# Henderson-Hasselbalch equation

**Editor-In-Chief:** C. Michael Gibson, M.S., M.D. [2]; **Associate Editor(s)-in-Chief: ** Rim Halaby, M.D. [3]

## Overview

In chemistry, the Henderson-Hasselbalch (frequently misspelled Henderson-Hasselbach) equation describes the derivation of pH as a measure of acidity (using pK_{a}, the acid dissociation constant) in biological and chemical systems. The equation is also useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid-base reactions (it is widely used to calculate isoelectric point of the proteins).

## Historical Perspective

Lawrence Joseph Henderson wrote an equation, in 1908, describing the use of carbonic acid as a buffer solution.^{[1]} Hasselbalch was using the formula to study metabolic acidosis, which results from carbonic acid in the blood.

## Henderson-Hasselbalch equation

Two equivalent forms of the equation are

pH = pK_{a} + log ([A^{-}]/[HA]) |

and

pH = pK_{a} + log ([Base]/[Acid]) |

Here, pK_{a} is -log K_{a} where K_{a} is the acid dissociation constant, that is:

pK_{a} = -log K_{a} = -log ([H_{3}O^{+}][A^{-}]/[HA]) |

for the non-specific Brønsted acid-base reaction:

HA + H_{2}O ↔ A^{-} + H_{3}O^{+} |

In these equations, A^{-} denotes the ionic form of the relevant acid. Bracketed quantities such as [Base] and [Acid] denote the molar concentration of the quantity enclosed.

In analogy to the above equations, the following equation is valid:

pOH = pK_{b} + log ([BH+]/[B]) |

where B+ denotes the salt of the corresponding base B.

## Derivation

The Henderson–Hasselbalch equation can be applied to relate the pH of blood to constituents of the bicarbonate buffering system:^{[2]}

pH = pK_{a}_{H2CO3} + log ([HCO_{3}^{-}]/[H_{2}CO_{3}]) |

Taken together, the following equation can be used to relate the pH of blood to the concentration of bicarbonate and the partial pressure of carbon dioxide:

pH = 6.1 + log {[HCO_{3}^{-}]/(0.03 x PCO_{2})} |

where pH is the acidity in the blood, [HCO_{3}-] is the concentration of bicarbonate in the blood, and pCO_{2} is the partial pressure of carbon dioxide in the blood. For clinical application, the equation can be simplified as:

[H^{+}] (nmol/L) x [HCO_{3}^{-}] (mmol/L) = 24 x PCO_{2} (mm Hg) |

## Limitations

There are some significant approximations implicit in the Henderson-Hasselbalch equation. The most significant is the assumption that the concentration of the acid and its conjugate base at equilibrium will remain the same as the formal concentration. This neglects the dissociation of the acid and the hydrolysis of the base. The dissociation of water itself is neglected as well. These approximations will fail when dealing with relatively strong acids or bases (pKa more than a couple units away from 7), dilute or very concentrated solutions (less than 1 mM or greater than 1M), or heavily skewed acid/base ratios (more than 100 to 1).

## See also

## External links

- Henderson-Hasselbalch Calculator
- Derivation and detailed discussion of Henderson-Hasselbalch equation
- True example of using Henderson-Hasselbalch equation for calculation net charge of proteins

## Further reading

- Lawrence J. Henderson (1 May 1908). "Concerning the relationship between the strength of acids and their capacity to preserve neutrality" (Abstract).
*Am. J. Physiol.***21**(4): 173–179. - Hasselbalch, K. A. (1917). "Die Berechnung der Wasserstoffzahl des Blutes aus der freien und gebundenen Kohlensäure desselben, und die Sauerstoffbindung des Blutes als Funktion der Wasserstoffzahl".
*Biochemische Zeitschrift*.**78**: 112–144. - Po, Henry N.; Senozan, N. M. (2001). "Henderson–Hasselbalch Equation: Its History and Limitations".
*J. Chem. Educ.***78**(11): 1499–1503. Bibcode:2001JChEd..78.1499P. doi:10.1021/ed078p1499. - de Levie, Robert. (2003). "The Henderson–Hasselbalch Equation: Its History and Limitations".
*J. Chem. Educ.***80**(2): 146. Bibcode:2003JChEd..80..146D. doi:10.1021/ed080p146. - de Levie, Robert (2002). "The Henderson Approximation and the Mass Action Law of Guldberg and Waage".
*The Chemical Educator*.**7**(3): 132–135. doi:10.1007/s00897020562a.

## References

- ↑ Karl Albert Hasselbalch later re-expressed that formula in logarithmic terms, resulting in the Henderson-Hasselbalch equation [1]
- ↑ Henderson Hasselbalch Equation: Derivation of pKa and pKb