## Henderson Hasselbalch Equation

The Henderson-Hasselbalch equation describes the relationship between Pco2 pH, and [HCO3-] in human blood as follows:

pH = 6.1 + log([HC0-]/0.03 -[PCO2), where [HCO-] is the bicarbonate concentration in millimoles per liter, and 0.03 PCO2 is the total dissolved CO2 concentration, also in millimoles per liter (0.03 mmol/L per mm Hg is the solubility of CO2 in water).

As described in Chapter 31, the Henderson-Hasselbalch equation is based on the chemical equilibrium between carbonic acid and its dissociation products:

The dissociation constant for a weak acid (Ka), like carbonic acid, is calculated from the law of mass action as:

By definition, pH = -log10[H+], and pKa = -log10(Ka). Therefore, taking the logarithm10 of both sides and rearranging the preceding equation results in a general form of the Henderson-Hasselbalch equation:

For human blood, pKa = 6.1, which is essentially constant in human blood under physiologic conditions, and [H2C03] = [0.03 • Pco2], because total carbonic acid is proportional to dissolved CO2 in blood.

The normal human value for arterial pH (pHa) is 7.4, and this can be calculated from the Henderson-Hasselbalch equation using other normal values. In human blood, pKa = 6.1, and it is essentially constant under physiologic conditions. Pco2 = 40 mm Hg and [HCO3-] = 24 mmol/L in normal arterial blood. Therefore:

pH = 6:1 + log(24/[0:03 • 40]) = 6.1 + log(20) =7:4:

At a normal arterial pH of 7.4, the [H+] is only 40 mmol/ L, or significantly less than many other important ions in the body, such as Na+, C1-, or HCO-, which occur in the millimole per liter range. Small changes in pH, corresponding to very small changes in [H+] (see Table 1 in Chapter 31), can lead to large changes in physiologic function. The effects of pH on organ function are discussed in individual chapters throughout this book.

The Henderson-Hasselbalch equation shows how the physiologic control of pH depends on the ratio of [HCO-] to [0.03 Pco2]. Notice that a normal pH of 7.4 could occur with a variety of [HCO-] and Pco2 values, so pH = 7.4 does not necessarily indicate normal acid-base status (see later discussion).

Arterial PCO2 (PaCO2) is determined by alveolar ventilation at any given metabolic rate (as described in Chapter 21). Increasing ventilation will decrease PaCO2 and increase pHa; decreasing ventilation will have the opposite effects. Therefore, ventilation is an extremely effective mechanism for changing pHa quickly, and ventilatory reflex responses to pH (described in Chapter 22) are the most important physiologic mechanisms for rapid control of pH. The kidneys can also control pH by changing [HCO-] independent of C02 changes, as described in Chapter 31. The kidneys process large amounts of [HCO-] filtered from the plasma, so blood [HCO-] depends on bicarbonate reabsorption and generation of new bicarbonate in renal tubules. Also, the kidneys are responsible for processing H+ from fixed acids (other than carbonic acid, which is considered a volatile acid because CO2 is a gas). Finally, renal processing of other ions, such as K+, can affect blood pH. Acid-base balance is described here in terms of the Henderson-Hasselbalch equation, but another approach emphasizes the control of pH by concentration differences between strong ions, such as sodium and chloride. Details on the strong ion approach to acid-base diagnosis can be found in the suggested readings listed at the end of this chapter.

### Bicarbonate-pH Diagram

The bicarbonate-pH diagram, also called a Hastings-Davenport diagram, illustrates the three primary variables in the Henderson-Hasselbalch equation (Fig. 6A). This diagram plots [HCO—] as a function of pH. The blue lines are called PCO2 isobars, and they show the various combinations of [HCO—] and pH values that can occur with any given Pco2. Moving along a Pco2 isobar shows how increasing [HCO—] buffers H+ ions and increases pH for a given amount of carbonic acid. Moving between Pco2 isobars shows how [HCO—] and pH change with changes in total carbonic acid. If carbonic acid is increased (moving from point A to B in Fig. 6A), then pH not only decreases, but the amount of base, i.e., [HCO—], increases also. Conversely, decreasing carbonic acid (point A to C in Fig. 6A) increases pH but decreases [HCO—]. This is a graphical alternative to the system of equations describing acid-base control in Chapter 31, and readers can use whichever method they find most helpful.

Respiratory pH changes result from changes in PCO2. Pure respiratory changes in pH occur along a blood-buffer line, shown as the dark line connecting points A-B-C in Fig. 6A. If the blood-buffer line is steeper, then pH will change less for a given change in acid (i.e., Pco2). Because hemoglobin is a major buffer of H+ in blood, increasing [Hb] causes the slope of the blood-buffer line to increase. Therefore, the slope of the blood-buffer line is steeper than the slope of the buffer line for plasma. However, the slope of the blood-buffer line measured in vivo, by sampling pHa in a person at different PaCO2 levels, is less than the in vitro slope, measured by changing PCO2 in a blood sample in a test tube. This is because the whole body includes interstitial fluid and other fluid compartments that do not contain hemoglobin and cannot buffer PCO2 changes as well as blood.

Metabolic pH changes refer to changes in [H+] and [HCO—] that are not caused by Pco2 changes. As described in Chapter 31, this generally involves renal processing of HCO3— and fixed acids. Pure metabolic changes in pH will shift the blood-buffer line up or down without changing its slope on the bicarbonate-pH diagram (moving between points A and D on Fig. 6A). Base excess is used to quantify the magnitude of a metabolic change in pH, and it equals the vertical displacement of the blood-buffer line. Conceptually,

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