Two gases are mixed in a 10.0L fixed volume flask: 8.0 L of O2 at 2.00 atm and 2.0 L of N2 at 3.00 atm.

A) Calculate the partial pressure for each gas and the total pressure.

I got ...
PO2 = 1.60 atm
PN2= 0.600 atm

B) How much (volume in liters) argon at 5.0 atm must be added to the 10.0 L flask to lower the mole fraction of oxygen to 1/2 ( i.e., to get XO2=0.5)?
Hint: maybe it is easier to do part C first?

C) What is the total pressure from part B (Ar, O2, N2)?

See your post above.

To calculate the partial pressure of each gas and the total pressure, you can use the ideal gas law equation:

PV = nRT

Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature

A) For the given conditions, you have 8.0 L of O2 at 2.00 atm and 2.0 L of N2 at 3.00 atm. To calculate the partial pressure of each gas, you can use the formula:

Partial Pressure = (Volume of Gas / Total Volume) * Total Pressure

1. For O2:
Partial Pressure of O2 = (8.0 L / 10.0 L) * 2.00 atm = 1.60 atm

2. For N2:
Partial Pressure of N2 = (2.0 L / 10.0 L) * 3.00 atm = 0.600 atm

Therefore, the partial pressure of O2 is 1.60 atm and the partial pressure of N2 is 0.600 atm. The total pressure is the sum of the partial pressures of both gases, so:

Total Pressure = Partial Pressure of O2 + Partial Pressure of N2 = 1.60 atm + 0.600 atm = 2.20 atm

B) Now, to calculate how much argon at 5.0 atm must be added to the 10.0 L flask to lower the mole fraction of oxygen to 1/2, you need to calculate the mole fraction of oxygen (XO2) before adding argon.

The mole fraction of a gas is given by the formula:

XO2 = (moles of O2) / (total moles of all gases)

Since the volume and pressure are constant, the number of moles is directly proportional to the partial pressure. Therefore, the mole fraction of oxygen can be calculated as:

XO2 = (Partial Pressure of O2) / (Total Pressure)

From part A, we know the partial pressure of O2 is 1.60 atm and the total pressure is 2.20 atm. Therefore:

XO2 = 1.60 atm / 2.20 atm = 0.727

To achieve a mole fraction of oxygen (XO2) of 0.5, you need to subtract the desired mole fraction from 1:

1 - 0.5 = 0.5

The final mole fraction of argon (XAr) would be 0.5. Now we can set up a proportion:

XAr = (moles of Ar) / (total moles of all gases)

Since the volume and pressure are constant, the number of moles is directly proportional to the partial pressure. Therefore, the mole fraction of argon can be calculated as:

XAr = (Partial Pressure of Ar) / (Total Pressure) = (5.0 atm) / (Total Pressure)

To solve for the total pressure, we set up a proportion:

0.5 = (5.0 atm) / (Total Pressure)

Cross multiplying, we get:

Total Pressure = (5.0 atm) / 0.5 = 10 atm

C) The total pressure from part B is 10 atm (which includes the argon, oxygen, and nitrogen gases).