Final answer:
To find the molar mass of the compound, we calculated the freezing point depression, used it to find the molality, then determined the moles of solute, and finally divided the mass of the compound by the number of moles to get a molar mass of 249.97 g/mol.
Step-by-step explanation:
To calculate the molar mass of the non-ionizing compound, we will use the freezing point depression formula ΔT_f = K_f × m, where ΔT_f is the freezing point depression, K_f is the cryoscopic constant, and m is the molality of the solution.
First, you need to calculate the freezing point depression (ΔT_f) which is the difference between the normal freezing point of naphthalene and the observed freezing point after adding the compound.
ΔT_f = normal freezing point - observed freezing point
= 80.26°C - 75.63°C
= 4.63°C
We then use this value to find the molality (m) of the solution.
m = ΔT_f / K_f
= 4.63°C / 6.940 °C/m
= 0.667 mol/kg
Next, to find the number of moles of solute we have: moles of solute = molality × mass of solvent in kg
= 0.667 mol/kg × 0.0326 kg
= 0.02175 mol
Last, divide the mass of the compound by the number of moles to get the molar mass:
molar mass = mass of solute / moles of solute
= 5.434 g / 0.02175 mol
= 249.97 g/mol