Why does final total pressure = average of the pressure of each component?

[brood910]

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Why does final total pressure = average of the pressure of each component when the same volume of each gas was mixed? I thought Ptotal = P1 + P2 ?

 

[brood910]

bump

 

[brood910]

Anyone understands this? Or should I make my question clearer? It is from TPRH workbook.

 

[Itskinetic]

what number is it?

 

[brood910]

It is from TPRH science workbook (chem section). Passage #50 Q#3.
"Given that Flasks A and B have the same volume, which of the following gas mixtures did not react?"
The answer key says "In the case of inert mixture of gases, the final P within the apparatus should be equal to the avg of the pressure of each component. That is, Final total p = Pa + Pb/2 since the V of Flasks A and B are equal."

And since 620 + 450 = 1070. 1070/2 = 535 = final P of apparatus, F and N gases did not react.

Hm.. so my understanding of this so far is that Ptotal = Pa + Pb works only if gases react with each other? Otherwise, this equation does not work and we have to find avg of pressures?

Also, what if this question said DIFFERENT VOLUMES of the gases were mixed instead of the same volumes? How would you calculate the P?

 

[Itskinetic]

I actually just did this one like 15 minutes ago. So, the "Same volume" means the "same molar amount" when dealing with ideal gases (1 mol= 22.4 L).
What your missing in your equation is that Greek X that stands for mole fraction (moles of something/total moles). Ptotal= X1P1 + X2P2.. etc. so since the molar amounts are the same then you get 1/2P1 + 1/2 P2= Total pressure. Since the total pressure is just the same as would be predicted by this formula, then no reaction occurred. If something has more moles than something else, then you would expect that to contribute more to the total pressure then the other one.

 

[Itskinetic]

so thus its only an average in this scenario because the molar amounts/volumes are the same.

 

[brood910]

Where does the passage say the gases were under STP conditions tho?

 

[Itskinetic]

its not that its STP, its actually not STP because its not at 1 atm. But its an ideal gas-- you can assume that all gases are ideal unless its really low temperatures or really high pressure. this passage doesn't deal with low temperatures or really high pressures- so thus these are ideal gases and volume is proportional to number of moles.

 

[brood910]

I think it kinda makes sense now since for all ideal gases, volume fraction = mole fraction.
So, do I just assume that all gases are ideal unless the questions say otherwise?

Thanks a bunch btw. I cant believe I forgot to put mole fractions in front of pressures.

 

[Itskinetic]

ya that's what i've gathered. unless it specifically says non ideal or unless it says really low temperature or really high pressure. it would be pretty clear if there is some deviation from ideal gases.

 

[brood910]

Thanks!!