If four grams of Oxygen and four grams of Helium are placed in a five liter vessel at 338 K, what will be the partial pressure of each gas and the total pressure in the vessel?
Use PV = nRT to calculate pressure of each gas. n = grams/molar mass
Then Ptotal = pO2 + pHe
To find the partial pressure of each gas and the total pressure in the vessel, we need to use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature in Kelvin
First, let's calculate the number of moles for each gas using their respective molar masses:
For Oxygen (O2):
Molar mass of Oxygen (O2) = 32 g/mol
Number of moles of Oxygen (O2) = mass / molar mass = 4 g / 32 g/mol = 0.125 mol
For Helium (He):
Molar mass of Helium (He) = 4 g/mol
Number of moles of Helium (He) = mass / molar mass = 4 g / 4 g/mol = 1 mol
Now, let's calculate the partial pressures of each gas:
Partial pressure of Oxygen (PO2):
PO2 = (nO2 * R * T) / V
Substituting the values we have:
PO2 = (0.125 mol * 0.0821 L·atm/(mol·K) * 338 K) / 5 L ≈ 0.560 atm
Partial pressure of Helium (PHe):
PHe = (nHe * R * T) / V
Substituting the values we have:
PHe = (1 mol * 0.0821 L·atm/(mol·K) * 338 K) / 5 L ≈ 5.589 atm
Finally, to calculate the total pressure, we sum up the partial pressures of each gas:
Total pressure (Ptotal) = PO2 + PHe
Ptotal = 0.560 atm + 5.589 atm ≈ 6.149 atm
Therefore, the partial pressure of oxygen is approximately 0.560 atm, the partial pressure of helium is approximately 5.589 atm, and the total pressure in the vessel is approximately 6.149 atm.