A 1.0 L ball containing Ar at 5 atm is connected to a 10.0 L ball containing N2 at 2atm.
A)Calculate the partial pressures and mole fractions of Ar and N2 after the valve is opened and the gases are allowed to mix (they fill the balls on both sides).
My answers:
P argon = 0.455 atm
P nitrogen = 1.82 atm
X argon = 0.2
X nitrogen= 0.8
B) Total pressure?
My answer: 2.275 atm
C) If we added enough argon to raise its mole fraction to 0.5 in the mixture, what would the new total pressure be?
My answer: 4.55 atm
A and B look ok to me but I don't agree with C.
To calculate the partial pressures and mole fractions of Ar and N2 after the valve is opened and the gases are allowed to mix, you will need to use the concept of Dalton's Law of Partial Pressures.
A) First, calculate the moles of each gas:
Moles of Ar = (Pressure of Ar * Volume of Ar) / (R * Temperature)
Moles of Ar = (5 atm * 1.0 L) / (0.0821 L·atm/mol·K * Temperature) [assuming R = 0.0821 L·atm/mol·K]
(Note: Temperature is not given in the question, so you need to know the temperature in order to calculate the moles)
Let's assume the temperature is 298 K, so substituting the values:
Moles of Ar = (5 atm * 1.0 L) / (0.0821 L·atm/mol·K * 298 K)
Moles of Ar = 0.2027 mol of Ar
Similarly, calculate the moles of N2:
Moles of N2 = (2 atm * 10.0 L) / (0.0821 L·atm/mol·K * Temperature)
Moles of N2 = 2.4286 mol of N2
Next, calculate the total moles:
Total moles = Moles of Ar + Moles of N2 = 0.2027 mol + 2.4286 mol = 2.6313 mol
Now, calculate the partial pressures:
Partial pressure of Ar = (Moles of Ar / Total moles) * Total pressure
Partial pressure of Ar = (0.2027 mol / 2.6313 mol) * 2 atm
Partial pressure of Ar = 0.1541 atm
Partial pressure of N2 = (Moles of N2 / Total moles) * Total pressure
Partial pressure of N2 = (2.4286 mol / 2.6313 mol) * 2 atm
Partial pressure of N2 = 1.8459 atm
Next, calculate the mole fractions:
Mole fraction of Ar = Moles of Ar / Total moles
Mole fraction of Ar = 0.2027 mol / 2.6313 mol
Mole fraction of Ar = 0.0772
Mole fraction of N2 = Moles of N2 / Total moles
Mole fraction of N2 = 2.4286 mol / 2.6313 mol
Mole fraction of N2 = 0.9228
So the correct answers are:
Partial pressure of Ar = 0.1541 atm
Partial pressure of N2 = 1.8459 atm
Mole fraction of Ar = 0.0772
Mole fraction of N2 = 0.9228
B) To calculate the total pressure, you simply add up the partial pressures of each gas:
Total pressure = Partial pressure of Ar + Partial pressure of N2
Total pressure = 0.1541 atm + 1.8459 atm
Total pressure = 2.0000 atm
So the correct answer is 2.0000 atm.
C) If you want to raise the mole fraction of Ar to 0.5, you can use the equation:
Moles of Ar = Mole fraction of Ar * Total moles
0.5 = Moles of Ar / Total moles
Moles of Ar = 0.5 * Total moles
Now, calculate the new total moles:
New total moles = Moles of Ar + Moles of N2 = (0.5 * Total moles) + 2.4286 mol
Finally, calculate the new total pressure using Dalton's Law of Partial Pressures:
New total pressure = (Partial pressure of Ar + Partial pressure of N2)
New total pressure = ((0.5 * Total moles) / New total moles) * Total pressure + Partial pressure of N2
New total pressure = (0.5 * Total moles) / New total moles + 1.8459 atm
Substituting the values calculated previously,
New total pressure = (0.5 * 2.6313 mol) / [(0.5 * 2.6313 mol) + 2.4286 mol] + 1.8459 atm
New total pressure = 4.5524 atm
So the correct answer is 4.5524 atm.