H+ combines with 12 mmol/L of HCO3− to form 12 mmol/L of H2CO3, which is converted to 12 mmol/L of CO2 in the presence of carbonic anhydrase. After this buffering reaction occurs, the new HCO3− concentration will be 12 mmol/L instead of the original 24 mmol/L. The new CO2 concentration will be the original concentration of 1.2 mmol/L (i.e., 40 mm Hg × 0.03) plus the 12 mmol/L that is generated in the buffering reaction. Assuming for a moment that the additional CO2 generated cannot be expired by the lungs, the new pH will be
Clearly, a pH this low (6.06) would be fatal! There is, however, a second protective mechanism, respiratory compensation, which prevents the pH from falling to this fatally low value. Acidemia stimulates chemoreceptors in the carotid bodies that produce an immediate increase in the ventilation rate (hyperventilation): All of the excess CO2, plus more, is expired by the lungs. This response, called respiratory compensation, drives the PCO2 down to lower than normal values (e.g., to 24 mm Hg). Substituting these values in the Henderson-Hasselbalch equation, another pH can be calculated:
The combination of buffering by HCO3− and respiratory compensation (i.e., hyperventilation) results in an almost normal pH (normal = 7.4). Although both the HCO3− concentration and the PCO2 are severely reduced, the pH is nearly normal. Full restoration of acid-base balance depends on the kidneys. Eventually, by processes described later in this chapter, the kidneys secrete H+ and synthesize “new” HCO3− to replace the HCO3− that was consumed in buffering the added fixed H+.
Inorganic phosphate also serves as a buffer. Its titration curve can be compared with that for HCO3− (see Fig. 7-3). Recall that the pK for HCO3−/CO2 is 6.1, with the linear portion of the titration curve extending from pH 5.1 to 7.1; technically, the linear portion is outside the buffering range for a pH of 7.4. On the other hand, the pK of the HPO4−2/H2PO4− buffer is 6.8, with the linear portion of its curve extending from pH 5.8 to 7.8. It seems that inorganic phosphate would be a more important physiologic buffer than HCO3−, because its effective buffering range is closer to 7.4, the pH of blood. However, two features of the HCO3−/CO2 buffer make it the more effective buffer: (1) HCO3− is in much higher concentration (24 mmol/L) than phosphate (1 to 2 mmol/L). (2) The acid form of the HCO3−/CO2 buffer is CO2, which is volatile and can be expired by the lungs.
Intracellular Fluid Buffers
There are vast quantities of intracellular buffers, which include organic phosphates and proteins. To utilize these ICF buffers in acid-base disturbances, H+ first must cross the cell membrane by one of the following three mechanisms: (1) In conditions where there is an excess or a deficit of CO2, as in respiratory acid-base disturbances, CO2itself can cross the cell membranes. For example, in respiratory acidosis, there is excess CO2, which generates H+ that must be buffered. CO2 rapidly enters the cells, and the H+ it generates is buffered by intracellular buffers. (2) In conditions where there is an excess or a deficit of fixed acid, H+ can enter or leave the cell with an organic anion such as lactate. For example, in metabolic acidosis caused by increased levels of lactic acid, excess H+ is produced along with lactate and H+ and lactate enter the cells together, preserving electroneutrality. (3) In other cases of excess or deficit of fixed H+ in which there is no accompanying organic anion, H+ exchanges with K+ to preserve electroneutrality.
Although they are not present in ICF, plasma proteins also buffer H+. A relationship exists between plasma proteins, H+, and calcium (Ca2+), which results in changes in ionized Ca2+ concentration when there is an acid-base disturbance. (See Chapter 9, Fig. 9-34.) The mechanism is as follows: Negatively charged groups on plasma proteins (e.g., albumin) can bind either H+ or Ca2+. (Protein-binding of Ca2+ is extensive and accounts for 40% of total Ca2+.) In acidemia, there is an excess of H+ in blood. Because more H+ is bound to plasma proteins, less Ca2+ is bound, producing an increase in free Ca2+concentration. In alkalemia, there is a deficit of H+ in blood. Because less H+is bound to plasma proteins, more Ca2+ is bound, producing a decrease in free Ca2+ concentration (hypocalcemia). Symptoms of hypocalcemia commonly occur in respiratory alkalosis and include tingling, numbness, and tetany.
Organic phosphates in ICF include adenosine triphosphate (ATP), adenosine diphosphate (ADP), adenosine monophosphate (AMP), glucose-1-phosphate, and 2,3-diphosphoglycerate (2,3-DPG). H+ is buffered by the phosphate moiety of these organic molecules. The pKs for these organic phosphates range from 6.0 to 7.5, ideal for effective physiologic buffering.
Intracellular proteins serve as buffers because they contain a large number of acidic or basic groups such as −COOH/−COO− or −NH3+/−NH2. Of all the dissociable groups on proteins, those with a pK in the physiologic range are the imidazole group of histidine (pK 6.4 to 7.0) and the α amino groups (pK 7.4 to 7.9).
The most significant intracellular buffer is hemoglobin, which is present in high concentration inside red blood cells. Each hemoglobin molecule has a total of 36 histidine residues (9 on each of the 4 polypeptide chains). The pK of oxyhemoglobin is 6.7, which is in the range for effective physiologic buffering. Deoxyhemoglobin, however, is an even more effective buffer with a pK of 7.9. The change in the pK of hemoglobin when it releases oxygen (O2) has physiologic significance. As blood flows through the systemic capillaries, oxyhemoglobin releases O2 to the tissues and is converted to deoxyhemoglobin. At the same time, CO2 is added to systemic capillary blood from the tissues. This CO2 diffuses into the red blood cells and combines with H2O to form H2CO3. The H2CO3 then dissociates into H+ and HCO3−. The H+ generated is buffered by hemoglobin, which now is conveniently in its deoxygenated form. Deoxyhemoglobin certainly must be an excellent buffer for H+: The pH of venous blood is 7.37, which is only 0.03 pH units more acidic than the pH of arterial blood despite the addition of large amounts of acid as CO2.