The Henderson-Hasselbalch Equation (H-H)

H-H equation mathematically illustrates how the pH of a solution is influenced by the HCO3 to H2CO3 ratio (the bicarbonate buffer system); the base to acid ratio

H-H equation is written as follows:

hh equa.jpg

pK is derived from the dissociation constant of the acid portion of the buffer combination

pK is 6:1 and, under normal conditions, the HCO3 to H2CO3 ratio is 20:1

Clinically, the dissolved CO2 (PCO2 x 0.03) can be used for the denominator of the H-H equations, instead of the H2CO3  

This is possible since the dissolved carbon dioxide is in equilibrium with, and directly proportional to, the blood [H2CO3], the PaCO2 is easily measured via blood gas analysis and can easily be converted to mmol/L (same as mEq/L).

Thus, the H-H equation can be written as follows:

hh2.jpg

H-H Equation Applied During Normal Conditions

When the HCO3 is 24 mEq/L, and the PaCO2 is 40 mm Hg, the base to acid ratio is 20:1 and the pH is 7.4 (normal). 

H-H equation confirms the 20:1 ratio and pH of 7.4 as follows:

app HH.jpg

The ratio is the important factor, not the individual concentrations.

A HCO3- of 48 and a PCO2 of 80 would still give a ratio of 20/1

H-H Equation Applied During Abnormal Conditions

 When the HCO3 is 29 mEq/L, and the PaCO2 is 80 mm Hg, the base to acid ratio decreases to 12:1 and the pH is 7.18 (acidic) 

H-H equation confirms the 12:1 ratio and the pH of 7.18 as follows:

 

abn hh.jpg

In contrast, when the HCO3 is 20 mEq/L, and the PaCO2 is 20 mm Hg, the base to acid ratio increases to 33:1 and the pH is 7.62 (alkalotic) 

H-H equation confirms the 33:1 ratio and the pH of 7.62 as follows:

abn hh alk.jpg