What is the PCO2 if the dissolved carbon dioxide (dCO2) is 1.8 mmol/L?

To determine the partial pressure of carbon dioxide (PCO2) from the concentration of dissolved carbon dioxide (dCO2), we can use the relationship defined by Henry's law. This law states that the amount of gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid.

The relationship can be expressed as:

[ PCO2 = k_H \times dCO2 ]

where ( k_H ) is the solubility coefficient of carbon dioxide in plasma. For carbon dioxide at body temperature, the solubility coefficient is approximately 0.03 mmol/L/mm Hg.

Now, using the provided value of dCO2 (1.8 mmol/L), we can substitute it into the equation:

[ PCO2 = \frac{dCO2}{k_H} ]

Substituting the known values:

[ PCO2 = \frac{1.8 , \text{mmol/L}}{0.03 , \text{mmol/L/mm Hg}} ]

Calculating this gives:

[ PCO2 = 60 , \text{mm Hg} ]

This indicates that when the dissolved carbon dioxide is at 1.8 mmol/L