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Topic: Partial pressure and concentration  (Read 9788 times)

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Offline Big-Daddy

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Partial pressure and concentration
« on: May 18, 2013, 10:43:32 AM »
Is it correct to say, for any ideal gas, that

[tex]P_{gas} = M_{gas} \cdot RT \\[/tex]

As this seems to follow from the ideal gas equation.
(Pgas is the partial pressure of the gas, Mgas is the gas' molar concentration, R is the ideal gas constant, T is the absolute temperature)

Is the usual modification for non-ideality to rewrite this:

[tex]P_{gas} = M_{gas} \cdot γRT \\[/tex]

(γ is the activity coefficient.)

Offline billnotgatez

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Re: Partial pressure and concentration
« Reply #1 on: May 18, 2013, 11:30:27 AM »
I am curious
Did you derive this yourself using
PV=nRT
where
n=m/M

http://en.wikipedia.org/wiki/Ideal_gas_law

Offline Big-Daddy

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Re: Partial pressure and concentration
« Reply #2 on: May 18, 2013, 12:50:05 PM »
I am curious
Did you derive this yourself using
PV=nRT
where
n=m/M

http://en.wikipedia.org/wiki/Ideal_gas_law

As I explained, M is not Mr in my expression but rather molarity (molar concentration). I derived the expression from PV=nRT, n=MgasV. As for the activity coefficient thing, I read that somewhere and it seems to make sense.

Is this correct?

Offline curiouscat

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Re: Partial pressure and concentration
« Reply #3 on: May 18, 2013, 02:29:55 PM »

As I explained, M is not Mr in my expression but rather molarity (molar concentration).


The needless perils of non standard notation. Most of us use M for Mol Wt and c for molar concentration.

Offline curiouscat

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Re: Partial pressure and concentration
« Reply #4 on: May 18, 2013, 02:35:27 PM »

As I explained, M is not Mr in my expression but rather molarity (molar concentration). I derived the expression from PV=nRT, n=MgasV. As for the activity coefficient thing, I read that somewhere and it seems to make sense.

Is this correct?

I don't think I've seen activity coefficients used for a gas. I may be wrong.

Fugacity / Fugacity coefficient seems more like what you'd want.

Offline Big-Daddy

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Re: Partial pressure and concentration
« Reply #5 on: May 18, 2013, 06:56:03 PM »
Fugacity / Fugacity coefficient seems more like what you'd want.

I've seen a few websites use γ, but ok the overall point is the same. It's a constant with its own separate method of determination, usually temperature-dependent, such that PA=γRTcA (using the notation you want.)

The needless perils of non standard notation. Most of us use M for Mol Wt and c for molar concentration.

In general I could sympathize. I will use c generally in the future. But as you told me recently the most important thing is to define your units and be quantitative. Given that I wrote Mgas is the gas' molar concentration, directly under my formula, I don't think there was any ambiguity.

Offline billnotgatez

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Re: Partial pressure and concentration
« Reply #6 on: May 18, 2013, 08:15:53 PM »
I was confused thanks for the clarification

Offline curiouscat

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Re: Partial pressure and concentration
« Reply #7 on: May 18, 2013, 10:33:06 PM »
Fugacity / Fugacity coefficient seems more like what you'd want.

I've seen a few websites use γ, but ok the overall point is the same.


Which sites? Can you provide links?

I am curious to see how.

Offline Big-Daddy

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Re: Partial pressure and concentration
« Reply #8 on: May 19, 2013, 06:24:02 AM »
Which sites? Can you provide links?

http://www.life.illinois.edu/crofts/bioph354/thermo_eq.htm

They do not really explain what the activity coefficient γ is or how it's calculated, so it's quite possible that this is similar to what you meant by fugacity coefficient.

Offline Big-Daddy

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Re: Partial pressure and concentration
« Reply #9 on: May 21, 2013, 02:09:55 PM »
Is the principle correct? That, for a real gas, we are trying to work out a constant which mainly is dependent on temperature, and then we would write

[tex]P_{gas}=c_{gas} \cdot k(t) \cdot RT

Where k(t) is the constant, which is the function of temperature we need. I suppose this k(t) would be a fugacity coefficient, or could be something else, I'm not sure.

This then modifies the ideal gas conversion to a real gas conversion. k(t) could be a polynomial, then the more terms we add the more accurate the conversion will be (though more terms means more constants are needed too).

Is that right?

Edit: As an aside - and I'm expecting a 1-word answer really - is it ever possible for anything besides a gas (i.e. a liquid or solution) to contribute at all towards pressure in a system, or to have partial pressure? (If by "pressure" we mean what we normally mean when we talk about pressure.) I'm counting things like the vapour released from the surface as gases.

Offline curiouscat

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Re: Partial pressure and concentration
« Reply #10 on: May 21, 2013, 02:48:16 PM »


Edit: As an aside - and I'm expecting a 1-word answer really - is it ever possible for anything besides a gas (i.e. a liquid or solution) to contribute at all towards pressure in a system,


Yes. Liquids exert pressure too. Try Scuba Diving.

Offline Big-Daddy

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Re: Partial pressure and concentration
« Reply #11 on: May 21, 2013, 06:17:03 PM »
Liquids exert pressure too.

That's a different kind of pressure, isn't it? Not the sort of thing we would add to the pressure exerted by the gases. If we had a container with both gases and liquids inside it, do the liquids contribute at all to what we call "the pressure" inside the container? (Besides just decreasing the volume available to the gases) Or does "the pressure" usually refer to just the gases, when gases are present, with no contribution from anything in any other state?

Offline Corribus

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Re: Partial pressure and concentration
« Reply #12 on: May 21, 2013, 09:18:03 PM »
That's a different kind of pressure, isn't it? Not the sort of thing we would add to the pressure exerted by the gases. If we had a container with both gases and liquids inside it, do the liquids contribute at all to what we call "the pressure" inside the container? (Besides just decreasing the volume available to the gases) Or does "the pressure" usually refer to just the gases, when gases are present, with no contribution from anything in any other state?
Well for one thing, liquids exist in equilibrium with vapor, which contributes to the gas pressure.*

Pressure is any force divided by the area over which it is applied.  Liquids are condensed phases, and thus the intermolecular forces generally exceed the other forces involved in creating gas pressure.  Liquids and gasses are both fluids, though - in some ways you can think of a liquid as just a very nonideal gas.  However liquids still exert pressure on a container because of gravity, which tends to pull the fluid toward the earth.  (This is why there is enormous pressure against the walls of a hydroelectric dam and also why there is incredible pressure at the bottom of the ocean.) 

* Speaking of gas pressure, it is often said that the pressure is caused by collisions between moving gas molecules and the container walls.  Google "what causes gas pressure" and you'll see 99% of answers refer to such collisions, including previous topics here.  However this is actually a simplification of what causes the pressure of an ideal gas. Can you think of another explanation?

Hint: Remember pressure has to be caused by a force.   What force causes the pressure in an ideal gas?  If it helps, what "force" causes a gas to expand into any available space? (And yes the stock quotes are purposely placed.)
 
« Last Edit: May 21, 2013, 09:29:21 PM by Corribus »
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

Offline Big-Daddy

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Re: Partial pressure and concentration
« Reply #13 on: May 22, 2013, 05:02:20 AM »
Pressure is any force divided by the area over which it is applied.  Liquids are condensed phases, and thus the intermolecular forces generally exceed the other forces involved in creating gas pressure.  Liquids and gasses are both fluids, though - in some ways you can think of a liquid as just a very nonideal gas.  However liquids still exert pressure on a container because of gravity, which tends to pull the fluid toward the earth.  (This is why there is enormous pressure against the walls of a hydroelectric dam and also why there is incredible pressure at the bottom of the ocean.)


OK. So do we quantify this separately, e.g. as "liquid pressure"? If we have a container with both a liquid or mixture of liquids and gas(es), then do we have a separate "liquid pressure" and "gas pressure", the latter being what we normally refer to when in chemistry we say "pressure", where the gases do not at all affect the liquid pressure and the liquids do not affect the gas pressure? (Except for in the phase exchange equilibria, but even there, it's the gaseous molecules of vapor that affect the gas pressure, not the liquid, which plays no part.)

However this is actually a simplification of what causes the pressure of an ideal gas. Can you think of another explanation?

Hint: Remember pressure has to be caused by a force.   What force causes the pressure in an ideal gas?  If it helps, what "force" causes a gas to expand into any available space? (And yes the stock quotes are purposely placed.)

Not sure what you mean by force. Maybe the lack of attraction between the particles?

Offline Corribus

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Re: Partial pressure and concentration
« Reply #14 on: May 22, 2013, 10:08:31 AM »
OK. So do we quantify this separately, e.g. as "liquid pressure"?
Well I would say so.  If you want to know the total force acting on something, you add up all the different forces (and their vector directions).  I would think pressure little different.

Not sure what you mean by force. Maybe the lack of attraction between the particles?
What I mean is, for there to be pressure on the walls of the container, there has to be a force that pushes against them.  What is the force in this case?  We can say that it is collisions between the moving gas particles and the container walls, but this begs the question - what is causing gas molecules to collide against the walls?  Why do gasses expand outward?

Maybe it helps to consider that for an ideal gas, the energy does not depend on the volume.  It only depends on the temperature.  When you take a certain volume of ideal gas and cram it into a smaller volume at the same temperature, the internal energy does not change.  Yet the pressure (average force) goes up.  Why?  This would almost seem to be contradictory - if the energy of the gas doesn't increase as the volume decrease, how can the pressure increase?  What factor is missing that causes this "force"?

(Note that the energy of a REAL gas IS dependent on volume.  If you compress a real gas, the internal energy DOES change.  WHY?)
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

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