A 1.00-L gas sample at 100.°C and 611 torr contains 50.0% helium and 50.0% xenon by mass. What are the partial pressures of the individual gases?
Assume any mass you wish.
moles He = grams/molar mass
moles Xe = grams/molar mass.
total moles = moles He + moles Xe.
mole fraction He = moles He/total moles.
mole fraction Xe = moles Xe/total moles.
PHe = mole fraction He x 611.
PXe = moles fractiion Xe x 611.
Note: You may think this strange that you may use any convenient number for mass Xe and mass He but you can check this if you wish with the following:
Use PV = nRT and calculate n = total number moles. (But you don't know how to divide that since it's percent by mass and not percent by moles.)
After you have gone through the mole fraction and calculated the PHe and PXe, then use PV = nRT, and plug in P, V, R, an T and solve for n for EACH, then add the moles He and moles Xe and you will come out with the same number as total moles from the original PV = nRT.
To find the partial pressures of the individual gases, we'll first need to calculate the moles of helium and xenon in the gas sample.
1. Start with the given information:
- Volume of the gas sample (V) = 1.00 L
- Temperature (T) = 100°C = 373.15 K
- Total pressure (P) = 611 torr
2. Convert the temperature to Kelvin by adding 273.15:
T = 100°C + 273.15 = 373.15 K
3. Convert the mass percentages to masses:
Let's assume 100 grams of the gas sample, so:
- Mass of helium = 50.0% of 100 g = 50 g
- Mass of xenon = 50.0% of 100 g = 50 g
4. Calculate the moles of each gas, using their molar masses:
- Molar mass of helium (He) = 4.00 g/mol
- Molar mass of xenon (Xe) = 131.29 g/mol
Moles of helium (n_He) = Mass of helium / Molar mass of helium
= 50 g / 4.00 g/mol
= 12.5 mol
Moles of xenon (n_Xe) = Mass of xenon / Molar mass of xenon
= 50 g / 131.29 g/mol
= 0.38 mol
5. Now, we can calculate the partial pressures of each gas using the ideal gas law equation:
PV = nRT
For helium:
Partial pressure of helium (P_He) = n_He * R * T / V
For xenon:
Partial pressure of xenon (P_Xe) = n_Xe * R * T / V
Where:
- R is the ideal gas constant, which is equal to 0.0821 L·atm/mol·K
- T is the temperature in Kelvin
- V is the volume in liters
Let's substitute the values:
P_He = (12.5 mol) * (0.0821 L·atm/mol·K) * (373.15 K) / (1.00 L)
P_Xe = (0.38 mol) * (0.0821 L·atm/mol·K) * (373.15 K) / (1.00 L)
6. Calculate the partial pressures:
P_He = 3.11 atm
P_Xe = 0.09 atm
Therefore, the partial pressure of helium is 3.11 atm, and the partial pressure of xenon is 0.09 atm.