Use PV = nRT and calculate pressure for methane. Convert 8.00 (WHAT) to moles.
Do the same for 18.0 WHAT ethane.
Then partial pressure CH4 + partial pressure ethane + partial pressure unknown = 3 atm.
Do the same for 18.0 WHAT ethane.
Then partial pressure CH4 + partial pressure ethane + partial pressure unknown = 3 atm.
Step 1: Convert the given masses of each gas to moles.
The molar mass of methane (CH4) is 16.04 g/mol.
Number of moles of methane = mass of methane / molar mass of methane
= 8.00 g / 16.04 g/mol
≈ 0.499 mol
The molar mass of ethane (C2H6) is 30.07 g/mol.
Number of moles of ethane = mass of ethane / molar mass of ethane
= 18.0 g / 30.07 g/mol
≈ 0.598 mol
We don't have the mass of propane, but we can use the ideal gas law to find the number of moles of propane. The ideal gas law is given by the equation: 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.
Step 2: Convert the given total pressure to Kelvin.
Temperature in Kelvin = 23.0 °C + 273.15 = 296.15 K
Step 3: Use the ideal gas law to find the number of moles of propane.
(3.60 atm) * (10.0 L) = n(propane) * (0.0821 L.atm/mol.K) * (296.15 K)
n(propane) ≈ (3.60 atm * 10.0 L) / (0.0821 L.atm/mol.K * 296.15 K)
≈ 0.488 mol
Step 4: Calculate the partial pressure of each gas.
Total moles of gases = moles of methane + moles of ethane + moles of propane
≈ 0.499 mol + 0.598 mol + 0.488 mol
≈ 1.585 mol
Partial pressure of methane = (moles of methane / total moles of gases) * total pressure
≈ (0.499 mol / 1.585 mol) * 3.60 atm
≈ 1.135 atm
Partial pressure of ethane = (moles of ethane / total moles of gases) * total pressure
≈ (0.598 mol / 1.585 mol) * 3.60 atm
≈ 1.357 atm
Partial pressure of propane = (moles of propane / total moles of gases) * total pressure
≈ (0.488 mol / 1.585 mol) * 3.60 atm
≈ 1.108 atm
So, the partial pressure of methane, ethane, and propane in the container are approximately 1.135 atm, 1.357 atm, and 1.108 atm, respectively.