Partial Pressure in beaker of water

[mtc1973]

I have a little question regarding partial pressure. Partial pressure I understand fully, when we talk of an ideal gas mix. The partial pressure is product of the fractional concentration and the total barometric pressure. And in thinking in molecular terms that is like saying the amount of collisions between the gas molecules, for that single gas, and the container wall. Whereas the total barometric pressure is the sum of all collisions for all gases.
So my question is about partial pressure in e.g. a closed system like a sealed beaker of water.
Lets say the dissolved gases saturated the water (Henry's Law) and then we seal the system. So the partial pressure of the gases in the water are whatever the partial pressure of the gases were that were in contact with the liquid before it was sealed - let's assume full equilibration.
At the molecular level however, the partial pressure of the dissovled gases, is like the collisions between that gas and the container walls. Just like before. My question is therefore, why do we treat the water molecules differently - why do we not have a partial pressure for the water molecules? At a molecular level the collision of the water molecules with the container wall is no different to the collision of the dissolved gas components and the container wall. What is it about the state transition of water from a gas to a liquid that makes us not consider the collisions of the water molecules against the container wall when we talk of partial pressure?

Obviously we don't - since in a beaker of water - the vast majority of molecules are water - therefore the fractional concentration of water will be 99.9% and the partial pressure would be 99.9%. I understand that this is not the case - but why is it not? What am I fundamentally missing about liquid that we do not consider the molecular collisions?

 

[Mapes]

At the molecular level however, the partial pressure of the dissovled gases, is like the collisions between that gas and the container walls. Just like before.

The error in reasoning is here; the fraction of wall collisions in a liquid is not equivalent to partial pressure.

 

[mtc1973]

absolutely my point - but why?

Let me put it another way. If a water molecule finds itself in air - we consider that it has a partial pressure. At body temperature that is equivalent to 47 mm Hg. But as soon as that same water molecule finds itself surrounded by other water molecules in a liquid - its collisions are no longer considered to be a part of partial pressure. So I guess my question is - what are the conditions that need to be met to consider collisions contributing to partial pressure?

 

[Mapes]

A high partial pressure value means that the material is abundant and volatile. Water is abundant in a liquid solution of water and dissolved gases, but it is relatively non-volatile.

 

[mtc1973]

All accepted. But that still doesn't explain why. What is different about a volatile and non volatile particle collision, even when it is the same particle as in our example with a water molecule. Is it simply that there is an energy threshold? i

 

[mtc1973]

i.e the water molecule needs a minimum speed and momentum to be considered as contributing to partial pressure. And if so what is the fundamental difference between that collision and the high energy one? Is it a simple matter of the magnitude of energy transfer?

 

[mtc1973]

Also you said that the fraction if wall collisions in a luquid is not equivalent to partial pressure, so in a luquid what does constitute partial pressure? Or indeed is partial pressure just an abstracted idea when looking at a liquid, that's to say the partial pressure is just mass dissolved divided by solubility - giving a partial pressure - but not in the real sense if pressure as we know it in terms of wall collisions?

 

[mtc1973]

Bad spelling sorry! Itouch screen!

 

[Mapes]

Partial pressure is essentially the concentration of different components in the vapor above the liquid. The relative concentration in the liquid is measured by, well, the concentration. The reason why these values differ is that certain components tend to evaporate more readily than others. For example, the acetone vapor above liquid acetone has a higher pressure than the water vapor above liquid water, which has a much higher pressure than the copper vapor above solid copper. Does this make sense?

 

[mtc1973]

I get the situation in gas, no problem. My question arises because in medical physiology we do use partial pressure to refer to dissolved gas components in eg blood or alveolar fluid. Gas content or concentration is not used when we consider gas transport because dissolved gases travel down partial pressure gradients not concentration gradients. Granted this is usually not a problem, bur if compartments have wildly different oxygen solubilities they have wildly different concentrations bur no transport if there is no partial pressure gradient. So I was trying to figure what we are really referring to at a molecular level when we talk of partial pressure in a liquid. It can't be molecular collisions, and the more u think on it it must just be an abstracted idea of pressure from mass and solubility. But in molecular collusion terms not equivalent to partial pressure as occurs in a gas.

 

[mtc1973]

So for those interested in the answer to what a partial pressure is in a liquid - I finally found out.

Incidentally the reason we use partial pressure in biological systems is because the concentration or mass of a gas in a fluid does not tell us how gas will be transported between compartments. In biological systems dissolved gas concentrations become far less meaningful than partial pressure. Gas always travel down partial pressure gradients between biological compartments, gases may or may not travel down concentration gradients - hence why concentration is a useless index for gas transport in biological systems. We need to know the partial pressure of the dissolved gas in a liquid - because it is partial pressure gradients alone that define how gas moves between compartments, e.g. alveolar fluid and blood. An easy way to understand why concentration is irrelevant is this

imagine that we have 2 compartments exposed to 150 mm Hg of O2. One compartment is aqueous and one is oil/lipid based. Oil/lipid has a higher oxygen solubility than an aqueous compartment. So for 150 mm Hg the aqeous compartment may have a gas content of e.g. 0.45 ml per deciliter (medical units!) which is the PO2 x solubility (150 x 0.03 ml dl-1). In the lipid compartment the same PO2 gives us a content of e.g. 20.1 ml dl-1 (PO2 x solubility 150 x 0.134). i.e. it is the solubility term that strongly affects mass dissolved. However, there would be no gas transport between these compartments because both compartments have a PO2 of 150 mm Hg. A large concentration gradient exists, but no flux. Because once a compartment is saturated with as much oxygen it can hold - it is saturated! It can't take any more. So this is why partial pressure gradients in solution are so important. The only way to get gas to flow between compartments is to set up partial pressure gradients. So what is a partial pressure in solution phase -

well it is essentially the situation that would arise as follows, if a solution has a partial pressure of oxygen of e.g. PO2 150 mm Hg - by taking that solution into contact with gas with a PO2 of 150 mm Hg we would have no net movement of gas into or out of the solution - net flux = zero. And that is basically it. The partial pressure of gas in a liquid is the pressure at which there is not net transport of that gas from a gas phase into the liquid. So indeed - in gas phase partial pressure indicates the wall collisions for that gas as a fraction of the whole mix. For a liquid it is not the same. So in these terms a partial pressure in liquid has nothing to do with molecular events (unlike the situation for gas), all it is telling us is what partial pressure of gas that will give you a net flux of zero with your liquid compartment.

The real important thing to remember, is that biologically speaking - dissolved gas concentrations are a very poor predictor of gas transport. Use partial pressures.

 

[Mapes]

Nice!

Note that most generally, the chemical potential $\mu$ controls how substances diffuse: all substances diffuse down their chemical potential gradient, no exceptions. Continuing, the equation

$$\mu=\mu_0+RT\ln a$$

relates the chemical potential to the activity a, where a is a measure of "effective concentration" of a material. For gases, the activity is equivalent to the fugacity f normalized to a reference pressure, and the fugacity is equal to the partial pressure for ideal gases. So for ideal gases, we find a monotonic relationship between partial pressure and chemical potential.

 

[mtc1973]

Thanks mapes - I usually deal with charged particle movement hence you can expand your equation, as I'm sure you are perfectly aware, to include the electric potential too. One question though, in the situation where 2 compartments are fully saturated, surely we can have a standing chemical gradient without flux, ie the compartment is fully saturated and just can't accept more. Presumably then a corrective factor is included for the 'effective' concentration gradient.
Incidentally this whole partial pressure thing becomes critical to control anesthetic agents since most are volitive gases. And rather counterintuitively the best anesthetic agents are those with low solubility. Reason being that you can rapidly control partial pressure with a small flux of dissolved gas ie partial pressure rapidly equilibrates.
On a more general note - I'm not a physicist - I'd still like to learn why wall collisions are not equivalent in liquids.

 

[willians]

I'd still like to learn why wall collisions are not equivalent in liquids.

In an ideal gas there is no attraction between the particles (whether molecules or atoms). This gas can not become fluid, so the walls of the vessel that contains it suffer collisions. Let us create the abstraction of an ideal liquid: in this liquid, the attraction between the particles is such that there is no escape for the molecules to the gas phase, ie, its vapor pressure is zero. A certain mass of this liquid could float like a big drop in a cabin in zero gravity and the particles would not break away and thus they would not exert pressure on the walls of the cabin. Now reduce the size of the cabin until it becomes a container and its walls touch the liquid mass and you'll realize that the liquid in fact continues not to exert partial pressure on the walls. If a liquid is not ideal, there is a detachment of some molecules that collide with the walls and exert pressure on her, but that pressure is precisely the partial vapor pressure of the this liquid.

 

[willians]

[...]This gas can not become fluid[...]

The correct is: [...]This gas [the ideal gas] can not become liquid[...]