# What does "partial pressure" mean in the setting of arterial CO₂?

I am currently learning renal physiology and was just introduced to the concept of partial arterial pressure of CO2, and I am a bit confused. I'll start with what I know and then move on to what I am confused about:

I believe that all the CO2 in the blood are dissolved in plasma. I think this is true because if it weren't, the effects on the body would be similar to that of the bends (decompression sickness), where gas bubbles form inside the blood. Am I correct on that?

And per a quick Google search, the consensus was that dissolved gases do not exert a pressure (it does expand the volume of the solvent a bit but the increase in pressure from that is negligible). In other words, 1 mole of gas that normally exerts 20 mmHg of pressure on a container would not increase the pressure of a liquid by 20 mmHg if it were dissolved within it.

So what I am wondering is, is the paCO2 the pressure that the dissolved CO2 would exert if it were removed from solution, and the volume kept the same? (The volume in this case would be the sum of the volume of all blood vessel lumens). Am I correct in my thinking?

You’re right that gases (including carbon dioxide) are mainly transported in solution. As you say, dissolved gasses do not exert a pressure. Your intuition about what partial pressure means in this context is almost correct.

# Partial Pressures

From the Deranged Physiology resource:

A dissolved gas, however, exerts no such pressure, and cannot be described in terms of manometry. However, following from Henry's law, the dissolved fraction exists in equilibrium with the gaseous fraction, and therefore for every tension, there is a corresponding partial pressure.

By convention we refer to gas tension of a solution as the partial pressure of a gas with which that solution is in equilibrium.

So the partial pressure of a gas in solution refers to the pressure of a gaseous phase with which it would be in equilibrium.

To clarify the term equilibrium, Henry’s Law states the following:

The amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant.

The point at which equilibrium is achieved depends on the solubility of the gas in that solvent.

Gases dissolve in liquids to form solutions. This dissolution is an equilibrium process for which an equilibrium constant can be written.

For example, the equilibrium between oxygen gas and dissolved oxygen in water is O2(aq) <=> O2(g). The equilibrium constant for this equilibrium is K = p(O2)/c(O2).

The above resource from Deranged Physiology is a very good primer on this concept in the context of biological systems: Partial pressure and the solubility of gases in biological systems.

# Carbon Dioxide Transport

To elaborate a little on carbon dioxide transport, it is actually transported by one of several means:

• Dissolved gas
• Bicarbonate
• Carbaminohemoglobin bound to hemoglobin (and other proteins)

Most of the carbon dioxide diffusing through the capillaries and ultimately into the red blood cells combines with water via a chemical reaction catalyzed by the enzyme carbonic anhydrase, forming carbonic acid.

Carbonic acid almost immediately dissociates into a bicarbonate anion (HCO3-) and a proton. Thus, bicarbonate is the primary means by which carbon dioxide is transported throughout the bloodstream according to the equation CO2 + H2O -> H2CO3 -> H+ + HCO3-.

Ooh, this is an interesting question. I'll try to go over each of your questions one by one here.

1. I believe that all the CO2 in the blood are dissolved in plasma. I think this is true because if it weren't, the effects on the body would be similar to that of the bends (decompression sickness), where gas bubbles form inside the blood. Am I correct on that?

Yes, all of the of of the CO2 in the blood is dissolved. Carbonic anhydrase helps to catalyze the reaction of CO2 into carbonic acid.

1. And per a quick Google search, the consensus was that dissolved gases do not exert a pressure (it does expand the volume of the solvent a bit but the increase in pressure from that is negligible). In other words, 1 mole of gas that normally exerts 20 mmHg of pressure on a container would not increase the pressure of a liquid by 20 mmHg if it were dissolved within it.

This statement is interesting. What you are missing here appears to be the difference between compressible and incompressible fluids. For all intents and purposes, almost all (if not all) liquids are incompressible. Incompressible fluids don't expand.

@Chris gave some good references regarding what a partial pressure is, and his descriptions are accurate. If you still need help with partial pressures though, try to think of them like this:

Gas A is in the top half of a container with liquid L. Initially, both are pure. Due to diffusion, A wants to be everywhere in the container, and so does L. As a result, A starts to mix in with L in the liquid stage by dissolving. Simultaneously, all of the molecules of L are jostling around in the bottom of the container, and some of them get kicked up into the air where they transition to a gaseous state and mix with A. These two processes continue until enough molecules of A are bouncing around, dissolved in the liquid that they kick a molecule out for every molecule that dissolves and vice-versa for L.

So, that's how partial pressures work for an ideal gas.

# Wait a second... IDEAL?

You caught me. CO2 is not an Ideal Gas. When it dissolves in water, it undergoes a reaction that results in carbonic acid.

In fact, it's not even close enough to an ideal gas that we can model it dissolving in water using our collection of laws for ideal gasses. It's slow to dissolve in water AND blood plasma, like really slow. That makes it hard for lifeforms to expel CO2 from their systems.

But life finds a way.

## Carbonic Anhydrase

The solution comes in the form of an enzyme called Carbonic Anhydrase. As I mentioned before, this enzyme helps by catalyzing the reaction of CO2 into carbonic acid and back again to CO2. By speeding up the reaction between CO2 and Carbonic Acid, our bodies are able to expel gaseous CO2 and keep respiration going.

## I lied again actually, it's story time with Catachan now:

I actually worked on a bit of similar research several years ago when I was a software engineer working on an ECMO system. I was trying to solve an issue we were having with our FeCO2 monitors needing to be recalibrated during heating or cooling of the patient. Temperature has a direct impact on the solubility of CO2 in the blood, and I spent ages looking for research papers that discussed the rate of dissolution of CO2 in the blood. I was hoping that I could expand on their models to include temperature, and then determine a rate for dissolution based on changes in temperature. I knew about the carbonic acid reaction, so I was sure that the ideal gas law wouldn't apply.

Here's the thing, I never could find any papers regarding the rate of CO2 dissolving in blood. It drove me nuts, so I started collecting my own data in our lab. It turned out that in normal water, the rate at which CO2 dissolves is fast enough that you can generally apply the ideal gas laws after all. I don't remember the specifics, I no longer have the raw data (I'm not with that company anymore, though it was fun), and honestly, even if I had the data, I'm not sure I could share it here due to IP reasons, but the numbers I recorded and my calculations matched the time based gas laws out to several decimal places. So I guess you can treat CO2 as an ideal gas when it comes to dissolving after all.

If anyone has some information related to the rate at which CO2 dissolves in water and/or blood and would like to correct me on this, please do. My failure to find proper references back then haunts me to this day.

• Hello Catachan, welcome to Medical Sciences. Answers here are expected to include references to back up claims and information in them. Please edit your answer to include your sources. Here is a list of reliable sources to get you started in case you need them. Apr 22 at 21:11