4 L of oxygen at a pressure of 400 Kpa and 1L of nitrogen at 200 Kpa were introduced in to 2 L vessel.

(A)What is the total pressure of the gases in the vessel.
(B)What is the mole fraction of each gas?

Use P1V1 = P2V2 to convert each gas from starting conditions to ending conditions in the 2L container.

a. Ptotal = pO2 + pN2.
b. XO2 = pO2/Ptotal
and XN2 = pN2/Ptotal.

To solve this problem, we need to use the ideal gas law and the concept of mole fraction.

The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin.

(A) To find the total pressure of the gases in the vessel, we need to add up the partial pressures of oxygen and nitrogen. The partial pressure of a gas is determined by multiplying the mole fraction of that gas by the total pressure.

The mole fraction of a gas is the ratio of the number of moles of that gas to the total number of moles of all the gases present.

Let's calculate the total number of moles of oxygen first:
Volume of oxygen (V_oxygen) = 4 L
Pressure of oxygen (P_oxygen) = 400 kPa

Using the ideal gas law:
n_oxygen = (P_oxygen * V_oxygen) / (R * T)

Now, let's calculate the total number of moles of nitrogen:
Volume of nitrogen (V_nitrogen) = 1 L
Pressure of nitrogen (P_nitrogen) = 200 kPa

Using the ideal gas law:
n_nitrogen = (P_nitrogen * V_nitrogen) / (R * T)

Next, we need to find the total number of moles of both gases:
n_total = n_oxygen + n_nitrogen

Now, we can calculate the mole fraction of each gas:
Mole fraction of oxygen (X_oxygen) = n_oxygen / n_total
Mole fraction of nitrogen (X_nitrogen) = n_nitrogen / n_total

Finally, to find the total pressure of the gases in the vessel, we multiply the mole fractions by the total number of moles and then sum up the partial pressures:
Total pressure (P_total) = (X_oxygen * n_total + X_nitrogen * n_total) * R * T / V_vessel

(B) Using the mole fractions calculated above, we can find the mole fraction of each gas.

Remember, the mole fraction is the ratio of the number of moles of a specific gas to the total number of moles of all gases present. So:

Mole fraction of oxygen = n_oxygen / n_total
Mole fraction of nitrogen = n_nitrogen / n_total

I hope this explanation helps you understand the steps to solve this problem.