Definition of Acid and Base

According to the widely accepted Brønsted-Lowry theory, an acid is any substance that donates a proton (H⁺) to an aqueous solution; a base is any substance that accepts a proton, removing it from solution. By this definition, an H⁺ donor is an acid and an H⁺ acceptor is a base.

Body fluids are acidic if they have an abnormally high [H⁺]. Increased [H⁺] in the blood is called acidemia. Acidosis refers to a general condition characterized by the accumulation of H⁺ in body fluids.

The term alkali is synonymous with base. Originally, alkali referred to strong bases formed by metallic hydroxides, such as sodium hydroxide (NaOH) and potassium hydroxide (KOH). In medicine, the term alkali refers to any base (i.e., any H⁺ acceptor). Body fluids are alkaline (or basic) if they contain abnormally high amounts of base or if they contain abnormally low amounts of H⁺ compared with base. Therefore a body fluid can be alkaline even if the absolute concentration of base is normal. Increased base or reduced H⁺ in the blood is called alkalemia; alkalosis refers to an alkaline condition of body fluids.

Acids and bases dissociate or ionize in solution to form their component ions:

The double arrows mean that this process is reversible; equilibrium is rapidly established between undissociated molecules and their dissociated ions.

Acids and bases react with one another in an aqueous solution to form a salt and water, neutralizing one another (i.e., the products are neither acidic nor basic), as the following reaction shows:

In this reaction, hydrogen chloride (HCl) (hydrochloric acid) donates H⁺, which is accepted by the base component (OH⁻) of NaOH. A neutral salt, sodium chloride (NaCl), and water (H₂O) are the results of this reaction.

Strong and Weak Acids and Bases: Equilibrium Constants

Strong acids and bases ionize almost completely in an aqueous solution; weak acids and bases ionize only to a slight extent. An example of a strong acid is HCl; nearly 100% of HCl molecules dissociate to form H⁺ and Cl⁻, as the following reaction shows:

HCl→H++Cl− 1.

1.

At equilibrium, the concentration of HCl is extremely small compared with the concentration of H⁺ and Cl⁻. No arrow points to the left, emphasizing that HCl ionizes almost completely.

In contrast, a weak acid dissociates only partially as the following shows:

HCl→H++Cl− 2.

2.

In this reaction, HA is a generic representation of an undissociated weak acid; H⁺ and A⁻ represent the dissociated components of the weak acid. The short arrow pointing to the right indicates that at equilibrium the concentration of undissociated HA molecules is far greater than the concentrations of A⁻ or H⁺.

The equilibrium constant of an acid is a measure of the extent to which the acid molecules dissociate (ionize). The law of mass action states that the velocity of a reaction is proportional to the product of the concentrations of the reactants. The following dissociation of the generic weak acid HA illustrates this concept:

HCl→H++Cl− 3.

3.

Velocity 1 (V₁) is proportional to [HA], and velocity 2 (V₂) is proportional to [A⁻] multiplied by [H⁺]. At equilibrium, the number of HA molecules dissociating is equal to the number of A⁻ and H⁺ associating (i.e., V₁ and V₂ are equal). In this state, no further net change occurs in [HA], [A⁻], or [H⁺]. The following equation represents conditions at equilibrium:

[A−]×[H+][HA]=KA (small) 4.

4.

In equation 4, K_A represents the equilibrium constant for HA. (K_A is also known as the acid’s ionization or dissociation constant.) In this example, the weak acid HA has an extremely small K_A because the denominator [HA] is quite large with respect to the numerator ([H⁺] multiplied by [A⁻]). At a given temperature, the value of K_A is always the same for this particular weak acid (HA) regardless of its initial concentration. Each acid has its own unique ionization constant.

A strong acid, such as HCl, has a large K_A because the denominator [HCl] is extremely small compared with the numerator ([H⁺] multiplied by [Cl⁻]). This is shown as follows:

[H+]×[Cl−][HCl]=KA (large) 5.

5.

As shown by equations 4 and 5, K_A indicates an acid’s strength; the greater the value of K_A, the stronger the acid—that is, the more completely it dissociates.

Carbonic acid (H₂CO₃)—the product of the reaction between CO₂ and H₂O—is often described as a weak acid, when in reality it is a moderately strong acid. In the pH environment of the blood, H₂CO₃ dissociates instantly and almost completely as soon as it is formed.¹ The idea that H₂CO₃ is a weak acid comes from the fact that the reaction between dissolved CO₂ and H₂O is quite slow in blood plasma, and from the fact that the sum of dissolved CO₂ and H₂CO₃ is commonly lumped together and treated as the undissociated acid. This practice is sensible because H₂CO₃ and dissolved CO₂ are indistinguishable from one other by chemical analysis (see Chapter 9). Even though H₂CO₃ is a relatively strong acid, (1) its treatment as being synonymous with dissolved CO₂ and (2) its slow formation make it appear to be a weak acid.¹

Measuring Hydrogen Ion Concentration: The Concept of pH

[H⁺] in body fluids is extremely small (normally about 40 × 10⁻⁹ mol/L, or 40 billionths of 1 mole per liter [0.000000040 mol/L]). The prefix “nano” means billionths; therefore, [H⁺] of body fluids is about 40 nmol/L. In clinical medicine, acidity is generally expressed in terms of pH rather than nmol/L[H⁺].

The concept of pH was developed by Sørenson in 1909. The pH scale ranges from 0 to 14 pH units. The dissociation of pure water molecules (H₂O, or HOH) helps explain this concept:

[H+]×[Cl−][HCl]=KA (large) 6.

6.

The dissociation of H₂O is extremely slight. Therefore, water’s K_A is exceedingly small, as the following shows:

[H+]×[OH−][HOH]=KA 7.

7.

Equation 7 can be rearranged to yield the following:

[H+]×[OH−]=[HOH]KA 8.

8.

In practical terms, [HOH] is constant because of its extremely slight dissociation. Therefore, the right side of equation 8 can be considered constant:

[HOH]KA=KW 9.

9.

In equation 9, K_w represents the dissociation constant of water. Equation 8 then becomes the following:

[H+]×[OH−]=KW 10.

10.

The numerical value of K_w is about 10⁻¹⁴. At equilibrium, pure water contains 10⁻⁷ mol/L of H⁺ and 10⁻⁷ mol/L of OH⁻. If the value of [H⁺] is known, the value of [OH⁻] can be calculated because of the reciprocal relationship between [H⁺] and [OH⁻]. For example, if [H⁺] equals 10⁻³ mol/L, [OH⁻] equals 10⁻¹¹ mol/L.

pH is defined as the negative logarithm, or exponent (to the base 10), of [H⁺]; this is shown as follows:

pH=−log[H+] 11.

11.

Water’s pH ([H⁺] = 10⁻⁷ mol/L) is calculated as follows:

pH=−log(10−7)pH=−(−7)pH=7 12.

12.

A pH of 7 corresponds to [H⁺] of 100 nmol/L:

10−7mol/L=0.0000001 mol/L=0.000000100 mol/L

Because pH is the negative logarithm of [H⁺], a decrease in pH indicates an increase in [H⁺] (Box 10-1).

BOX 10-1   pH Scale: [H⁺] [OH^–] = 10^–14 mol/L

A chemically neutral solution (neither acidic nor basic) has a pH of 7.0. To the chemist, a solution with a pH less than 7.0 is acidic, and a solution with a pH greater than 7.0 is alkaline (see Box 10-1). By this standard, body fluids are slightly alkaline, as the following shows:

Body fluid [H+]=40×10−9 mol/L                       pH=−log (40×10−9)                       pH=−log 40+(−log 10−9)                       pH=−1.6+(−[−9])                       pH=−1.6+9                       pH=7.40

Because pH is a logarithmic scale, a change of one pH unit corresponds to a 10-fold change in [H⁺] (Figure 10-1). [H⁺] at a pH of 7.0 (100 nmol/L) is 10 times the [H⁺] at a pH of 8.0 (10 nmol/L). Figure 10-1 shows that the relationship between pH and [H⁺] is linear in the normal physiological range of body fluids (pH = 7.35 to 7.45). Table 10-1 shows that in the physiological range, a 1-nmol/L change in [H⁺] produces a 0.01 change in pH. The pH-to-[H⁺] relationship maintains some degree of linearity between pH values of 7.20 and 7.55. However, below a pH of 7.20, linearity deteriorates rapidly (see Figure 10-1).

Overview of Hydrogen Ion Regulation in Body Fluids

The body continually produces hydrogen ions, but the pH of body fluids varies minimally between 7.35 and 7.45 (45 to 35 nmol/L [H⁺]). As noted previously, this rigid control is necessary to sustain vital cellular enzyme activity. Hydrogen ions formed in the body arise from either volatile acids or nonvolatile acids, or fixed acids. Volatile acids in the blood arise from and are in equilibrium with a dissolved gas. The only volatile acid of physiological significance in the body is carbonic acid (H₂CO₃), which is in equilibrium with dissolved CO₂. Normal aerobic metabolism generates about 13,000 mM of CO₂ each day, producing an equal amount of H⁺:

In a process called isohydric buffering,¹ most of the hydrogen ions produced cause no pH change at the tissue level because newly forming deoxygenated hemoglobin immediately combines with the hydrogen ions (see Chapter 9). When blood reaches the lungs, hemoglobin releases these hydrogen ions, which combine with plasma bicarbonate ion (HCO3−) to form CO₂:

Ventilation eliminates carbonic acid (CO₂), keeping pace with its production. Isohydric buffering and ventilation are the two major mechanisms responsible for maintaining a stable pH in the face of massive CO₂ production.²

Catabolism of proteins continually produces fixed acids such as sulfuric and phosphoric acids. In addition, anaerobic metabolism produces lactic acid, another fixed acid. In contrast to carbonic acid, these fixed acids are nonvolatile and are not in equilibrium with a gaseous component. Therefore, the hydrogen ions of fixed acids must be buffered by bases in the body or eliminated in the urine by the kidneys. Compared with daily CO₂ production, fixed acid production is small, averaging only about 50 to 70 mEq per day.³ Certain diseases, such as untreated diabetes, increase fixed acid production. The resulting hydrogen ions stimulate the respiratory centers in the brain, increasing ventilation and CO₂ elimination, pulling the CO₂ hydration reaction to the left:

Thus, the respiratory system compensates for fixed acid accumulation, preventing a significant increase in [H⁺].

Bicarbonate and Nonbicarbonate Buffer Systems

Blood buffers are classified as either bicarbonate or nonbicarbonate buffer systems. The bicarbonate buffer system consists of carbonic acid (H₂CO₃) and its conjugate base, HCO3−. The nonbicarbonate buffer system consists mainly of phosphates and proteins, including hemoglobin. The blood buffer base is the sum of bicarbonate and nonbicarbonate bases, measured in millimoles per liter of blood.

The bicarbonate system is called an open buffer system because H₂CO₃ is in equilibrium with dissolved CO₂, which is readily removed by ventilation. That is, when HCO3− buffers H⁺, the product, H₂CO₃, is broken down into CO₂ and H₂O; ventilation continually removes CO₂ from the reaction, preventing it from reaching equilibrium. As long as ventilation is adequate, buffering activity continues without being slowed or stopped:

HCO3−+H+→H2CO3→H2O+CO2(exhaledgas)

Nonbicarbonate buffers are closed buffer systems because all components of acid-base reactions remain in the system. (In the following discussions, nonbicarbonate buffer systems are collectively represented as HBuf/Buf⁻, where HBuf is the weak acid, and Buf⁻ is the conjugate base.) When Buf⁻ buffers H⁺, the product, HBuf, builds up and eventually reaches equilibrium with the reactants, preventing further buffering activity:

HCO3−+H+→H2CO3→H2O+CO2(exhaledgas)

Table 10-2 summarizes the characteristics and components of bicarbonate and nonbicarbonate buffer systems.

Open and closed buffer systems differ in their ability to buffer fixed and volatile acids. They also differ in their ability to function in wide-ranging pH environments. Both systems are physiologically important, each playing a unique and essential role in maintaining pH homeostasis. Table 10-3 summarizes the approximate contributions of various blood buffers to the total buffer base. The bicarbonate buffer system has the greatest buffering capacity because it is an open system.

Bicarbonate and nonbicarbonate buffer systems do not function in isolation from one another; they are intermingled in the same solution (whole blood) and are in equilibrium with the same [H⁺] (Figure 10-2). As Figure 10-2 shows, increased ventilation increases the CO₂ removal rate, ultimately causing nonbicarbonate buffers (HBuf) to release H⁺. Conversely, cessation of ventilation reverses the reaction; CO₂ builds up, more H⁺ is generated, and, ultimately, more HBuf is formed.

pH of a Buffer System and Henderson-Hasselbalch Equation

Physiological buffer solutions consist mostly of undissociated acid molecules and only a small amount of H⁺ and conjugate base anions. The [H⁺] of a buffer solution can be calculated if the concentrations of its components and the acid’s equilibrium constant are known. Consider the bicarbonate buffer system:

HCO3−+H+→H2CO3→H2O+CO2(exhaledgas)

The equilibrium constant (K_A) for H₂CO₃ is as follows:

KA=[[H+]×[HCO3−][H2CO3]]

[H⁺] can be isolated through the following algebraic rearrangement of this equation:

[H+]=KA×[[H2CO3][HCO3−]]

The [H⁺] is determined by the ratio between undissociated acid molecules [H₂CO₃] and base anions [HCO3−].

Henderson-Hasselbalch Equation

The foregoing concept is the basis for the Henderson-Hasselbalch (H-H) equation. The H-H equation is specific for calculating the pH of the blood’s bicarbonate buffer system, which is the same as the pH of the plasma. That is, because all buffer systems in the blood are in equilibrium with the same pH, the pH of any one buffer system is equal to the pH of the entire plasma solution (the isohydric principle).²

The H-H equation is derived from the equilibrium constant for H₂CO₃:

[[H+]×[HCO3−][H2CO3]]=KA

To express [H⁺] in terms of pH, the logarithm of both sides of the equation is determined:

log[[H+]×[HCO3−][H2CO3]]=log KA

This equation is algebraically equivalent to the following:

log[H+]+log[[HCO3−][H2CO3]]=log KA

Transposing:

log[H+]=log KA−log[[HCO3−][H2CO3]]

Multiplying both sides of the equation by −1 produces the following:

−log[H+]=−log KA+log[[HCO3−][H2CO3]]

The pH (i.e., −log [H⁺]) is now on the left side of the equation; the negative logarithm of K_A is the definition of pK, which is the pH of the buffer system when H₂CO₃ is exactly 50% dissociated. Substituting, the equation becomes the following:

pH=pK+log[[HCO3−][H2CO3]]

The H-H equation substitutes dissolved CO₂ (PCO₂ × 0.03 mmol/L/mm Hg) for [H₂CO₃]. This is legitimate because dissolved CO₂ is in equilibrium with and directly proportional to the blood’s [H₂CO₃], as explained in Chapter 9. In contrast to H₂CO₃, dissolved CO₂ is easily calculated from the blood’s carbon dioxide pressure (PCO₂). For these reasons, dissolved CO₂ is treated as though it were the acid instead of H₂CO₃. The H-H equation is as follows:

pH=pK′+log[[HCO3−](PCO2×0.03)]

The substitution of (PCO₂ × 0.03) for [H₂CO₃] produces a different pK—hence the term pK′. The pK′ for the (HCO3−)/(PCO₂ × 0.03) system is 6.1, which is a different value than the pK of the HCO3−/H₂CO₃ system. (Using the pK′ of 6.1 is incorrect if H₂CO₃ is used in the equation’s denominator.) The clinical form of the H-H equation is as follows:

pH=6.1+log[[HCO3−](PCO2×0.03)]

Clinical Use of Henderson-Hasselbalch Equation

The H-H equation allows the computation of pH, [HCO3−], or PCO₂ if two of these three variables are known. Blood gas analyzers measure pH and PCO₂ but compute [HCO3−]. Assuming a normal arterial pH of 7.40 and arterial carbon dioxide pressure (PaCO₂) of 40 mm Hg, arterial [HCO3−] can be calculated as follows:

 pH=6.1+log[[HCO3−]/(PCO2×0.03)]7.40=6.1+log[[HCO3−]/[40×0.03]]7.40=6.1+log[[HCO3−]/1.2]

[HCO3−] is solved as follows:

[HCO3−]=antilog(7.40−6.1)×1.2              =antilog(1.3)×1.2              =20×1.2              =24 mEq/L

The different forms of the H-H equation needed to calculate pH, PCO₂, and HCO3− are shown in Box 10-2.

BOX 10-2   Using the Henderson-Hasselbalch Equation

1. Known: PCO₂ and [HCO3−]; calculate pH as follows:

pH=6.1+log[[HCO3−][PCO2×0.03]]

2. Known: PCO₂ and pH; calculate [HCO3−] as follows:

[HCO3−]=antilog(pH−6.1)×(PCO2×0.03)

3. Known: pH and [HCO3−]; calculate PCO₂ as follows:

PCO2=[[HCO3−](antilog[pH−6.1])×0.03]

The H-H equation is useful for checking a clinical blood gas report to determine whether the pH, PCO₂, and [HCO3−] values are compatible with one another. In this way, transcription errors (which are common) can be detected. Experienced clinicians can often spot combinations of blood gas values that seem incompatible; the H-H equation is helpful in verifying such incompatibilities.

In mechanically ventilated patients, it also may be clinically useful to predict the effect that a change in tidal volume or rate (minute ventilation) would have on the arterial pH. In other words, the predicted PaCO₂ that would result from a change in ventilation can be calculated and “plugged in” to the H-H equation to compute the new projected pH (see Clinical Focus 10-2).

Buffer Strength

The strength of a buffer solution is determined by measuring the number of hydrogen ions that must be added to or taken away from the solution to change its pH by one unit. A buffer solution’s strength varies, depending on its initial pH, before hydrogen ions are added or subtracted. A given buffer solution has its own unique pH range in which it most effectively resists pH changes. The titration curve for the bicarbonate buffer system, HCO3−/(PCO₂ × 0.03), illustrates this point (Figure 10-3).

This titration curve shows the degree to which pH changes when hydrogen ions are added to or subtracted from a bicarbonate buffer solution. The upper right side of the graph shows a hypothetical condition in which the solution’s concentration of HCO3− is 100% and that of dissolved CO₂ is 0% (i.e., no H⁺ ions exist in this imaginary solution). As H⁺ ions are added to the solution, the pH decreases rapidly at first. The amount of H⁺ needed to change the buffer solution’s pH one unit, from 7.9 to 6.9, is represented by the width of the orange-shaded band at the upper left corner of the graph. Progressively greater amounts of H⁺ are required to reduce the pH by one unit as the buffer solution’s pH decreases. As H⁺ ions are added, the decrease in the buffer solution’s pH follows the S-shaped titration curve (see Figure 10-3) from right to left. The curve is steepest when the buffer solution contains 50% dissolved CO₂ and 50% HCO3−, which corresponds to a solution pH of 6.1. At this point, the solution’s ability to resist a pH change is at its maximum. A relatively large amount of H⁺ must be added to decrease the solution’s pH by one unit, from 6.5 to 5.5; it takes a much smaller amount of H⁺ to cause the pH to decrease from 7.9 to 6.9. (Compare the widths of the orange-shaded bands on the left side of the graph.) The buffer solution’s pH at its maximal buffering power (point A on the steepest part of the titration curve) is known as the pK, which is 6.1 for the HCO3−/dissolved CO₂ system. A given buffer solution is most effective in resisting pH changes when it operates in a pH environment near its pK.

Physiological Importance of Bicarbonate Buffer System

The HCO3−/dissolved CO₂ system would appear to be an ineffective buffer in humans because the system’s pK of 6.1 is well out of the physiological pH range for body fluids. Why then is the bicarbonate buffer system so effective in the blood? The answer is simply that HCO3−/dissolved CO₂ is an open buffer system; that is, one of its components, CO₂, is continually removed through ventilation:

HCO3−+H+→H2CO3→H2O+CO2↑(exhaledgas)

HCO3− is able to continue buffering H⁺ as long as ventilation continues to remove CO₂ effectively; hypothetically, this buffering activity could continue until all body sources of HCO3− are used up in binding H⁺ ions.

To understand the effectiveness of the open bicarbonate buffer system in the body, it is helpful to visualize what would happen if this system were closed, as illustrated in Figure 10-4. In this figure, containers A and B have a bicarbonate buffer dissolved in 1 L of solution. Initially, the buffer solution has HCO3− and dissolved CO₂ concentrations equal to the concentrations of normal blood plasma, and the pH is 7.40, according to the H-H equation (see Figure 10-4, A). When 12 mM of a strong acid (HCl) is added, 12 mM of HCO3− is converted to 12 mM of CO₂, which decreases the HCO3− concentration from 24 mM to 12 mM and increases the dissolved CO₂ from 1.2 mM to 13.2 mM (see Figure 10-4, B). Because the CO₂ produced by this reaction cannot escape from the system, the denominator of the H-H equation (dissolved CO₂) is increased, causing pH to decrease to 6.06 (see Figure 10-4, B).

Figure 10-5 illustrates why the open bicarbonate buffer system is more effective in resisting pH changes produced by the addition of 12 mM of HCl. To simulate normal ventilation, a gas with a PCO₂ of 40 mm Hg is continuously bubbled through the bicarbonate buffer solution in Figure 10-5. This keeps the PCO₂ of the solution at 40 mm Hg, and keeps the dissolved CO₂ concentration constant at 1.2 mM/L (40 mm Hg × 0.03 = 1.2 mM/L). Figure 10-5, A, represents normal plasma values for HCO3−, dissolved CO₂, and pH. As in the closed system (see Figure 10-4), adding 12 mM of HCl converts an equal amount of HCO3− to dissolved CO₂. HCO3− decreases from 24 mM to 12 mM, but the simultaneously generated 12 mM of CO₂ is bubbled out of the solution to the atmosphere (see Figure 10-5, B). This keeps the denominator of the H-H equation (dissolved CO₂) constant at 1.2 mM/L. As shown in Figure 10-5, B, the pH decreased to only 7.07 because CO₂ cannot build up in the solution, as it did in the closed system. Thus, the bicarbonate buffer system is effective in buffering fixed acid even though it operates in a pH environment of 7.40 rather than its pK of 6.1. However, the effectiveness of the bicarbonate buffering system depends on the ability of the lungs to produce adequate ventilation.

Physiological Roles of Bicarbonate and Nonbicarbonate Buffer Systems

The functions of bicarbonate and nonbicarbonate buffer systems are summarized in Table 10-4.

Bicarbonate Buffer System

The bicarbonate buffer system can buffer only fixed acids. An increased fixed acid load in the body reacts with HCO3− of the bicarbonate buffer system in the following way:

This reaction shows that the process of buffering fixed acid produces CO₂, which is eliminated in exhaled gas. Large amounts of acid are buffered in this fashion.

The bicarbonate buffer system cannot buffer its own acid (carbonic acid), which builds up in the blood when ventilation is inadequate. As long as inadequate ventilation (hypoventilation) persists, CO₂ continues to build up and drive the hydration reaction in the direction that produces more carbonic acid, hydrogen, and bicarbonate ions:

H⁺ created in this manner cannot be buffered by HCO3− because the reaction cannot reverse its direction when hypoventilation is present. H⁺ arising from increased blood levels of CO₂ must be buffered by the nonbicarbonate (closed) buffer system.

Nonbicarbonate Buffer System

Table 10-3 lists the nonbicarbonate buffers in the blood. Of these, hemoglobin is the most important because it is the most abundant. These buffers are the only ones available to buffer carbonic acid. However, they can buffer H⁺ produced by any acid, fixed or volatile. Because nonbicarbonate buffers (HBuf/Buf⁻) function in closed systems, the products of their buffering activity build up, slowing or stopping further buffering activity:

HCO3−+H+→H2CO3→H2O+CO2↑(exhaledgas)

This means not all of the Buf⁻ is available for buffering activity. At equilibrium (denoted by the double arrow), Buf⁻ still exists in the solution but cannot combine further with H⁺. In contrast, virtually all of the HCO3− in the bicarbonate buffer system is available for buffering activity because it functions in an open system where equilibrium between reactants and products never occurs. Both open and closed systems function in a common fluid compartment (blood plasma) as the following reactions illustrate:

Most of the added fixed acid is buffered by HCO3− because increased ventilation continually pulls the reaction to the left. Smaller amounts of H⁺ react with Buf⁻ because equilibrium is approached, slowing this reaction. Although all HCO3− could theoretically be depleted in buffering fixed acids, this never happens because metabolically produced CO₂ provides a continual source of HCO3−; that is, at the tissue level, CO₂ diffuses into the erythrocyte where it reacts with H₂O to form H⁺ and HCO3−; hemoglobin’s subsequent buffering of H⁺ causes HCO3− to be continuously generated, as described in Chapter 9.

CONCEPT QUESTION 10-5

Normal arterial [HCO₃⁻] is about 24 mEq/L, and normal PaCO₂ is about 40 mm Hg. How much does [HCO₃⁻] need to increase above normal to maintain a pH of 7.40 if PaCO₂ increases to 60 mm Hg?

Lungs

Normal oxidative (aerobic) metabolism produces CO₂, forming more than 10,000 mEq of H₂CO₃ per day.⁴ Because H₂CO₃

CLINICAL FOCUS 10-2   Using the Henderson-Hasselbalch Equation to Predict Arterial pH for a Given Change in Arterial Carbon Dioxide Pressure

A patient with acute respiratory distress syndrome whose lungs are mechanically ventilated is in the intensive care unit. Current arterial blood gas values are as follows:

pH = 7.34

PaCO₂ = 50 mm Hg

HCO3− = 26 mEq/L

The patient’s lungs have such low compliance that dangerously high pressures are required to maintain normal tidal volumes and alveolar ventilation (V˙_A). The respiratory therapist and attending physician decide to decrease the tidal volume delivered by the ventilator to prevent structural damage to lung tissue. In this way, alveolar pressures and the risk of alveolar rupture can be decreased. However, the decrease in tidal volume will cause the PaCO₂, which is already above normal, to increase further, decreasing the arterial pH even more. Nevertheless, some degree of hypercapnia and acidemia is acceptable if the detrimental effect of pressure-induced alveolar trauma (barotrauma) is avoidable. The respiratory therapist and physician decide they will not allow the pH to decrease below 7.25.

The patient’s lungs are being ventilated with a tidal volume of 700 mL at a frequency of 10 breaths per minute for a V˙_E of 7 L per minute. How high can the PaCO₂ be allowed to increase without decreasing the arterial pH below 7.25, and how much should the tidal volume be decreased to accomplish this?

Discussion

First, the PaCO₂ that will produce a pH of 7.25 needs to be calculated as follows, using known values:

PaCO2=26mEq/L0.03×antilog(7.25−6.1)

PaCO2=260.03×14.13=260.42

PaCO2=61.9or62mmHg

A PaCO₂ of 62 mm Hg will produce a pH of about 7.25.^∗

Next, V˙_E required to produce a PaCO₂ of 62 mm Hg must be calculated. Chapter 9 indicated that V˙_E is inversely proportional to PaCO₂, as the following equation shows:

(V˙E)1×(PaCO2)1=(V˙E)2×(PaCO2)2

In this equation, subscripts 1 and 2 represent current and future values. The solution for (V˙_E)₂ is as follows:

7L/min×50mmHg=(V˙E)2×62mmHg(7×50)/62=(V˙E)25.65L/min=(V˙E)2

Decreasing V˙_E from the current value of 7 L per minute to 5.65 L per minute produces a PaCO₂ of approximately 62 mm Hg and a pH of 7.25. The newly calculated V˙_E of 5.65 L per minute is divided by the respiratory frequency (10 breaths per minute) to calculate the new tidal volume (V_T = 5.65 L/min ÷ 10 = 0.565 L or 565 mL). A tidal volume of 565 mL at a respiratory rate of 10 breaths per minute should produce a pH of about 7.25 in the patient. This example is more theoretical than it is practical; in the clinical setting, the patient’s minute ventilation would be gradually reduced over time to allow the kidneys to compensate (retain HCO3− ions) and keep the pH closer to the normal range.

---

^∗This calculation is an oversimplification because of the CO₂ hydration effect: An increased PaCO₂ causes a small increase in [HCO₃⁻]. A decrease in V_T without changing the respiratory rate would directly decrease alveolar ventilation without affecting anatomical dead space ventilation; this would increase the V_D/V_T ratio, resulting in a higher PaCO₂ than predicted by this calculation.

is in equilibrium with dissolved CO₂, the lungs can lower blood H₂CO₃ concentration by eliminating CO₂ in exhaled gas. Neurochemical mechanisms control ventilation in such a way that CO₂ elimination matches CO₂ production while keeping PaCO₂ and pH near 40 mm Hg and 7.40.

In addition to production of H₂CO₃ via aerobic metabolism, H₂CO₃ and ultimately CO₂ are generated by the reaction between fixed acids and HCO3− buffers. The lung eliminates CO₂ from both sources. In this way, the lung can eliminate large amounts of volatile acid (H₂CO₃) in seconds, producing rapid pH changes. CO₂ elimination by the lungs does not physically remove H⁺ from the body, but its removal causes the hydration reaction to proceed in the direction that converts H⁺ ions to harmless H₂O molecules, as follows:

H++ HCO3−→H2CO3→H2O+CO2

Kidneys (Renal System)

The kidneys physically remove hydrogen ions from the body; the amount eliminated depends on the blood level of hydrogen ions—the higher the blood levels, the more hydrogen ions excreted. Blood hydrogen ions may originate from H₂CO₃ (when PaCO₂ is high) or from a buildup of fixed acids. The kidneys excrete less than 100 mEq of fixed acid per day, a relatively small amount compared with the lung’s excretion of volatile H₂CO₃. Besides excreting H⁺, the kidneys also influence blood pH by reabsorbing HCO3− from the filtrate into the blood or by eliminating HCO3− in the urine. If PaCO₂ is high (creating high levels of H₂CO₃), the kidneys not only excrete greater amounts of H⁺, but they also return all of the kidney filtrate’s HCO3− to the blood. The opposite happens when PaCO₂ is low—the kidneys excrete less H⁺ but more HCO3−. In this way, the kidneys work to maintain a normal blood pH when the lungs fail to maintain normal CO₂ levels. Compared with the lung’s ability to change the PaCO₂ in seconds, the renal process is slow, requiring hours to days. Renal regulation of acid-base and electrolyte balance is discussed in detail in Chapter 22.

Normal Acid-Base Balance

Normally, alveolar ventilation maintains a PaCO₂ of about 40 mm Hg, whereas the kidneys maintain a plasma HCO3− concentration of about 24 mEq/L. These normal values produce an arterial pH of 7.40, as the H-H equation shows:

pH=6.1+log[[HCO3−](PCO2×0.03)]pH=6.1+log[24(40×0.03)]pH=6.1+log(20)pH=6.1+1.3=7.40

The pH is determined by the ratio of [HCO3−] to dissolved CO₂, not by the absolute concentrations of these substances. As long as the ratio of [HCO3−] to dissolved CO₂ is 20:1, the pH is normal at 7.40. Because the kidneys control the plasma [HCO3−] and the lungs control blood CO₂ levels, the H-H equation can be conceptually rewritten as follows:

pH=[Kidney control of [HCO3−]Lungcontrol of PCO2]

From this relationship, it is apparent that an increase in [HCO3−] or a decrease in PCO₂ (hyperventilation) increases the pH, leading to alkalemia. Both situations produce an [HCO3−]-to-(PCO₂ × 0.03) ratio greater than 20:1 (e.g., 25:1). Similarly, a decreased [HCO3−] or an increased PCO₂ (hypoventilation) decreases the pH, leading to acidemia; this produces an [HCO3−]-to-(PCO₂ × 0.03) ratio less than 20:1 (e.g., 15:1). The normal ranges for arterial pH, PCO₂, and [HCO3−] are as follows:

pH=7.35to7.45PaCO2=35to45mmHg[HCO3−]=22to26mEq/L

Alkalemia is defined as a blood pH greater than 7.45; acidemia is defined as a blood pH less than 7.35. Hyperventilation is defined as a PaCO₂ less than 35 mm Hg; hypoventilation is defined as a PaCO₂ greater than 45 mm Hg.

Primary Respiratory Disturbances

PaCO₂ abnormalities that cause abnormal arterial pH values are called primary respiratory disturbances because alveolar ventilation controls the PCO₂ of arterial blood. Respiratory disturbances affect the denominator of the H-H equation. An elevated PaCO₂ increases dissolved CO₂, decreasing the pH:

↓pH∝[→HCO3−↑PaCO2]

In this equation, ↓ represents a decrease, → represents no change, and ↑ represents an increase. Respiratory disturbances causing acidemia produce respiratory acidosis. A low PaCO₂ decreases dissolved CO₂, increasing the pH. This is called respiratory alkalosis:

↑pH∝[→HCO3−↓PaCO2]

Hypoventilation leads to respiratory acidosis, whereas hyperventilation leads to respiratory alkalosis.

Primary Metabolic (Nonrespiratory) Disturbances

Nonrespiratory processes change the arterial pH by changing [HCO3−]; these processes are called primary metabolic disturbances. The term metabolic in this context is arbitrary, but by convention it refers to all nonrespiratory acid-base disturbances. These disturbances involve a gain or loss of either fixed acids or HCO3−. Such processes affect the numerator of the H-H equation. For example, an accumulation of fixed acid in the body is buffered by bicarbonate, lowering the plasma [HCO3−] and decreasing the pH:

↓pH∝[↓HCO3−→PaCO2]

Exactly the same effect is created by a loss of HCO3−. Nonrespiratory processes causing acidemia produce metabolic acidosis.

In contrast, the ingestion of too much alkali (e.g., NaHCO₃ or other antacids) raises [HCO3−], increasing pH:

↑pH∝[↑HCO3−→PaCO2]

Plasma [HCO3−] can be increased either by its addition (as in the previous example) or by its generation (as occurs when fixed acid is lost from the body). For example, HCl is lost after a person vomits large amounts of gastric secretions. Nasogastric suction catheters, often placed in critically ill patients, also deplete gastric HCl. A loss of HCl generates HCO3−, as the following reaction shows:

Processes that increase the arterial pH by losing fixed acid or gaining HCO3− produce a condition called metabolic alkalosis. Because HCO3− can be added or lost through mechanisms not related to metabolism (alkali ingestion or vomiting), the term metabolic acidosis is misleading. Similarly, acid not produced by metabolism (e.g., salicylic acid [aspirin]) can be ingested, producing so-called metabolic acidosis. The term metabolic has been entrenched by tradition and continues to be used. Table 10-5 shows the four primary acid-base disturbances causing alkalemia and acidemia.

TABLE 10-5

Primary Acid-Base Disturbances

pH Change	Main Abnormality	Designation
Alkalemia (pH >7.45)	Decreased PCO2	Respiratory alkalosis
	Increased HCO3−	Metabolic (nonrespiratory alkalosis)
Acidemia (pH <7.35)	Increased PCO2	Respiratory acidosis
	Decreased HCO3−	Metabolic (nonrespiratory acidosis)

Compensation: Restoring pH to Normal

When any primary acid-base defect occurs, the organ system not responsible immediately initiates a compensatory process, counteracting the primary defect. For example, if reduced ventilation is the primary defect (respiratory acidosis), the kidneys work to restore the pH to normal by returning HCO3− to the blood. In contrast, the compensatory renal response to hyperventilation (respiratory alkalosis) is the urinary elimination of HCO3− (bicarbonate diuresis).

Similarly, if a nonrespiratory process increases or decreases [HCO3−], the lungs compensate for this defect by eliminating CO₂ (hyperventilating) or retaining CO₂ (hypoventilating), restoring the pH to the normal range. Consider the example of pure (uncompensated) respiratory acidosis in which PaCO₂ increases to 60 mm Hg, creating an [HCO3−]-to-dissolved CO₂ ratio of about 13:1, as shown:

pH=6.1+log[24mEq/L60mmHg×0.03]pH=6.1+log(13.3)pH=7.22

The kidneys compensate, restoring the [HCO3−]-to-dissolved CO₂ ratio by actively reabsorbing HCO3− into the blood:

pH=6.1+log[34mEq/L60mmHg×0.03]pH=6.1+log(18.9)pH=7.38

By increasing the plasma [HCO3−] level to 34 mEq/L in this example, the kidneys brought the [HCO3−]-to-dissolved CO₂ ratio back to about 19:1, restoring the pH to the normal range (7.35 to 7.45); the PCO₂ remains abnormally elevated. The elevated plasma [HCO3−] brought about by the kidneys’ compensatory response should not be misconstrued as metabolic alkalosis. Compensatory HCO3− retention is a normal secondary response to the primary event of respiratory acidosis.

The lungs normally compensate quickly for metabolic acid-base defects because ventilation can change PaCO₂ in seconds. The kidneys require more time to retain or excrete significant amounts of HCO3−, and they compensate for respiratory defects at a much slower pace. Table 10-6 summarizes the four primary acid-base disturbances and the body’s compensatory responses. (Primary and compensatory responses appear in bold font.)

TABLE 10-6

Primary Acid-Base Disorders and Compensatory Responses

Acid-Base Disorder	Primary Defect	Compensatory Response
Respiratory acidosis	[→HCO3−↑PaCO2]=↓pH	[↑HCO3−↑PaCO2]=→pH
Respiratory alkalosis	[→HCO3−↓PaCO2]=↑pH	[↓HCO3−↓PaCO2]=→pH
Metabolic acidosis	[↓HCO3−→PaCO2]=↓pH	[↓HCO3−↓PaCO2]=→pH
Metabolic alkalosis	[↑HCO3−→PaCO2]=↑pH	[↑HCO3−↑PaCO2]=→pH

→, No change, or normal; ↓, decrease; ↑, increase.

Effect of Carbon Dioxide Hydration Reaction on Bicarbonate Ion Concentration

In the foregoing examples of pure (uncompensated) respiratory acidosis and alkalosis, it was assumed that [HCO3−] did not change when PaCO₂ increased or decreased. This simplification was made to emphasize that PaCO₂, not HCO3−, is the primary abnormality in respiratory acidosis or alkalosis. However, arterial [HCO3−] does slightly increase as PaCO₂ increases secondary to HCO3− generation in the erythrocyte through the hydration reaction. As explained in Chapter 9, the hydration reaction occurs primarily in the red blood cell because the catalytic enzyme carbonic anhydrase is present. This is shown as follows:

CO2+H2O (carbonicanhydrase)→H2CO3→H++HCO3−

As H⁺ and HCO3− are rapidly produced, hemoglobin immediately buffers H⁺, generating HCO3− in the process:

The extent to which [HCO3−] increases for a given increase in PaCO₂ depends on how much nonbicarbonate buffer (mainly hemoglobin) is present to accept the hydrogen ions produced by the hydration reaction. In other words, the increase in the number of plasma bicarbonate ions is exactly equal to the number of hydrogen ions buffered by the nonbicarbonate buffers. Generally, when the nonbicarbonate buffer concentration is normal, an acute PaCO₂ increase of 10 mm Hg causes [HCO3−] to increase by about 1 mEq/L; this is a clinically useful rule of thumb. A slight increase in [HCO3−] is a natural consequence of an acute increase in PaCO₂. This small increase in [HCO3−] should not be confused with compensatory renal HCO3− retention.

Figure 10-6 illustrates what would happen if the blood contained no nonbicarbonate buffers. In Figure 10-6, A, the solution’s PCO₂ is 40 mm Hg, the [HCO3−] is 24 mEq/L, and the pH is 7.40. If the PCO₂ of gas bubbling through the solution suddenly increases to 80 mm Hg (see Figure 10-6, B), dissolved CO₂ (PCO₂ × 0.03) increases to 2.4 mM/L, and the pH decreases to 7.10. These events are recorded on the pH-[HCO3−] diagram in Figure 10-7. The conditions shown in Figure 10-6, A, are represented by point A on the pH-[HCO3−] diagram. (The curved lines are PCO₂ isobars, constructed by maintaining the PCO₂ of the gas bubbling through the solution constant while adding or subtracting a strong acid.) [HCO3−] did not change when the PCO₂ increased to 80 mm Hg (from point A to point B in Figure 10-7). The lack of a perceptible change might seem odd because an increase in PCO₂ from 40 mm Hg to 80 mm Hg would double the H₂CO₃ concentration, which means that [HCO3−] would increase to some extent when H₂CO₃ dissociates into bicarbonate and hydrogen ions. Any such increase in bicarbonate ions would have to be equal to the increase in hydrogen ions because each molecule of H₂CO₃ produces one H⁺ and one HCO3−. As estimated from the decrease in pH from 7.40 to 7.10, the increase in [H⁺] is about 40 nmol/L (see Table 10-1), which means that the [HCO3−] would also increase by about 40 nmol/L. This minuscule increase in [HCO3−] cannot be accurately measured or plotted on the pH-[HCO3−] diagram in Figure 10-7 and can be ignored.

The reason [HCO3−] did not increase perceptibly in the example just described is that nonbicarbonate buffers were not present to accept the H⁺ produced by the hydration reaction. In whole blood, nonbicarbonate buffers are plentiful. As described earlier, when they buffer H⁺, HCO3− is generated. Figure 10-8 is a pH-[HCO3−] diagram for whole blood. A normal status is represented by point A (PCO₂ of 40 mm Hg, pH of 7.40, and plasma [HCO3−] of 24 mEq/L). An acute increase in PCO₂ to 80 mm Hg proceeds along the nonbicarbonate blood buffer line (BAC) to point D, where the buffer line intersects the 80-mm Hg PCO₂ isobar. Point D indicates an increase in [HCO3−] of about 4.5 mEq/L, which is exactly the same as the amount of H⁺ buffered by nonbicarbonate buffers. This corresponds to a pH of 7.18 compared with the pH of 7.10 in Figure 10-7, in which nonbicarbonate buffers are absent. The slope of BAC is a measure of the amount of nonbicarbonate buffer present; the slope is steeper if greater amounts of nonbicarbonate buffer are present. For example, if hemoglobin concentration increases, an acute increase in PCO₂ from point A (see Figure 10-8) to 80 mm Hg proceeds along a steeper line (dashed line); at the 80-mm Hg PCO₂ isobar, [HCO3−] and pH are higher because hemoglobin buffered greater amounts of H⁺.

As a general rule, the hydration reaction, in the presence of normal nonbicarbonate buffer concentration, increases the plasma [HCO3−] about 1 mEq/L for every 10-mm Hg increase in PCO₂ greater than 40 mm Hg. However, this relationship is not linear; [HCO3−] is reduced about 1 mEq/L for every 5-mm Hg PCO₂ decrease less than 40 mm Hg.