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
To calculate the partial pressures and mole fractions of Ar and N2 after the valve is opened, you can use the ideal gas law. The ideal gas law equation is:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's calculate the number of moles of Ar and N2 in each ball.
For the 1.0 L ball containing Ar at 5 atm:
P(Ar) = 5 atm
V(Ar) = 1.0 L
R = 0.0821 L·atm/(mol·K) (ideal gas constant)
T is not given, so assume it is constant.
Using the ideal gas law, we can rearrange the equation to solve for n(Ar):
n(Ar) = (P(Ar) × V(Ar)) / (R × T)
Next, let's calculate the number of moles of N2 in the 10.0 L ball:
P(N2) = 2 atm
V(N2) = 10.0 L
Using the ideal gas law, we can solve for n(N2):
n(N2) = (P(N2) × V(N2)) / (R × T)
Since the gases mix, the total number of moles is conserved. Therefore, we can add the moles of Ar and N2 to get the total moles in the mixture.
n(total) = n(Ar) + n(N2)
Now, we can calculate the partial pressures of Ar and N2 using the mole fractions. The mole fraction (X) of a component is defined as the ratio of moles of that component to the total moles:
X(Ar) = n(Ar) / n(total)
X(N2) = n(N2) / n(total)
Finally, we can calculate the partial pressures using the partial pressure equation:
P(partial) = X(partial) × P(total)
where P(partial) is the partial pressure of a component and P(total) is the total pressure.
To calculate the total pressure, you can sum the partial pressures of Ar and N2:
P(total) = P(Ar) + P(N2)
Let's now plug in the given values and calculate the answers:
A)
P(Ar) = X(Ar) × P(total) = (n(Ar) / n(total)) × P(total)
P(N2) = X(N2) × P(total) = (n(N2) / n(total)) × P(total)
B)
P(total) = P(Ar) + P(N2)
C)
To calculate the new total pressure when the mole fraction of Ar is increased to 0.5, you can adjust the number of moles of Ar and adjust the total pressure accordingly. The mole fractions and partial pressures of N2 will remain the same. Use the mole fraction equation to solve for n(Ar) when X(Ar) is 0.5. Then, calculate the new total pressure using the equation from part B.
P(new total) = P(Ar) + P(N2)
Let's now plug in the values and calculate the answers: