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 small extent. An example of a strong acid is hydrochloric acid (HCl). Nearly 100% of the HCl molecules dissociate to form H⁺ and Cl⁻:

< ?xml:namespace prefix = "mml" />HClH++Cl− (1)

(1)

At equilibrium, the concentration of HCl is extremely small compared with either [H⁺] or [Cl⁻]. There is no arrow pointing to the left in Reaction 1, emphasizing that HCl ionizes almost completely in solution. In contrast, carbonic acid is an example of a relatively weak acid:

H2CO3⇄HCO3−+H+ (2)

(2)

The long arrow pointing to the left indicates that at equilibrium, the concentration of undissociated H₂CO₃ molecules is far greater than the concentration of HCO₃⁻ or H⁺.

The equilibrium constant of an acid is a measure of the extent to which the acid molecules dissociate (ionize). At equilibrium, the number of dissociating H₂CO₃ molecules in Reaction 2 is equal to the number of associating HCO₃⁻ and H⁺, even though the concentrations of reactants and products are unequal. In this state, no further change occurs in [H₂CO₃], [HCO₃⁻], or [H⁺]. At equilibrium, the following is true:

[H+]×[HCO3−][H2CO3]=KA(Small) (3)

(3)

Where K_A is the equilibrium constant for H₂CO₃. (K_A is also known as the acid’s ionization or dissociation constant.)

K_A is small because the H₂CO₃ concentration is quite large with respect to the numerator of Reaction 3. The value of K_A is always the same for H₂CO₃ at equilibrium, regardless of the initial concentration of H₂CO₃.

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

[H+]×[Cl−][HCl]=KA(Large) (4)

(4)

As shown by Equations 3 and 4, K_A indicates the strength of an acid.

Buffer Solution Characteristics

A buffer solution resists changes in pH when an acid or a base is added to it. Buffer solutions are mixtures of acids and bases. The acid component is the H⁺ cation, formed when a weak acid dissociates in solution. The base component is the remaining anion portion of the acid molecule, known as the conjugate base. An important blood buffer system is a solution of carbonic acid and its conjugate base, HCO₃⁻:

H2CO3(Acid)⇄HCO3−(Conjugate base)+H+

In the blood, HCO₃⁻ combines with sodium ions (Na⁺) to form sodium bicarbonate (NaHCO₃). If hydrogen chloride, a strong acid, is added to the H₂CO₃/NaHCO₃ buffer solution, HCO₃⁻ reacts with the added H⁺ to form weaker carbonic acid molecules and a neutral salt:

HCl+H2CO3/Na+HCO3−→2H2CO3+NaCl

The strong acidity of HCl is converted to the relatively weak acidity of H₂CO₃, preventing a large decrease in pH.

Similarly, if sodium hydroxide, a strong base, is added to this buffer solution, it reacts with the carbonic acid molecule to form the weak base, NaHCO₃, and H₂O:

NaOH+H2CO3/NaHCO3→2NaHCO3+H2O

The strong alkalinity of NaOH is changed to the relatively weak alkalinity of NaHCO₃. pH change is minimized.

Bicarbonate and Nonbicarbonate Buffer Systems

Blood buffers are classified as bicarbonate or nonbicarbonate buffer systems. The bicarbonate buffer system consists of H₂CO₃ and its conjugate base, HCO₃⁻. The nonbicarbonate buffer system consists mainly of phosphates and proteins, including Hb. 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 H⁺ is buffered by HCO₃⁻, the product, H₂CO₃, is broken down into H₂O and CO₂ as long as ventilation removes CO₂. The removal of CO₂ from the reaction prevents it from reaching equilibrium with the reactants. For this reason, buffering activity can continue without being slowed or stopped:

HCO3−+H+→H2CO3→H2O+CO2(Exhaled gas)

A nonbicarbonate buffer system is called a closed buffer system because all the 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 H⁺ is buffered by Buf⁻, the product, HBuf, accumulates and eventually reaches equilibrium with the reactants, preventing further buffering activity:

Buf−+H+↔Hbuf

Box 13-1 summarizes the characteristics and components of bicarbonate and nonbicarbonate buffer systems.

Open and closed buffer systems play different roles in buffering fixed and volatile acids, and they differ in their ability to function in wide-ranging pH environments. Volatile acid (H₂CO₃) accumulates only if ventilation cannot eliminate CO₂ fast enough to keep up with the body’s CO₂ production. In such a case, the reaction between CO₂ and H₂O moves continually to the right, creating more H₂CO₃ and, ultimately, more H⁺ and HCO₃⁻. The HCO₃⁻ produced in this way is incapable of buffering the H⁺ with which it was coproduced. The only buffer system that can buffer the H⁺ of volatile acid is the nonbicarbonate buffer system. Both nonbicarbonate and bicarbonate buffer systems can buffer the H⁺ produced by fixed acids; this is true of the bicarbonate buffer system only if ventilation is not impaired and CO₂ can be adequately eliminated. Both systems are physiologically important, each playing a unique and essential role in maintaining pH homeostasis. Table 13-1 summarizes the approximate contributions of various blood buffers to the total buffer base. Bicarbonate buffers have the greatest buffering capacity because they function in an open system.

Bicarbonate and nonbicarbonate buffer systems do not function in isolation from one another but are intermingled in the same solution (whole blood), in equilibrium with the same [H⁺] (Figure 13-1). Increased ventilation increases the CO₂ removal rate, causing nonbicarbonate buffers (Hbuf) to release H⁺. Decreased ventilation ultimately causes Hbuf to accept more H⁺.

pH of a Buffer System: Henderson-Hasselbalch Equation

Buffer solutions in body fluids consist of mostly 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 the buffer’s components and the acid’s equilibrium constant are known. Consider the bicarbonate buffer system. As described earlier, the equilibrium constant (K_A) for H₂CO₃ is as follows:

KA=[H+]×[HCO3−][H2CO3]

[H⁺] can be calculated by algebraic rearrangement of this equation, as follows:

[H+]=KA×[H2CO3][HCO3]

[H⁺] is determined by the ratio between undissociated acid molecules [H₂CO₃] and base anions [HCO₃⁻]. This equation is the basis for deriving the Henderson-Hasselbalch (H-H) equation:

pH=6.1+log⁡[HCO3−]PaCO2×0.03

pH is a logarithmic expression of [H⁺], and the term 6.1 is the logarithmic expression of the H₂CO₃ equilibrium constant. Because dissolved carbon dioxide (Pco₂ × 0.03) is in equilibrium with and directly proportional to blood [H₂CO₃], and because blood Pco₂ is more easily measured than [H₂CO₃], dissolved CO₂ is used in the denominator of the H-H equation. The H-H equation is specific for calculating the pH of the bicarbonate buffer system of the blood. The calculation of this pH is important because it equals the pH of blood plasma; because all buffer systems in the blood are in equilibrium with the same pH, the pH of one buffer system is the same as the pH of the entire plasma solution (the isohydric principle).¹

Clinical Use of Henderson-Hasselbalch Equation

The H-H equation allows the pH, [HCO₃⁻], or Pco₂ to be computed if two of these three variables are known (shown as follows for Pco₂ and HCO₃⁻):

pH=6.1+log⁡[HCO3−]PaCO2×0.03

pH=6.1+log⁡[HCO3−]PaCO2×0.03

Blood gas analyzers measure pH and PCO₂ but compute [HCO₃⁻]. Assuming a normal arterial pH of 7.40 and a 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)

Solving for [HCO₃⁻]:

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

The H-H equation is useful for checking a clinical blood gas report to see if the pH, PCO₂, and [HCO₃⁻] values are compatible with one another. In this way, transcription errors and analyzer inaccuracies can be detected. It is also clinically useful to predict what effect changing one H-H equation component will have on the other components. For example, a clinician may want to know how low the arterial blood pH will fall for a given increase in PaCO₂.

Mini Clini

Applying the Henderson-Hasselbalch Equation in a Clinical Setting

 Problem

The respiratory therapist (RT) is caring for a mechanically ventilated patient. The patient has a tidal volume (V_T) of 800 ml and a breathing frequency of 10/min, yielding a minute ventilation () of 8 L/min. The patient’s PaCO₂ is 55 mm Hg, pH is 7.30, and bicarbonate is 26 mEq/L, and the therapist wishes to maintain a pH of 7.35. How much does the RT need to change the PaCO₂ to achieve this desired pH, and what change in the patient’s V_T does this require?

Solution

First, the therapist needs to calculate the PaCO₂ required to achieve a pH of 7.35 using the known values:

PaCO2=26 mEq/L0.03×antilog(7.35−6.1)

PaCO2=260.53

PaCO2=49 mm Hg

Next, the RT must calculate the required to produce a PaCO₂ of 49 mm Hg. Because is inversely proportional to PaCO₂, the following can be stated:

(V˙E)1×(PaCO2)1=(V˙E)2×(PaCO2)2

Where subscripts 1 and 2 represent current and future values. The RT then solves for ()₂ as follows:

(8L/min)×55 mm Hg=(V˙E)2×49 mm Hg

(8×55)49=(V˙E)2

8.98 L/min=(V˙E)2

Increasing the patient’s from 8 L/min to approximately 9 L/min yields a PaCO₂ of 49 mm Hg and a pH of approximately 7.35. Now the RT divides the new of 9 L/min by the respiratory frequency to calculate the new V_T required:

9 L/min/10=900 ml

A V_T of 900 mL at a rate of 10 breaths/min should produce an arterial pH of 7.35, according to the H-H equation.

Physiologic Roles of Bicarbonate and Nonbicarbonate Buffer Systems

The functions of bicarbonate and nonbicarbonate buffer systems are summarized in Table 13-2.

Bicarbonate Buffer System

The bicarbonate buffer system is particularly effective in the body because it is an open system—that is, one of its components (CO₂) is continually removed through ventilation:

(Exhaled gas)←CO2+H2O←H2CO3←HCO3−+H+

In this way, HCO₃⁻ continues to buffer H⁺ as long as ventilation continues. Hypothetically, this buffering activity can continue until all body sources of HCO₃⁻ are used up in binding H⁺.

The bicarbonate buffer system can buffer only fixed acid. An increased fixed acid load in the body (e.g., lactic acid) reacts with HCO₃⁻ of the bicarbonate buffer system:

As shown, the process of buffering fixed acid produces CO₂, which is eliminated in exhaled gas. Large amounts of acid are buffered in this fashion. If the ability to ventilate is impaired, this type of buffering cannot occur.

The bicarbonate buffer system cannot buffer carbonic (volatile) acid, which accumulates in the blood whenever ventilation fails to eliminate CO₂ as fast as it is produced (hypoventilation). The resulting accumulation of CO₂ drives the hydration reaction in the direction that produces more carbonic acid, H⁺, and HCO₃⁻, as shown:

H⁺ produced by dissociating H₂CO₃ molecules cannot be buffered by the simultaneously produced HCO₃⁻ because hypoventilation prevents the reaction from reversing its direction. The closed nonbicarbonate buffer systems are the only buffers that can buffer carbonic acid.

Nonbicarbonate Buffer System

Table 13-1 lists the nonbicarbonate buffers in the blood. Of these, Hb is the most important because it is the most abundant. As mentioned, 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 (Buf⁻/HBuf) function in closed systems, the products of their buffering activity eventually accumulate, slowing or stopping further buffering activity:

H++Buf−↔HBuf

This slowing or stopping of buffering activity means that not all of the Buf⁻ is available for buffering activity. At equilibrium (denoted by the double arrow), Buf⁻ still exists in solution but cannot combine further with H⁺. In contrast, most 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 does not occur. Both open and closed systems function in a common fluid compartment (blood plasma) as illustrated in the following equation:

Most of the added fixed acid is buffered by HCO₃⁻ because ventilation continually pulls the reaction to the left. Smaller amounts of H⁺ react with Buf⁻ because equilibrium is approached, slowing the reaction.

Lungs

Because the volatile acid H₂CO₃ is in equilibrium with dissolved CO₂, the lungs can decrease blood H₂CO₃ concentration through ventilation. The elimination of CO₂ is crucial because normal aerobic metabolism produces large quantities of CO₂, which reacts with H₂O to form large quantities of H₂CO₃. The reaction between fixed acids and bicarbonate buffers also produces H₂CO₃. H₂CO₃ generated by both pathways is eliminated as CO₂ through the lungs. Approximately 24,000 mmol/L of CO₂ is removed from the body daily through normal ventilation. CO₂ excretion of the lungs does not remove H⁺ from the body. Instead, the chemical reaction that breaks down H₂CO₃ to form CO₂ binds H⁺ in the harmless H₂O molecule:

H++HCO3−→