A mole of air (80% Nitrogen, and 20% Oxygen by volume) at 298.15K is brought into contact with liquid water which has a vapor pressure of 3168Pa at this temperature.
a) what is the volume of the dry air if the pressure is 1 bar?
b) what is the final volume of the air saturated with water vapor if the total pressure is maintained at 1 bar?
c) what are the mole fractions of N2, O2, and H20 in the moist air? Assume all gases are ideal
To solve these problems, we need to use the Ideal Gas Law and Dalton's Law of Partial Pressures.
a) To find the volume of the dry air, we can assume that the air is behaving ideally. 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.
Given that we have a mole of air, we can find the volume using the standard conditions at 1 bar of pressure:
P = 1 bar = 10^5 Pa (since 1 bar is equal to 10^5 Pa)
T = 298.15 K
We can rearrange the Ideal Gas Law equation to solve for V:
V = nRT / P
First, we calculate the number of moles of air. Since the mole fraction of nitrogen is 80% and oxygen is 20%, we can assume we have 0.8 moles of nitrogen and 0.2 moles of oxygen in one mole of air:
Number of moles of air = 0.8 moles N2 + 0.2 moles O2 = 1 mole
Using the given values, we can plug in the values and calculate the volume:
V = (1 mole) * (8.314 J/(mol·K)) * (298.15 K) / (10^5 Pa)
Converting from units of J to m^3 using the conversion factor (1 J = 1 Pa·m^3):
V = [(1 mole) * (8.314 J/(mol·K)) * (298.15 K)] / [(10^5 Pa) * (1 Pa·m^3 / 1 J)]
b) To find the final volume of the air saturated with water vapor, we need to consider the partial pressure of the water vapor. The total pressure is still 1 bar, so the partial pressure of water vapor will be:
Partial pressure of water vapor = Total pressure - Vapor pressure of water
Since the vapor pressure of water at 298.15 K is given as 3168 Pa, the partial pressure of water vapor is:
Partial pressure of water vapor = 1 bar - 3168 Pa
Using this partial pressure, we can use the Ideal Gas Law equation again to calculate the volume of the air saturated with water vapor.
c) To find the mole fractions of N2, O2, and H2O in the moist air, we need to calculate the moles of each gas and divide it by the total number of moles.
Number of moles of N2 = (Partial pressure of N2) / P * (Total number of moles of air)
Number of moles of O2 = (Partial pressure of O2) / P * (Total number of moles of air)
Number of moles of H2O = (Partial pressure of H2O) / P * (Total number of moles of air)
Then, we can find the mole fractions by dividing the number of moles of each component by the total number of moles in the moist air:
Mole fraction of N2 = (Number of moles of N2) / (Total number of moles of air)
Mole fraction of O2 = (Number of moles of O2) / (Total number of moles of air)
Mole fraction of H2O = (Number of moles of H2O) / (Total number of moles of air)
By following these steps, you can find the answers to the given questions a), b), and c).