A 500 mL flask has a measured volume of 586.0 mL. A 0.608g sample of an unknown vapor occupies the flask at 373K at a pressure of 0.981atm. Assume the vapor behaves ideally. What is the molecular weight of the unknown vapor?
Use PV = nRT and solve for n = number of mols. Then n = grams/molar mass. You know mols and grams, solve for molar mass.
To find the molecular weight of the unknown vapor, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
In this case, we know the following values:
- Pressure (P) = 0.981 atm
- Volume (V) = 586.0 mL = 0.586 L
- Temperature (T) = 373 K
- Gas constant (R) = 0.0821 L·atm/(K·mol) (this is a common value used in many calculations)
We need to solve for the number of moles (n) using the ideal gas law equation.
Step 1: Convert the volume from milliliters to liters.
0.586 L = 586.0 mL ÷ 1000
Step 2: Plug the values into the ideal gas law equation.
0.981 atm * 0.586 L = n * 0.0821 L·atm/(K·mol) * 373 K
Step 3: Simplify the equation.
0.574266 atm·L = n * 30.7033 L·atm/(K·mol)
Step 4: Solve for n (number of moles).
n = 0.574266 atm·L / 30.7033 L·atm/(K·mol)
Step 5: Calculate the number of moles (n).
n ≈ 0.0187 mol
Step 6: Calculate the molecular weight (M) using the formula: M = mass / moles.
Given that the mass of the sample is 0.608 g:
M = 0.608 g ÷ 0.0187 mol
Step 7: Calculate the molecular weight.
M ≈ 32.6 g/mol
Therefore, the molecular weight of the unknown vapor is approximately 32.6 g/mol.