Acid-Base Physiology

pH values vary enormously among different intracellular and extracellular compartments

According to Brønsted's definition, an acid N28-1 is any chemical substance (e.g., CH ₃ COOH, ) that can donate an H ⁺ . A base is any chemical substance (e.g., CH ₃ COO ⁻ , NH ₃ ) that can accept an H ⁺ . The term alkali can be used interchangeably with base.

[H ⁺ ] varies over a large range in biological solutions, from >100 mM in gastric secretions to <10 nM in pancreatic secretions. In 1909, the chemist Sørensen introduced the pH scale in an effort to simplify the notation in experiments in which he was examining the influence of [H ⁺ ] on enzymatic reactions. He based the pH scale on powers of 10: N28-2

Thus, when [H ⁺ ] is 10 ⁻⁷ M, the pH is 7.0. The higher the [H ⁺ ], the lower the pH ( Table 28-1 ). It is worth remembering that a 10-fold change in [H ⁺ ] corresponds to a pH shift of 1, whereas a 2-fold change in [H ⁺ ] corresponds to a pH shift of ~0.3.

Even small changes in pH can have substantial physiological consequences because most biologically important molecules contain chemical groups that can either donate an H ⁺ (e.g., R–COOH → R–COO ⁻ + H ⁺ ) and thereby act as a weak acid, or accept an H ⁺ (e.g., R–NH ₂ + H ⁺ → ) and thus behave as a weak base. To the extent that these groups donate or accept protons, a pH shift causes a change in net electrical charge (or valence) that can, in turn, alter biological activity either directly (e.g., by altering the affinity for a charged ligand) or indirectly (e.g., by altering molecular conformation).

pH-sensitive molecules include a variety of enzymes, receptors and their ligands, ion channels, transporters, and structural proteins. For most proteins, pH sensitivity is modest. The activity of the Na-K pump (see pp. 115–117 ), for example, falls by about half when the pH shifts by ~1 pH unit from the optimum pH, which is near the resting pH of the typical cell. However, the activity of phosphofructokinase, a key glycolytic enzyme (see p. 1176 ), falls by ~90% when pH falls by only 0.1. The overall impact of pH changes on cellular processes can be impressive. For example, cell proliferation in response to mitogenic activation is maximal at the normal, resting intracellular pH but may fall as much as 85% when intracellular pH falls by only 0.4.

Table 28-2 lists the pH values in several body fluids. Because the pH of neutral water at 37°C is 6.81, most major body compartments are alkaline.

Buffers minimize the size of the pH changes produced by adding acid or alkali to a solution

A buffer is any substance that reversibly consumes or releases H ⁺ . In this way, buffers help to stabilize pH. Buffers do not prevent pH changes, they only help to minimize them.

Consider a hypothetical buffer B for which the protonated form HB ⁽ⁿ⁺¹⁾ , with a valence of n + 1, is in equilibrium with its deprotonated form B ⁽ⁿ⁾ , which has the valence of n:

Here, HB ⁽ⁿ⁺¹⁾ is a weak acid because it does not fully dissociate; B ⁽ⁿ⁾ is its conjugate weak base. Conversely, B ⁽ⁿ⁾ is a weak base and HB ⁽ⁿ⁺¹⁾ is its conjugate weak acid. The total buffer concentration, [TB], is the sum of the concentrations of the protonated and unprotonated forms:

The valence of the acidic (i.e., protonated) form can be positive, zero, or negative:

In these examples,
(ammonium), H ₂ CO ₃ (carbonic acid), and
(“monobasic” inorganic phosphate) are all weak acids, whereas NH ₃ (ammonia),
(bicarbonate), and
(“dibasic” inorganic phosphate) are the respective conjugate weak bases. Each buffer reaction is governed by a dissociation constant, K

If we add to a physiological solution a small amount of HCl—which is a strong acid because it fully dissociates—the buffers in the solution consume almost all added H ⁺ :

For each H ⁺ buffered, one B ⁽ⁿ⁾ is consumed. The tiny amount of H ⁺ that is not buffered remains free in solution and is responsible for a decrease in pH.

If we instead titrate this same solution with a strong base such as NaOH, H ⁺ derived from HB ⁽ⁿ⁺¹⁾ neutralizes almost all the added OH ⁻ :

For each OH ⁻ buffered, one B ⁽ⁿ⁾ is formed. The tiny amount of added OH ⁻ that is not neutralized by the buffer equilibrates with H ⁺ and H ₂ O and is responsible for an increase in pH.
N28-3

A useful measure of the strength of a buffer is its buffering power (β), which is the number of moles of strong base (e.g., NaOH) that one must add to a liter of solution to increase pH by 1 pH unit. This value is equiv­alent to the amount of strong acid (e.g., HCl) that one must add to decrease the pH by 1 pH unit. Thus, buffering power is

In the absence of , the buffering power of whole blood (which contains erythrocytes, leukocytes, and platelets) is ~25 mM/pH unit. This value is known as the buffering power ( ). In other words, we would have to add 25 mmol of NaOH to a liter of whole blood to increase the pH by 1 unit, assuming that β is constant over this wide pH range. For blood plasma, which lacks the cellular elements of whole blood, is only ~5 mM/pH unit, which means that only about one fifth as much strong base would be needed to produce the same pH increase.

According to the Henderson-Hasselbalch equation, pH depends on the ratio [CO ₂ ]/[ ]

The most important physiological buffer pair is CO ₂ and . The impressive strength of this buffer pair is due to the volatility of CO ₂ , which allows the lungs to maintain stable CO ₂ concentrations in the blood plasma despite ongoing metabolic and buffer reactions that produce or consume CO ₂ . Imagine that a beaker contains an aqueous solution of 145 mM NaCl (pH = 6.81), but no buffers. We now expose this solution to an atmosphere containing CO ₂ ( Fig. 28-1 ). The concentration of dissolved CO ₂ ([CO ₂ ] _dis ) is governed by Henry's law (see Box 26-2 ):

At the temperature (37°C) and ionic strength of mammalian blood plasma, the solubility coefficient, s, is ~0.03 mM/mm Hg. Because the alveolar air with which arterial blood equilibrates has a of ~40 mm Hg, or torr, [CO ₂ ] _dis in arterial blood is

So far, the entry of CO ₂ from the atmosphere into the aqueous solution has had no effect on pH. The reason is that we have neither generated nor consumed H ⁺ . CO ₂ itself is neither an acid nor a base. If we were considering dissolved N ₂ or O ₂ , our analysis would end here because these gases do not further interact with simple aqueous solutions. The aqueous chemistry of CO ₂ , however, is more complicated, because CO ₂ reacts with the solvent (i.e., H ₂ O) to form carbonic acid:

This CO ₂ hydration reaction is very slow. N28-4 In fact, it is far too slow to meet certain physiological needs. The enzyme carbonic anhydrase, N18-3 present in erythrocytes and elsewhere, catalyzes a reaction that effectively bypasses this slow hydration reaction. Carbonic acid is a weak acid that rapidly dissociates into H ⁺ and :

N28-4

Out-of-Equilibrium
Solutions

As described on page 629 , adding CO ₂ to an aqueous solution initiates a series of two reactions that, in the end, produce and protons:

In the absence of carbonic anhydrase (CA), the first reaction—the hydration of CO ₂ to form carbonic acid—is extremely slow. The second is extremely fast. At equilibrium, the overall rate of the two forward reactions must be the same as the overall rate of the reverse reactions:

The first of these reverse reactions is extremely rapid, whereas the second—the dehydration of H ₂ CO ₃ to form CO ₂ and water—is extremely slow in the absence of CA. As noted in the text, we can treat the system as if only one reaction were involved:

Moreover, we can describe this pseudoreaction by a single equilibrium constant. As shown by Equation 28-15 , we can describe the equilibrium condition in logarithmic form by the following equation:

In other words, considering only equilibrium conditions, it is impossible to change pH or [ ] or [CO ₂ ] one at a time. If we change one of the three parameters (e.g., pH), we must change at least one of the other two (i.e., [ ] or [CO ₂ ]). Unfortunately, there are many cases in which the addition of CO ₂ and markedly enhances some process. For example, at identical values of intracellular pH, the activation of quiescent cells by mitogens is far more robust in the presence than in the absence of the physiological buffer. Which buffer component is critical in this case, CO ₂ or ? There are also many cases in which a stress such as respiratory acidosis or metabolic acidosis triggers a particular response. For example, respiratory acidosis stimulates reabsorption by the kidney—a metabolic compensation to a respiratory acidosis, as discussed beginning on pages 641–642 in the text. Again, we can ask which altered parameter signals the kidney to increase its reabsorption of , the rise in [CO ₂ ] or the fall in pH?

In the 1990s, the laboratory of Walter Boron realized that it could exploit the slow equilibrium CO ₂ + H ₂ O ⇄ H ₂ CO ₃ to create solutions that are temporarily out of equilibrium. eFigure 28-1 A illustrates how one can make an out-of-equilibrium (OOE) “pure” CO ₂ solution that contains a physiological level of CO ₂ , has a physiological pH, but contains virtually no . The approach is to use a dual syringe pump to rapidly mix the contents of two syringes, each flowing at the same rate. One syringe contains a double dose of CO ₂ (e.g., 10% CO ₂ ) at a pH that is so low (e.g., pH 5.40) that, given a p K of ~6.1, very little is present. The other syringe contains a well-buffered, relatively alkaline solution that contains no CO ₂ or . The pH of this second solution is chosen so that at the instant of mixing at the T connection, the solution has a pH of 7.40. Of course, the [CO ₂ ] after mixing is 5% (which corresponds to a of ~37 mm Hg), and the [ ] is virtually zero. The solutions flow so rapidly that they reach the cell of interest before any significant re-equilibration of the CO ₂ and . Moreover, a suction device continuously removes the solution. As a result, the cells are continuously exposed to a freshly generated OOE solution.

eFigure 28-1 B illustrates how one could make the opposite solution—a “pure” solution that has a physiological [ ] and pH but virtually no [CO ₂ ]. The OOE approach can be used to make solutions with virtually any combination of [CO ₂ ], [ ], and pH—at least for moderate pH values. At extremely alkaline pH values, the reaction CO ₂ + OH ⁻ → generates so fast that it effectively short-circuits the OOE approach. Conversely, at extremely acid pH values, the rapid reaction H ⁺ + ⇄ H ₂ CO ₃ creates relatively high levels of H ₂ CO ₃ so that even the uncatalyzed reaction H ₂ CO ₃ → CO ₂ + H ₂ O is high enough to short-circuit the OOE approach. Nevertheless, at almost any pH of interest to physiologists, OOE technology allows one to change [CO ₂ ], [ ], and pH one at a time.

Work on renal proximal tubules with OOE solutions has shown that proximal tubules have the ability to sense rapid shifts in the CO ₂ concentration of the basolateral (i.e., blood-side) solution that surrounds the outside of the tubule. This work suggests that the tubule has a sensor for CO ₂ that is independent of any changes in pH or . The tubule uses this CO ₂ -sensing mechanism in its response to respiratory acidosis (see pp. 637–638 ). This metabolic compensation involves a rapid increase in the rate at which it transports from the tubule lumen to the blood, and thus a partial correction of the acidosis.

Work on neurons cultured from the hippocampus suggests that certain neurons can detect rapid decreases in the extracellular concentration ( ), independent of any changes in pH _o or [CO ₂ ] _o . The cell may use this detection system to stabilize intracellular pH (pH _i ) during extracellular metabolic acidosis, which would otherwise lower pH _i .

References

• Ganz MB, Boyarsky G, Sterzel RB, et. al.: Arginine vasopressin enhances pH _i regulation in the presence of
  by stimulating three acid–base transport systems. Nature 1989; 337: pp. 648-651.
• Ganz MB, Perfetto MC, Boron WF: Effects of mitogens and other agents on mesangial cell proliferation, pH and Ca ² . Am J Physiol 1990; 259: pp. F269-F278.
• Zhao J, Hogan EM, Bevensee MO, et. al.: Out-of-equilibrium
  solutions and their use in characterizing a novel K/HCO ₃ cotransporter. Nature 1995; 374: pp. 636-639.
• Zhao J, Zhou Y, Boron WF: Effect of isolated removal of either basolateral
  or basolateral CO ₂ on
  reabsorption by rabbit S2 proximal tubule. Am J Physiol Renal Physiol 2003; 285: pp. F359-F369.

This dissociation reaction is the first point at which pH falls. Note that the formation of (the conjugate weak base of H ₂ CO ₃ ) necessarily accompanies the formation of H ⁺ in a stoichiometry of 1 : 1. The observation that pH decreases, even though the above reaction produces the weak base , is sometimes confusing. A safe way to reason through such an apparent paradox is to focus always on the fate of the proton: if the reaction forms H ⁺ , pH falls. Thus, even though the dissociation of H ₂ CO ₃ leads to generation of a weak base, pH falls because H ⁺ forms along with the weak base.

Unlike the hydration of CO ₂ , the dissociation of H ₂ CO ₃ is extremely fast. Thus, in the absence of carbonic anhydrase, the slow CO ₂ hydration reaction limits the speed at which increased [CO ₂ ] _dis leads to the production of H ⁺ . can accept a proton to form its conjugate weak acid (i.e., H ₂ CO ₃ ) or release a second proton to form its conjugate weak base (i.e., ). Because this latter reaction generally is of only minor physiological significance for buffering in mammals, we will not discuss it further.

We may treat the hydration and dissociation reactions that occur when we expose water to CO ₂ as if only one reaction were involved:

Moreover, we can define a dissociation constant for this pseudoequilibrium:

In logarithmic form, this equation becomes
N28-5

N28-5

Derivation of the Henderson-Hasselbalch Equation

As shown in Equation 28-13 ,

We can define a dissociation constant for this pseudoequilibrium:

Factoring out [H ₂ O], we can define an apparent equilibrium constant:

The equation immediately above is Equation 28-14 in the text. K at 37°C is ~10 ^−6.1 M or 10 ^−3.1 mM. Taking the log (to the base 10) of each side of this equation, and remembering that log( a × b ) = log( a ) + log( b ), we have

Remembering that log [H ⁺ ] ≡ −pH and log K ≡ −p K, we may insert these expressions into Equation NE 28-7 and rearrange to obtain

This expression is the same as Equation 28-15 in the text. Finally, we may express [CO ₂ ] in terms of , recalling from Henry's law that [CO ₂ ] = s × :

This is the Henderson-Hasselbalch equation, a logarithmic restatement of the equilibrium in Equation NE 28-5 above.

Finally, we may express [CO ₂ ] in terms of
, recalling from Henry's law that [CO ₂ ] = s ·
:

This is the Henderson-Hasselbalch equation, a loga­rithmic restatement of the equilibrium in Equation 28-14 . Its central message is that pH depends not on [ ] or per se, but on their ratio. Human arterial blood has a of ~40 mm Hg and an [ ] of ~24 mM. If we assume that the p K governing the equilibrium is 6.1 at 37°C, then

Thus, the Henderson-Hasselbalch equation correctly predicts the normal pH of arterial blood.

has a far higher buffering power in an open than in a closed system

The buffering power of a buffer pair such as depends on three factors:

• 1

  Total concentration of the buffer pair, [TB]. Other things being equal, β is proportional to [TB].

• 2

  The pH of the solution. The precise dependence on pH will become clear below.

• 3

  Whether the system is open or closed. That is, can one member of the buffer pair equilibrate between the “system” (the solution in which the buffer is dissolved) and the “environment” (everything else)?

If neither member of the buffer pair can enter or leave the system, then HB ⁽ⁿ⁺¹⁾ can become B ⁽ⁿ⁾ , and vice versa, but [TB] is fixed. This is a closed system. An example of a closed-system buffer is inorganic phosphate in a beaker of water, or a titratable group on a protein in blood plasma. In a closed system, the buffering power of a buffer pair is N28-6

N28-6

Derivation of Expressions for Buffering Power in Closed and Open Systems

How does buffering power, in either a closed or open system, depend on pH?

Closed System

We start with a restatement of Equation 28-8 , in which we define buffering power as the amount of strong base that we need to add (per liter of solution) in order to increase the pH by 1 pH unit. In differential form, this definition becomes the following:

Second, because the change in the concentration of the unprotonated form of the buffer, [B ⁽ⁿ⁾ ], is very nearly the same as the amount of strong base added (see Equation 28-7 ), Equation NE 28-10 becomes

The third step is to combine Equation 28-3 , reproduced below,

and Equation 28-5 , reproduced below,

to obtain an expression that describes how [B ⁽ⁿ⁾ ] depends on the concentration of total buffer, [TB], and [H ⁺ ]:

Finally, we obtain the closed-system buffering power by taking the derivative of [B ⁽ⁿ⁾ ] in Equation NE 28-14 with respect to pH. If we hold [TB] constant while taking this derivative (i.e., if we assume that the buffer can neither enter nor leave the system), we obtain the following expression for β _closed :

Open System

How does β _open depend on and pH? The first two steps of this derivation are the same as for the open system, except that we recognize that, for the buffer pair, [B ⁽ⁿ⁾ ] is [ ]:

For the open system, the third step is to rearrange the Henderson-Hasselbalch equation (see Equation 28-16 , reproduced below),

and rearrange it to solve for [ ]:

If we take the derivative of [ ] in the above equation with respect to pH, holding constant, the result is β _open :

Because Equation NE 28-18 tells us that everything after “2.3” in the above equation is, in fact, “[ ],” we obtain the final expression for β _open :

This is Equation 28-20 in the text.

Two aspects of Equation 28-18 are of interest. First, at a given [H ⁺ ], β _closed is proportional to [TB]. Second, at a given [TB], β _closed has a bell-shaped dependence on pH (green curve in Fig. 28-2 A ). β _closed is maximal when [H ⁺ ] = K (i.e., when pH = p K ). Most buffers in biological fluids behave as if they are in a closed system. Although many fluids are actually mixtures of several buffers, the total in such a mixture is the sum of their β _closed values, each described by Equation 28-18 . The red curve in Figure 28-2 B shows how total varies with pH for a solution containing a mixture of nine buffers (including the one described by the green curve), each present at a [TB] of 12.6 mM, with p K values evenly spaced at intervals of 0.5 pH unit. In this example, total is remarkably stable over a broad pH range and has a peak value that is the same as that of whole blood: 25 mM/pH unit. Indeed, whole blood is a complex mixture of many buffers. The most important of these are titratable groups on hemoglobin and, to a far lesser extent, other proteins. Even less important than the “other proteins” are small molecules such as inorganic phosphate. The [TB] values for these many buffers are not identical, and the p K values are not evenly spaced. Nevertheless, the buffering power of whole blood is nearly constant near the physiological pH.

The other physiologically important condition under which a buffer can function is in an open system. Here, one buffer species (e.g., CO ₂ ) equilibrates between the system and the environment. A laboratory example is a solution containing CO ₂ and in which dissolved CO ₂ equilibrates with gaseous CO ₂ in the atmosphere (see Fig. 28-1 ). A physiological example is blood plasma, in which dissolved CO ₂ equilibrates with gaseous CO ₂ in the alveoli. In either case, [CO ₂ ] _dis is fixed during buffering reactions. However, the total CO ₂ —[CO ₂ ] + [ ]—can vary widely. Because total CO ₂ can rise to very high values, in an open system can be an extremely powerful buffer. Consider, for example, a liter of a solution having a pH of 7.4, a of 40 mm Hg (1.2 mM CO ₂ ), and an [ ] of 24 mM— but no other buffers ( Fig. 28-3 , stage 1). What happens when we add 10 mmol of HCl? Available [ ] neutralizes almost all of the added H ⁺ , forming nearly 10 mmol H ₂ CO ₃ and then nearly 10 mmol CO ₂ plus nearly 10 mmol H ₂ O (see Fig. 28-3 , stage 2A). The CO ₂ that forms does not accumulate, but evolves to the atmosphere so that [CO ₂ ] _dis is constant. What is the final pH? If [CO ₂ ] _dis remains at 1.2 mM in our open system, and if [ ] decreases by almost exactly 10 mM (i.e., the amount of added H ⁺ ), from 24 to 14 mM, the Henderson-Hasselbalch equation predicts a fall in pH from 7.40 to 7.17, corresponding to an increase in free [H ⁺ ] of

Even though we have added 10 milli moles of HCl to 1 L, [H ⁺ ] increased by only 28 nano molar (see Fig. 28-3 , stage 3 A ). Therefore, the open-system buffer has neutralized 9.999,972 mmol of the added 10 mmol H ⁺ . The buffering provided by in an open system (β _open ) is so powerful because only depletion of limits neutralization of H ⁺ . The buildup of CO ₂ is not a limiting factor because the atmosphere is an infinite sink for newly produced CO ₂ .

The opposite acid-base disturbance occurs when we add a strong base such as NaOH. Here, the buffering reactions are just the reverse of those in the previous example. If we add 10 mmol of NaOH to 1 L of solution, almost all added OH ⁻ combines with H ⁺ derived from CO ₂ that enters from the atmosphere (see Fig. 28-3 , stage 2B). One ion forms for each OH ⁻ neutralized. Buffering power in this open system is far higher than that in a closed system because CO ₂ availability does not limit neutralization of added OH ⁻ . Only the buildup of limits neutralization of more OH ⁻ . In this example, even though we added 10 milli moles NaOH, free [H ⁺ ] decreased by only 12 nano molars (see Fig. 28-3 , stage 3B) as pH rose from 7.40 to 7.55.

Whether neutralizes an acid or a base, the open-system buffering power is N28-6

Notice that β _open does not have a maximum. Because β _open is proportional to [
], β _open rises exponentially with pH when
is fixed ( Fig. 28-4 , blue curve). In normal arterial blood (i.e., [
] = 24 mM), β _open is ~55 mM/pH unit. As we have already noted, the buffering power of all
buffers (
) in whole blood is ~25 mM/pH unit. Thus, in whole blood, β _open represents more than two thirds of the total buffering power. The relative contribution of β _open is far more striking in interstitial fluid, which lacks the cellular elements of blood and also has a lower protein concentration.

does not necessarily behave as an open-system buffer. In the previous example, we could have added NaOH to a solution in a capped syringe. In such a closed system, not only does accumulation of limit neutralization of OH ⁻ , but the availability of CO ₂ is limiting as well. Indeed, for fluid having the composition of normal arterial blood, the closed-system buffering power is only 2.6 mM/pH unit (see Fig. 28-4 , black curve), <5% of the β _open value of 55 mM/pH unit. You might think that the only reason the closed-system buffering power was so low in this example is that the pH of 7.4 was 1.3 pH units above the p K. However, even if pH were equal to the p K of 6.1, the closed-system buffering power in our example would be only ~14 mM/pH unit, about one quarter of the open-system value at pH 7.4. A physiological example in which the system is “poorly open” is ischemia, wherein a lack of blood flow minimizes the equilibration of tissue CO ₂ with blood CO ₂ . Thus, ischemic tissues are especially susceptible to large pH shifts.

In the absence of other buffers, doubling causes pH to fall by 0.3 but causes almost no change in [ ]

Figure 28-5 represents 1 L of a solution with the same composition as arterial blood plasma but no buffers other than . What are the consequences of increasing in the gas phase? The resulting increase in [CO ₂ ] _dis causes the equilibrium to shift toward formation of H ⁺ and . This disturbance is an example of a CO ₂ titration, because we initiated it by altering . More specifically, it is a respiratory acidosis —“acidosis” because pH falls, and “respiratory” because pulmonary problems ( Table 28-3 ) are the most common causes of an increase in the of arterial blood (see p. 680 ).

TABLE 28-3

The Four Major Acid-Base Disorders

DISORDER	PROXIMATE CAUSE(S)	CLINICAL CAUSES	CHANGES IN ARTERIAL ACID-BASE PARAMETERS
Respiratory acidosis	↑	↓ Alveolar ventilation (e.g., drug overdose) ↓ Lung-diffusing capacity (e.g., pulmonary edema) Ventilation-perfusion mismatch	pH: ↓ [ ]: ↑ : ↑
Respiratory alkalosis	↓	↑ Alveolar ventilation caused by: Hypoxia (e.g., acclimatization to high altitude) Anxiety Aspirin intoxication	pH: ↑ [ ]: ↓ : ↓
Metabolic acidosis	Addition of acids other than CO 2 or H 2 CO 3 Removal of alkali (fixed )	↓ Urinary secretion of H + (e.g., renal failure) Ketoacidosis (e.g., diabetes mellitus) Lactic acidosis (e.g., shock) loss (e.g., severe diarrhea)	pH: ↓ [ ]: ↓ : No change
Metabolic alkalosis	Addition of alkali Removal of acids other than CO 2 or H 2 CO 3 (fixed )	load (e.g., NaHCO 3 therapy) Loss of H + (e.g., severe vomiting)	pH: ↑ : ↑ : No change

In the absence of buffers, how far pH falls during respiratory acidosis depends on the initial pH and , as well as on the final . For example, doubling from 40 mm Hg (see Fig. 28-5 , stage 1) to 80 mm Hg causes [CO ₂ ] _dis to double to 2.4 mM (see Fig. 28-5 , stage 2A). At this point, the 1-L system is far out of equilibrium and can return to equilibrium only if some CO ₂ (X mmol) combines with X H ₂ O to form X H ⁺ and X . Thus, according to Equation 28-14 , the following must be true at equilibrium:

Solving this equation for X yields an extremely small value, nearly 40 nmol, or 0.000,040 mmol. X represents the flux of CO ₂ that passes through the reaction sequence CO ₂ + H ₂ O → H ₂ CO ₃ → H ⁺ + to re-establish the equilibrium. CO ₂ from the atmosphere replenishes the CO ₂ consumed in this reaction, so that [CO ₂ ] _dis remains at 2.4 mM after the new equilibrium is achieved (see Fig. 28-5 , stage 3A). The reason that the flux X is so small is that, with no other buffers present, every H ⁺ formed remains free in solution. Thus, only a minuscule amount of H ⁺ need be formed before [H ⁺ ] nearly doubles from 40 to nearly 80 nM. However, [ ] undergoes only a tiny fractional increase, from 24 to 24.000,040 mM. The doubling of the denominator in Equation 28-21 is matched by a doubling of the numerator, nearly all of which is due to the near-doubling of [H ⁺ ]. The final pH in this example of respiratory acidosis is

Another way of arriving at the same answer is to insert the final values for [ ] and into the Henderson-Hasselbalch equation:

The opposite acid-base disturbance, in which falls, is respiratory alkalosis. In a solution containing no buffers other than reducing by half, from 40 to 20 mm Hg, would cause all of the aforementioned reactions to shift in the opposite direction, so that pH would rise by 0.3, from 7.4 to 7.7. We could produce respiratory alkalosis in a beaker by lowering the in the gas phase. In humans, hyperventilation (see Table 28-3 ) lowers alveolar and thus arterial (see p. 680 ).

Thus, in the absence of buffers, doubling [CO ₂ ] causes pH to fall by 0.3, whereas halving [CO ₂ ] causes pH to rise by 0.3 (see Table 28-1 ). Remember, the log of 2 is 0.3.