How is the 0.03 Factor in the Henderson-Hasselbalch Equation Determined?

[Wek]

I'm given the following values: pH = 7.48, PO2 = 120mmHg, and PCO2 = 18mmHg.
I have to find the [HCO3] using these values. There's one thing I don't understand about the Henderson-Hasselbalch equation and that is how to calculate the [CO2]. I found out that [CO2] = 0.03*PCO2. My question is, what is the 0.03 that is multiplied to the PCO2 to get the [CO2] value?

One last thing, the pKa in the HH equation, is it of the HCO2?

Thanks

 

[Borek]

As far as I can tell pO₂ is irrelevant. You need to find concentration of H₂CO₃ (could be you are to assume it is identical with concentration of dissolved CO₂, that's a common approximation). Then you should use HH equation, pK_a1 describes equilibrium of the reaction

H₂CO₃ <-> H⁺ + HCO₃^-

and you have it either in your textbook or in any tables with Ka values.

 

[Wek]

Yes, I used the HH equation to find the [HCO3] and it came out to be 13. I' not given any concentration for CO2 or H2CO3. In this case, how would you be able to find the concentration of CO2 or even H2CO3, if its possible at all? The value I used for [CO2] was something I found on Cornell's website but it was not explain why they used that, which is what I'm asking.

 

[Borek]

Concentration of CO₂ is something that can be calculated - for known partial pressure - using Henry's law.

 

[DanP]

Yes, I used the HH equation to find the [HCO3] and it came out to be 13. I' not given any concentration for CO2 or H2CO3. In this case, how would you be able to find the concentration of CO2 or even H2CO3, if its possible at all? The value I used for [CO2] was something I found on Cornell's website but it was not explain why they used that, which is what I'm asking.

0.037 represents the solubility coefficient of C02 in plasma under physiological conditions. Units are mmol/mmHg/cc

Amount of C02 is a linear function of the product P(C02) and aforementioned solubility coefficient.
I believe pK is 6.1 in this case.

 

[Borek]

Amount of C02 is a linear function of the product P(C02) and aforementioned solubility coefficient.

That's Henry's law.

I believe pK is 6.1 in this case.

My tables give 6.4. It doesn't mean 6.1 is incorrect, could be that's value already corrected for the activity coefficients of all ions assuming ionic strength of plasma.