A steel container is filled with 5.00atm of nitrogen, 2.00atm of oxygen, and 0.50atm of argon. What is the total pressure in the vessel and the mole fraction of each gas?
Ptotal = pO2 + pAr + pN2.
XO2 = mols O2/total mols
XN2 = mols N2/total mols.
XAr = mols Ar/total mols.
To find the total pressure in the vessel, we need to add up the partial pressures of each gas. The partial pressure of a gas is the pressure exerted by that gas alone if it occupied the entire volume.
Given:
Partial pressure of nitrogen (P(N2)) = 5.00 atm
Partial pressure of oxygen (P(O2)) = 2.00 atm
Partial pressure of argon (P(Ar)) = 0.50 atm
Total pressure (P(total)) = P(N2) + P(O2) + P(Ar)
Substituting the given values:
P(total) = 5.00 atm + 2.00 atm + 0.50 atm
P(total) = 7.50 atm
Therefore, the total pressure in the vessel is 7.50 atm.
To find the mole fraction of each gas, we need to calculate the ratio of the moles of each gas to the total moles of gas in the vessel.
Mole fraction (X) of a gas = (moles of the gas) / (total moles of all gases)
To find the moles of each gas, we can use the ideal gas equation:
PV = nRT
Where:
P - pressure
V - volume
n - number of moles
R - ideal gas constant
T - temperature
Rearranging the equation to solve for n:
n = (PV) / (RT)
Given:
Pressure (P) = 7.50 atm
Volume (V) - Assume any volume or obtain the volume from the problem context
Temperature (T) - Assume any temperature or obtain the temperature from the problem context
First, calculate the moles of nitrogen (n(N2)):
n(N2) = (P(N2) * V) / (RT)
Substituting the given values:
n(N2) = (5.00 atm * V) / (RT)
Similarly, calculate the moles of oxygen (n(O2)) and argon (n(Ar)):
n(O2) = (P(O2) * V) / (RT)
n(Ar) = (P(Ar) * V) / (RT)
Once you have calculated the moles of each gas, you can find the total moles of gas (n(total)):
n(total) = n(N2) + n(O2) + n(Ar)
Finally, calculate the mole fraction of each gas:
X(N2) = n(N2) / n(total)
X(O2) = n(O2) / n(total)
X(Ar) = n(Ar) / n(total)
By finding the moles of each gas and applying the formulas above, you can determine the mole fraction of each gas in the steel container.