# The Henderson-Hasselbalch Equation (H-H)

H-H equation mathematically illustrates how the pH of a solution is influenced by the HCO_{3}^{–} to H_{2}CO_{3} ratio (the bicarbonate buffer system); the base to acid ratio

H-H equation is written as follows:

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

pK is 6:1 and, under normal conditions, the HCO_{3}^{–} to H_{2}CO_{3} ratio is 20:1

Clinically, the dissolved CO_{2} (PCO_{2} x 0.03) can be used for the denominator of the H-H equations, instead of the H_{2}CO_{3}

This is possible since the dissolved carbon dioxide is in equilibrium with, and directly proportional to, the blood [H_{2}CO_{3}], 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:

## H-H Equation Applied During Normal Conditions

When the HCO_{3}^{–} is 24 mEq/L, and the PaCO_{2} 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:

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

A HCO_{3}^{-} of 48 and a PCO_{2} of 80 would still give a ratio of 20/1

## H-H Equation Applied During Abnormal Conditions

When the HCO_{3}^{–} is 29 mEq/L, and the PaCO_{2} 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:

In contrast, when the HCO_{3}^{–} is 20 mEq/L, and the PaCO_{2} 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: