Final answer:
To calculate the molar mass of the solute, we can use the formula: Molality (m) = (ΔTf / Kf) * i. In this case, the freezing point depression is 0.780 K, and the freezing point depression constant of naphthalene is 6.80 K kg/mol. Assuming the compound is a non-electrolyte, the van't Hoff factor can be assumed to be 1. Plugging the values into the formula, the molar mass of the compound is calculated to be 177.93 g/mol.
Step-by-step explanation:
To calculate the molar mass of the solute, we can use the formula:
Molality (m) = (ΔTf / Kf) * i
Where ΔTf is the freezing point depression, Kf is the freezing point depression constant of the solvent, and i is the van't Hoff factor.
In this case, the freezing point depression is 0.780 K, and the freezing point depression constant of naphthalene is 6.80 K kg/mol. Assuming the compound is a non-electrolyte, the van't Hoff factor can be assumed to be 1.
Plugging the values into the formula:
m = (0.780 K / 6.80 K kg/mol) * 1 = 0.1147 mol/kg
The molality equation can be rearranged to solve for the moles of solute:
Moles of solute = m * mass of solvent
Mass of solvent = 250 g - 5.00 g = 245 g
Moles of solute = 0.1147 mol/kg * 0.245 kg = 0.0281 mol
Finally, to calculate the molar mass, divide the mass of the solute by the moles:
Molar mass = mass of solute / moles of solute = 5.00 g / 0.0281 mol = 177.93 g/mol