# How Is This Acid Base Map Established?

In the Acid-base map -shown below- each line denoted as an isohydric line shows the pairs of $$PCO_{2}$$ & $$[HCO_{3}^{-}]$$ that give a certain $$pH$$. So each line connects the values of $$PCO_{2}$$ & $$[HCO_{3}^{-}]$$ that give a value of $$pH$$ that is constant across that line..

The 7.4 line shows the isohydric line of physiological pH,the central ellipse shows the normal range.

I understand the Henderson–Hasselbalch equation:

$$\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}+\log _{10}\left(\frac{[\mathrm{Base}]}{[\mathrm{Acid}]}\right)$$

What I would like to know is how this map established either experimentally or mathematically or both preferably. The curves are rather obtained clinically, statistically evaluating diagnose, symptoms and results of clinical lab tests.

Metabolic curve follows malfunctioning metabolism keeping too low ( m. acidosis ) or too high ( m. alkalosis ) level of bicarbonate.

Respiratury curves follows states of too intense breathing ( r. alkalosis ) or too shallow breathing ( r. acidosis ), because of too low respectively high level of carbon dioxide partial pressure, caused by abnormal breathing.

Note that the $$K_{\ce{H, CO2}}$$ Henry constant or CO2 is $$\pu{29.41 atm/(mol/L)}$$. the value will be higher because of the body temperature, can be corrected by temperature dependent $$\ce{CO2}$$ solubility.

$$\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}+\log\left(\frac{[\mathrm{Base}]}{[\mathrm{Acid}]}\right)=\mathrm{p} K_{\mathrm{a}}+\log\left(\frac{[\ce{HCO3-}] \cdot K_{\ce{H, CO2}}}{p_{\ce{CO2}} }\right)$$

Where pKa of carbonic acid is 6.35, if counting the total $$\ce{CO2}$$ concentration.

There are 3 variables ( $$\mathrm{pH}$$, $$p$$, $$\ce{[HCO3-]}$$ ) and 2 degrees of freedom. $$\mathrm{p}$$ is controlled by breathing, $$\ce{[HCO3-]}$$ is controlled by metabolism. $$\mathrm{pH}$$ is result.

• Can the relationship between the 3 variables established mathematically? @Poutnik Oct 20 '20 at 12:15
• If we set a certain pH constant, how do we choose which other variable to make constant? @Poutnik Oct 20 '20 at 12:20
• What clinic state? @Poutnik Oct 20 '20 at 12:26
• Thanks for taking the time to answer, but I think the soluability should be multiplied by the PCO2 in the equation. Otherwise a great answer. @Poutnik Oct 20 '20 at 13:17
• [atm/(atm/(mol/L))]=[mol/L], so pCO2/KH = [CO2]. This KH is the pressure of CO2 needed to form CO2 solution 1 mol/L. Oct 20 '20 at 13:18