TBR Chem: Gases

[LuminousTruth]

What is observed over time if a mixture of H2 and D2 initially at 50% by moles H2, undergoes effusion through a small pore in the container?

A) PH2 decreases; XD2 decreases.
B) PH2 increases; XD2 decreases.
C) PD2 decreases; XD2 increases.
D) PD2 increases; XD2 increases.

The answer was "C"

I chose D. I thought P represented partial pressure. Since H2 leaves quicker than D2, there would be an increase in concentration of D2 and relative increase in partial pressure of D2 compared to H2. TBR says P is the absolute pressure. Isn't it supposed to represent partial pressure?

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[peacefulheart]

1. In this case, P is the absolute pressure and also partial pressure.

2. But, the sum of partial pressures of H2 and D2 is not equal to a constant. Actually, in this case, the Ptotal is decreased since both H2 AND D2 effused from the pole( Ptoal=PH2+PD2).

3. Thus, both partial pressures decrease.

thanks

 

[brood910]

1. In this case, P is the absolute pressure and also partial pressure.

2. But, the sum of partial pressures of H2 and D2 is not equal to a constant. Actually, in this case, the Ptotal is decreased since both H2 AND D2 effused from the pole( Ptoal=PH2+PD2).

3. Thus, both partial pressures decrease.

thanks

Sorry to bump this old topic, but I did not want to make another thread to ask the same question.

Doesnt Xtotal decrease as well though?
I do not understand how we are supposed to know that P is absolute pressure in this case when they didnt say a thing in the passage.

 

[Schenker]

P_H2 is the partial pressure of hydrogen gas, and P_D2 is the partial pressure of deuterium gas. Absolute pressure, or total pressure, is nowhere in the question. Peacefulheart meant that it doesn't matter which pressure quantity (P_H2, P_D2, or P_total) you think P stands for, as all three decrease anyways.

Unless the passage says differently, X_D2 is the mole fraction of D2, and X_H2 is the mole fraction of H2. Thus, X_total is always 1 by definition. Because H2 effuses through the hole more quickly than D2, X_H2 decreases while X_D2 increases; in other words, the gas mixture becomes enriched in D2, even though the molar quantities of both gases decrease.

 

[brood910]

I am still confused.

How can the partial pressure be different from the mole fraction when it is
nx/ntotal = px/ptotal?

 

[Schenker]

I am still confused.

How can the partial pressure be different from the mole fraction when it is
nx/ntotal = px/ptotal?

The sum of mole fractions of all compounds in the mixture must equal 1. This means if the mole fractions change for a two compound mixture, one mole fraction must increase (while the other one decreases), no matter what happens to the mixture.

Let's do a numerical example. Your nx/ntotal = px/ptotal condition stays satisfied throughout the example.

Say we have an equal mixture of compounds a and b, where na = 4, nb = 4, and thus ntotal = 8. Say pa = 2atm, pb = 2atm, and thus ptotal = 4atm. The mole fraction of compound a is 0.5 and so is the mole fraction of b.

Fast-forward in time after 1 mole of compound a has effused out and 3 moles of b have effused out. In other words, na = 3, nb = 1, and ntotal = 4. Half of the total mixture has effused out, so ptotal = 2atm, half as much as before. Since there is 3 times as much compound a as b, pa = 1.5atm, and pb = 0.5atm. The mole fraction of compound a is 0.75, and the mole fraction for compound b is 0.25.

In summary, the parameters for compound a change like so:

pa 2atm --> 1.5atm [decrease]
xa 0.5 ----> 0.75 [increase]​

 

[brood910]

Thank you so much!!

So for the question I asked, X of H2 will decrease and its pressure will decrease too, right?

 

[Schenker]

Yes, that's correct. Glad that helped!