We observe that 5 grams of a gaseous com-
pound occupies 2083 mL at 50 degrees C and 574 torr. What is the molecular weight of the compound?
Answer in units of g/mol
Use PV = nRT and solve for n.
Then n = grams/molar mass. Solve for molar mass.
To find the molecular weight of the gaseous compound, 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 ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the given values to the appropriate units.
The mass of the compound is given as 5 grams.
The volume is given as 2083 mL. We need to convert this to liters by dividing by 1000: 2083 mL ÷ 1000 = 2.083 L.
The temperature is given as 50 degrees Celsius. We need to convert this to Kelvin by adding 273: 50 + 273 = 323 K.
The pressure is given as 574 torr.
Now, we can rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT
Substituting the given values:
n = (574 torr)(2.083 L) / (0.0821 L·atm/(mol·K))(323 K)
Now, we can calculate the number of moles:
n ≈ 14.36
Finally, to find the molecular weight (molar mass) of the compound, we divide the mass by the number of moles:
Molecular weight = Mass / Moles
Molecular weight = 5 g / 14.36 mol
Calculating this value:
Molecular weight ≈ 0.348 g/mol
Therefore, the molecular weight of the compound is approximately 0.348 g/mol.