Why does nitrogen gas' pressure not change after an addition of helium

In summary, at the end of the 9-L vessel, there are 3 moles of helium and 3 moles of nitrogen at a pressure of 10 atm. Maintaining constant temperature, an additional 2 moles of helium are added. Assuming gases behave ideally, the partial pressure of nitrogen will increase by 5 atm and the partial pressure of helium will remain at 5 atm.
  • #1
dramadeur
19
0
a 9 L vessel contains 3 moles of helium and 3 moles of nitrogen at a pressure of 10 atm. Maintaining constant temperature, an additional 2 moles of helium are added. Assuming gases behave ideally, what are the partial pressures of nitrogen and helium at the end?

Initially there's: 3mol He/(3mol + 3mol) * 10 atm = 5 atm pressure of He
And: 3/6 * 10atm = 5 atm pressure of N2 as well

now that 2 moles of He are added to the vessel, why wouldn't N2's partial pressure increase? The way I see it, there are now more atoms, so more of them would knock on the walls, therefore pressure would increase overall, and since there are now more atoms, space between atoms is tightened, so ...
Anyway, overall pressure is P1/n1 = P2/n2
(10 atm/9 mol) = (P2/11 mol); P2 = 12.2 atm new total pressure
Partial PHe * Ptotal = 5/11 * 12.2 atm = 5.545 atm He
That's for He gas, but why shouldn't partial pressure change for N2 gas?
 
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  • #2
There are the same amount of nitrogen molecules so the nitrogen partial pressure does not change. Your total pressure is wrong. Where did 9 and 11 come from?
 
  • #3
This comes from the assumption of ideal gas behavior. The partial pressure of an ideal gas is the pressure of the same amount of the pure gas at the same temperature/volume as in the mixture. Ideal gases are assumed to have zero intermolecular interactions and particle volume, this greatly simplifies a lot of the mathematics and is a very good approximation to small (mon- and diatomic) gases at fairly low pressures. The greater the pressure or the larger the gas the greater the deviation from ideality which necessitates the use of "messy" http://www.chem.arizona.edu/~salzmanr/480a/480ants/VIRIAL/virial.html or Van der Waals equation to account for the intermolecular forces and non-negligible particle volume.

I'd recommend getting comfortable with the assumptions underlying the concept of an ideal gas.
 

1. Why does the pressure of nitrogen gas remain unchanged after adding helium?

The pressure of a gas is determined by its temperature, volume, and number of moles. When adding helium to a container of nitrogen gas, the temperature and volume remain constant, and the number of moles of nitrogen does not change. Therefore, the pressure of the nitrogen gas will not change.

2. How does the addition of helium affect the pressure of nitrogen gas?

The addition of helium does not directly affect the pressure of nitrogen gas. Rather, it dilutes the nitrogen gas, resulting in a lower partial pressure of nitrogen. However, the total pressure remains unchanged due to the ideal gas law (PV = nRT).

3. Why doesn't the pressure of nitrogen gas decrease when helium is added?

The pressure of nitrogen gas does not decrease because the addition of helium does not change the temperature, volume, or number of moles of nitrogen gas. These factors determine the pressure of a gas according to the ideal gas law.

4. Is the pressure of nitrogen gas affected by the addition of helium?

No, the pressure of nitrogen gas remains unchanged after adding helium. The only way to change the pressure of nitrogen gas in this scenario would be to change the temperature, volume, or number of moles of nitrogen gas.

5. How can the pressure of nitrogen gas remain constant after adding helium?

The pressure of nitrogen gas remains constant because, according to Dalton's law of partial pressures, the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas. In this case, the addition of helium decreases the partial pressure of nitrogen, but the total pressure remains constant due to the ideal gas law.

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