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Topic: Constant pressure  (Read 6095 times)

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Offline Big-Daddy

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Constant pressure
« on: February 08, 2014, 10:31:36 AM »
(Let's assume T is constant always, here.) If a reaction produces some gases which are held at constant partial pressure, and you know the volume of gas produced, you can calculate the (approximate) number of moles produced of each gas just from the ideal gas equation.

If a reaction produces gases which are held at constant total pressure instead (and these are the only gases exerting any pressure), and you know the volume of each gas produced, is it possible to find the number of moles of each gas produced (ideal gas approximations are ok)?

Also, what if you are told that the gases are each at constant partial pressure and given their volumes produced, but not told what those partial pressures (for each gas) are. Am I right to think that it is impossible to find how many moles of a certain gas were produced, given the volume of that gas produced but without the value of the constant partial pressure of that particular gas?
« Last Edit: February 08, 2014, 10:56:52 AM by Big-Daddy »

Offline curiouscat

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Re: Constant pressure
« Reply #1 on: February 09, 2014, 03:47:22 AM »
If a reaction produces gases which are held at constant total pressure instead (and these are the only gases exerting any pressure), and you know the volume of each gas produced, is it possible to find the number of moles of each gas produced (ideal gas approximations are ok)?

Sure. PV=nRT

T, P are const.  & known. Given V you know n.

Where's the problem?

Offline Big-Daddy

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Re: Constant pressure
« Reply #2 on: February 09, 2014, 01:22:37 PM »
Sure. PV=nRT

T, P are const.  & known. Given V you know n.

Where's the problem?

P is neither constant nor known, at least not directly. Total pressure is kept constant, but multiple gases are being produced here so each will have some share of the total pressure, and their partial pressures need not (by the confines of the problem) necessarily be constant. (But we could predict it by Pgas=Ptotal*xgas where xgas is the mole fraction of this particular gas throughout the gaseous phase consisting of all produced gases.) Only the volumes of each of these gases produced and the total pressure of the system can be identified. (At least, that's one case.)

Another interesting case is if you know the value of total pressure and you know that each partial pressure is constant but not the value of that constant partial pressure for any of the gases. Can you work out n in either of these cases?

Offline curiouscat

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Re: Constant pressure
« Reply #3 on: February 09, 2014, 02:29:54 PM »

P is neither constant nor known, at least not directly. Total pressure is kept constant,

Without reading anything else, here itself is a contradiction.

P is total pressure in PV=nRT the way I use it. You say P is not constant. Then you say it is constant.

What is it exactly?

Offline Big-Daddy

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Re: Constant pressure
« Reply #4 on: February 09, 2014, 03:42:29 PM »

P is neither constant nor known, at least not directly. Total pressure is kept constant,

Without reading anything else, here itself is a contradiction.

P is total pressure in PV=nRT the way I use it. You say P is not constant. Then you say it is constant.

What is it exactly?

In my gaseous mixture, the total combined mixture of all gases, as they are produced, will be held at a constant overall pressure for the combined mixture, regardless of how much volume or how many moles of each gas comes out.

But there are multiple gaseous species being produced by the reaction in this case and there is no guarantee that the partial pressure of each species is constant. (Just that the sum of the partial pressures, which is equal to the total pressure of the gaseous phase consisting of multiple gaseous species, is constant and known.) What is n in your equation PV=nRT? The answer is, total number of moles of gas (because P must refer in your equation to total pressure of the system rather than partial pressure because as I have said partial pressure does not have to be constant). But that is not relevant to what I'm asking, which is number of moles of each gaseous species in the phase, and whether you can calculate it.

Offline Borek

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Re: Constant pressure
« Reply #5 on: February 09, 2014, 04:03:50 PM »
If a reaction produces gases which are held at constant total pressure instead (and these are the only gases exerting any pressure), and you know the volume of each gas produced

If you know partial volumes, you can calculate partial pressures.
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Offline curiouscat

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Re: Constant pressure
« Reply #6 on: February 09, 2014, 04:28:34 PM »
Why don't you address the specific contradiction I pointed out:

Quote
P is neither constant nor known, at least not directly. Total pressure is kept constant,

What gives?

Offline Big-Daddy

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Re: Constant pressure
« Reply #7 on: February 10, 2014, 03:30:04 PM »
If you know partial volumes, you can calculate partial pressures.

Bearing in mind we have to calculate ("partial", i.e. for each species) number of moles. That is not given, only partial volume is given, and the sum of all partial pressures is given and constant. Is it then solvable ...

Maybe we can write a PV=nRT type equation, substitute P(species)=Ptotal*n(Species)/(Σ(n(Species))) and then do this for each species, solve the simultaneous equations to get the values of n for each species? Is that a well-determined set of equations which will work.

Why don't you address the specific contradiction I pointed out:

Quote
P is neither constant nor known, at least not directly. Total pressure is kept constant,

What gives?

Is there a difference between total pressure of a gaseous mixture and the partial pressure exerted by one of the species in that mixture?

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