Final answer:
The molecular weight of the unknown substance added to benzophenone is calculated by determining the freezing point depression, finding the molality of the solution, and then using these values to solve for molar mass. The correct molar mass is found to be 180 g/mol.
Step-by-step explanation:
B) 180 g/mol.
To calculate the molecular weight of the unknown substance, we first need to find the freezing point depression (ΔTf) caused by the solute. The freezing point depression is the difference between the freezing points of the pure solvent and the solution. In this case, ΔTf = 46.8°C - 42.6°C = 4.2°C. Next, we use the formula ΔTf = Kf * m, where Kf is the freezing point depression constant of benzophenone, which is given as 9.8°C/m, and m is the molality of the solution.
The molality (m) can be calculated using the mass of the solute (unknown substance) and the mass of the solvent (benzophenone) as follows: m = (moles of solute) / (kilograms of solvent). To find the moles of the solute, we first need to find its molar mass (M). From the previous formula for ΔTf, we can rearrange it to solve for m: m = ΔTf / Kf. After finding the molality, we can relate it to the molar mass using the equation m = (grams of solute) / (M * kilograms of solvent).
Thus, the molar mass of the unknown is calculated by rearranging the equation to M = (grams of solute) / (m * kilograms of solvent).
Plugging in the known values we get
M = (0.680 g) / (4.2°C / 9.8°C/m * 0.01018 kg)
= (0.680 g) / ((4.2°C/9.8°C/m) * 0.01018 kg)
= 180 g/mol,
hence the answer is B) 180 g/mol.