Lawrence Martin, MD, FACP, FCCP

4. Henderson-Hasselbalch Equation

Of the four equations in this paper, the Henderson-Hasselbalch is the one with which physicians are most familiar. The H-H equation is repeatedly emphasized in basic science courses and in renal and pulmonary pathophysiology lectures; students hear about it on many occasions.

The bicarbonate buffer system, quantitatively the largest in the extracellular fluid, instantaneously reflects any blood acid-base disturbance in one or both of its buffer components (HCO3- and PACO2). The ratio of HCO3- to PACO2 determines pH and therefore the acidity of the blood:


pH is the negative logarithm of the hydrogen ion concentration, [H+], in nM/L (nM = nanomole = 1 x 10-9 moles; pH 7.40 = 40 nM/L [H+]). Because of the negative logarithm, small numerical changes of pH in one direction represent large changes of [H+] in the other direction (Table II). An 0.1 unit fall in pH from 7.4 to 7.3 represents a 25% increase in [H+]; a similar percentage change in serum sodium would increase its value from a normal 140 mEq/L to 175 mEq/L!

TABLE II: pH and Hydrogen Ion Concentration
Blood pH [H+] (nM/L) % Change from normal
7.00 100 + 150
7.10 80 + 100
7.30 50 + 25
7.40 40
7.52 30 - 25
7.70 20 - 50
8.00 10 - 75

Unfortunately, the logarithmic nature of pH and the fact that acid-base disorders involve simultaneous changes in three biochemical variables and in the function of two organ systems (renal and respiratory), have all combined to made acid-base a difficult subject for many clinicians. In the 1970s nomograms incorporating the H-H variables and compensation bands for the four primary acid-base disorders were introduced as aids to determining a patient's acid-base status.3-8 While nomograms can be helpful if readily available and properly used, there is much to be gained by simply knowing the relationship among the three H-H variables and the type of changes expected with each disorder. In this regard the following items of clinical importance bear emphasis.

a) If any of the three H-H variables is truly abnormal the patient has an acid-base disturbance without exception. Thus any patient with an abnormal HCO3- or PaCO2, not just abnormal pH, has an acid-base disorder. Most hospitalized patients have at least one bicarbonate measurement as part of routine serum electrolytes; this is usually called the 'CO2' or 'total CO2' when measured in venous blood. (Total CO2 includes bicarbonate and the CO2 contributed by dissolved carbon dioxide, the latter 1.2 mEq/L when PaCO2 is 40 mm Hg. For this reason, and because bicarbonate concentration is slightly higher in venous than in arterial blood, total CO2 runs a few mEq/L higher than the bicarbonate value calculated using the H-H equation.) If total CO2 is truly abnormal the patient has an acid-base disorder. In Case 1 there were two sets of electrolyte measurements on the patient's chart when the sedative was ordered; both showed total CO2 elevated at 34 mEq/L. The patient had been taking a diuretic so it was probably assumed that her elevated total CO2 reflected a mild metabolic alkalosis. More likely, however, it represented chronic respiratory acidosis with renal compensation. When she arrived to the ICU her arterial blood gas showed pH 7.07, PaCO2 83 mm Hg, PaO2 55 mm Hg (breathing supplemental oxygen), HCO3- 23 mEq/L, values that reflected a worsening of previously- unrecognized respiratory acidosis plus a new metabolic acidosis (lactic acidosis from decreased organ perfusion). The patient's long smoking history and the physical findings suggested chronic obstructive lung disease (later confirmed by pulmonary function tests). Her anxiety prior to MICU transfer was related to worsening acidosis and dyspnea.

b) The simplified version of the H-H equation eliminates the log and the pK, and expresses the relationships among the three key values.


This version is sufficient for describing the four primary acid-base disturbances and their compensatory changes listed in
Table III. If the numerator is first to change the problem is either metabolic acidosis (reduced HCO3-) or metabolic alkalosis (elevated HCO3-); if the denominator is first to change the problem is either respiratory alkalosis (reduced PaCO2) or respiratory acidosis (elevated PaCO2).

TABLE III. The four primary acid-base disorders and their compensatory changes. The primary event leads to a large change in pH (larger arrows). Compensation (changes in HCO3- and PaCO2 represented by smaller arrows) attempts to normalize the ratio of HCO3-/PaCO2 and bring the pH back toward normal (smaller arrows next to pH). Each primary disorder may be caused by a variety of specific clinical conditions (see text).

Table III

c) By convention 'acidosis' and 'alkalosis' refer to in-vivo physiologic derangements and not to any change in pH. Each primary acid-base disorder arises from one or more specific clinical conditions, e.g., metabolic acidosis from diabetic ketoacidosis or hypoperfusion lactic acidosis; metabolic alkalosis from diuretics or nasogastric suctioning; etc. Thus the diagnosis of any primary acid-base disorder is analogous to diagnoses like "anemia" or "fever"; a specific cause must be sought in order to provide proper treatment. Because of the presence of more than one acid-base disorder ('mixed disorders') a patient with any acidosis or alkalosis may end up with a high, low or normal pH. For example, a patient with obvious metabolic acidosis from uremia could present with a high pH due to a concomitant metabolic alkalosis (which may not be as clinically obvious). Acidemia (low pH) and alkalemia (high pH) are terms reserved for derangements in blood pH only.

d) Compensation for a primary disorder takes place when the other component in the H-H ratio changes as a result of the primary event; these compensatory changes are not classified by the terms used for the four primary acid-base disturbances.9-10 For example, a patient who hyperventilates (lowers PaCO2) solely as compensation for metabolic acidosis does not have a primary respiratory alkalosis but simply compensatory hyperventilation. This terminology helps separate diagnosable and treatable clinical disorders from derangements in acid-base that exist only because of the primary disorder.

e) Compensatory changes for acute respiratory acidosis 11 and alkalosis,12 and metabolic acidosis 13,14 and alkalosis,15,16 occur in a predictable fashion, making it relatively easy to spot the presence of a mixed disorder in many situations. For example, single acid-base disorders do not lead to normal pH. Two or more disorders can be manifested by normal pH when they are opposing, e.g., respiratory alkalosis and metabolic acidosis in a septic patient. Although pH can end up in the normal range (7.35-7.45) in single disorders of a mild degree when fully compensated, a truly normal pH with abnormal HCO3- and PaCO2 should make one think of two or more primary acid-base disorders. Similarly, a high pH in a case of acidosis or a low pH in a case of alkalosis signifies two or more primary disorders.

f) Maximal respiratory compensation for a metabolic disorder takes about 12-24 hours and maximal renal compensation for a respiratory disorder takes up to several days. As a rule of thumb, in maximally compensated metabolic acidosis the last two digits of the pH approximate the PaCO2.17 For example, a patient with a disease causing uncomplicated metabolic acidosis over 24 hours' duration, whose pH is 7.25, should have a PaCO2 equal or close to 25 mm Hg. In metabolic alkalosis respiratory compensation is more variable and there is no simple relationship by which to predict the final PaCO2.16

CASE 2. A 31-year-old woman presented to the emergency room with mild diabetic ketoacidosis (DKA) and dyspnea; arterial pH was 7.25, PaCO2 34 mm Hg, HCO3- 16 mEq/L, blood sugar 475 mgm%. Her breathing difficulty was attributed to Kussmaul-type respirations characteristic of DKA. Judging her DKA non-critical, the admitting physician placed her on a general medical ward and began appropriate treatment with insulin and fluids. Four hours later she appeared more dyspneic; repeat blood gas showed pH 7.18, PaCO2 49 mm Hg, HCO3- 18, blood sugar 350 mgm%. She was transferred to MICU where she was noted to be wheezing; bronchodilator therapy was begun. Her pre-bronchodilator peak expiratory flow rate was 110 L/min, 25% of predicted. Two days later her ketoacidosis was fully corrected and peak flow was recorded at 350 L/min.
The mistake here was in not appreciating the patient's lack of appropriate hyperventilation for a state of ketoacidosis, and therefore in not diagnosing her respiratory impairment (she was not wheezing on arrival to ER). Similar cases have been reported in the literature.18

g) Acute, uncompensated respiratory alkalosis (acute hyperventilation) and acidosis (acute hypoventilation) cause predictable changes in pH and bicarbonate11,12 (Table IV). Bicarbonate increases slightly from the biochemical reaction of acutely retained CO2 and decreases when CO2 is acutely excreted;11,12 these changes are instantaneous and independent of any renal compensation. Extreme acute hyperventilation can lower the bicarbonate to about 15 mEq/L and extreme acute hypoventilation can raise it to about 29 mEq/L (Table IV); a bicarbonate value outside this range must indicate either a renal compensatory mechanism or a primary metabolic acid-base disorder. The biochemical changes in bicarbonate from acute shifts in PaCO2 point to another particularly useful clue to the presence of a mixed disorder: a higher- or lower-than- expected bicarbonate value with any change in PaCO2. Thus a slightly low HCO3- concentration in the presence of hypercapnia suggests a concomitant metabolic acidosis (e.g., PCO2 50 mm Hg, pH 7.27, HCO3- 22 mEq/L); a slightly elevated HCO3- in the presence of hypocapnia suggests a concomitant metabolic alkalosis (e.g. PCO2 30 mm Hg, pH 7.56, HCO3- 26 mEq/L).

TABLE IV. Changes in arterial pH and bicarbonate with acute changes in PaCO2. The ranges represent the 95% confidence limits for pH and bicarbonate when PaCO2 changes acutely (before any renal compensation takes place). Note that bicarbonate decreases with acute hyperventilation and increases with acute hypoventilation. (Data from references 11-12).

PaCO2 (mm Hg) pH HCO3-
15 7.61-7.74 15.3-20.5
20 7.55-7.66 17.7-22.8
30 7.45-7.53 21.0-25.6
40 7.38-7.45 22.8-26.8
50 7.31-7.36 24.1-27.5
60 7.24-7.29 25.1-27.9
70 7.19-7.23 25.7-28.5
80 7.14-7.18 26.2-28.9
90 7.13-7.09 26.5-29.2

h) The bicarbonate (or total CO2) should also be examined in relation to the other measured electrolytes, specifically to calculate the anion gap (AG). AG is the Na+ concentration minus (total CO2 + Cl-). The normal AG, 12 +/- 4 mEq/L, is an artifact of measurement since these three electrolytes are only the ones most commonly measured. (Since the value of K+ is small and relatively constant it is not usually used to calculate the AG; if K+ is used then the normal AG is about 16 +/- 4 mEq/L). If all the serum anions and cations were measured anions would equal cations and there would be no anion gap. The importance of the anion gap is that it can help both to diagnose the presence of a metabolic acidosis and characterize its cause. Thus, regardless of pH an elevated AG suggests a metabolic acidosis from unmeasured organic anions, e.g., lactic acidosis or ketoacidosis;19-21 the higher the AG the more likely it reflects an organic acidosis.19 On the other hand a normal AG in a patient with metabolic acidosis indicates a hyperchloremic acidosis, most commonly from renal or gastrointestinal bicarbonate loss, e.g., renal tubular acidosis or diarrhea.

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Copyright © 1996-2009 Lawrence Martin, M.D.