 by "Grog" (Alan W. Grogono), Professor Emeritus, Tulane University Department of Anesthesiology

# Interactive Henderson Equation ### Modified Henderson Equation

Henderson's equation quantifies the relationship between [H+], [HCO3-], and PCO2. In other words it performs precisely the same function as the more intimidating Henderson-Hasselbalch Equation. It does it, however, without using negative logarithms. It is, accordingly, much easier to understand:

#### PCO2 x k = [H+] x [HCO3–] "Without Hasselbalch the Equation is quite simple." No Hasselbalch! Click on the Blue Buttons for PCO2 and [H+]. As you adjust the PCO2, the SBE is held constant; when adjusting the [H+], the PCO2 is held constant.

 PCO2 40 × K 24 = [H+] 40 nanoEq/L × HCO3- 24 Canvas not supported!    pH 7.4 SBE 0 ### Henderson without the Hassel(balch) "Henderson really had it right - no logarithms." Henderson's Year: The year 1908 was a good year for acid-base balance - thanks to Henderson. In that year he appreciated the buffering power of CO2 and went on to apply the law of mass action to produce his simple formula which, rearranged, looks like this:

#### [H+] [HCO3–] = K [CO2] [H2O]

Simplification is possible because [H2O] remains constant and physicians are much more familiar with PCO2. This gives us the version used in the Interactive Equation:

#### [H+] [HCO3–] = k x PCO2

Easy to understand - most school children could grasp its meaning - which probably means that even medical students could, too (!) The simplicity, however, also guaranteed that it was of little "interest". Next year, 1909, was the start of a downhill slide: Sorensen introduced the negative logarithm (pH). This paved the way for Hasselbalch who in 1916 combined Henderson's excellent equation with Sorensen's pH to produce the dreaded Henderson-Hasselbalch equation.

Acid-base balance became instantly incomprehensible and, therefore, fascinating to teach. The new equation contained no extra information for physicians; it solved no medical problem; and it added nothing to our sum of acid-base physiology except obfuscation and unnecessary exam questions.

Three generations of doctors have endured the Henderson-Hasselbalch equation. It's time to make a stand. Enough! Play with the Modified Henderson Equation. Appreciate that it is the whole truth. If you must convert between pH and [H+], then do so, but do it in two simple steps. This way you may understand what you are doing:

1. Calculate the [H+] using the modified Henderson equation:

#### [H+] = K [CO2] / [HCO3–]

2. Take the negative logarithm of the [H+]

#### pH = - log [H+] Acid-Base Tutorial Alan W. Grogono Copyright Jan. 2020. All Rights Reserved 