Basic Concepts

PARTIAL PRESSURES

PV = nRT

Where P = pressure, V = volume, n = number of molecules, R = gas constant, T = temperature.

Before understanding partial pressures, we must first explore the properties of gases. Gases like to occupy a lot of space to move in. The larger the volume available to them, the more place they take. However, as the molecules of a gas move apart to fill a given volume, the pressure each molecule of gas exerts on the other molecules and on the container wall decreases. Thus, pressure is indirectly proportional to volume. This is very logical if we recall that pressure is defined as the force applied by a molecule per unit area.

It is important to remember that each gas molecule, regardless of its nature (ie. O2 or CO2) will exert the same amount of pressure in a given volume, as the other gas molecules next to it. The reason is that every gas has the same objective: to occupy as much volume as it can. Therefore, the molecules will share the given volume equally.

If you put 10 molecules of any gas in a closed container, the pressure in that container is proportional to the number of gas molecules.
Lets assume that pressure to be equal to 10.

Thus if you were to place 5 molecules of O2 and 5 molecules of CO2, the total pressure would still be equal to 10. However, should one want to calculate the exact pressure that only the O2 molecules are exerting, one would need to calculate the partial pressure of O2.

Remember that the pressure a gas exerts in a given volume is proportional to the number of molecules of that gas.

Therefore the partial pressure of O2, would be 5.

Now let's complicate the situation a little more. Let's put three different gases in a container the size of the earth.

The content of this large container is
21% O2
1%CO2
78% N2

The total pressure exerted by these gases is the atmospheric pressure, 760mmHg.

What would be the partial pressures of each of the different gases?

Partial Pressure of O2 = 21% * 760mmHg = 159.6mmHg

Partial Pressure of CO2 = 1% * 760mmHg = 7.6mmHg

Partial Pressure of N2 = 78% * 760mmHg = 592.8mmHg

Total Pressure = 760mmHg

Partial Pressures in a Liquid:

Now that we understand the idea of partial pressures of gases in air, lets explore the idea of partial pressures in a liquid.

According to what we have learned about pressures, we already understand that a gas, or any other fluid, is in constant search for equilibrium. Thus, a gas (or fluid) will flow from a higher pressure to a lower one, until an equilibrium is reached.

The same principle applies to gases going from air into a liquid. The gas will flow into the liquid until it is in equilibrium with the gas in the air.

One of the best examples of gas pressure in a liquid equalizing with the pressure of that gas in the air, is the example of a can of coke.
What happens when you open a can of coke? The CO2 that was compressed inside it, at a high pressure, will fizzle out of the liquid and into the air until an equilibrium is reached.

A pressure difference is not the only factor that determines the partial pressure of gases in liquids. Gas molecules place themselves in between liquid molecules according to their specific solubility in that liquid. Solubility is defined as the amount of solute (gas molecules) that can be dissolved in a given volume of solvent (liquid). Solubility of a gas refers to the number of molecules that can fit in the liquid. A high solubility gas will have more molecules dissolved in a liquid than a low solubility gas at the same partial pressure. Think about the low solubility gas a taking up a bit more space between the liquid molecules and so exerting a bit more pressure per molecule.

To best understand solubility, it is important to take into account a basic property of liquids. Liquids are incompressible. Therefore, liquids cannot be forced into a smaller volume. However, the molecules in a liquid are not as close together as the molecules in a solid and therefore, gas molecules can still place themselves between liquid molecules.
In fact, the number of gas molecules that will place themselves between liquid molecules depends on the solubility of that gas in that liquid. Oxygen is much more soluble in blood than in water because blood contains hemoglobin which is an ideal carrier of oxygen.

Thus, when we refer to the PO2 in blood, we are actually referring to the partial pressure of O2 in blood. The PO2 in blood will depend, among other things, on the partial pressure of O2 in air (21%) and on the solubility of O2 in blood.

It is important to understand that the number of gas molecules that are in a liquid depend both on the solubility of the liquid as well as the pressure in the container. The solubility of a gas in liquid is a property that does not change for a gas in a given liquid. Therefore the only way to increase the amount of gas molecules in a liquid is to increase the pressure. The best example of this is a can of coke. CO2 molecules are pumped into coke at a very high pressure and this allows for more CO2 molecules to enter the liquid. This does not mean that the solubility increased.

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