Final answer:
To calculate the molar mass from freezing point depression, the molality of the solution is found using ΔTf and Kf, then the number of moles of the solute is calculated based on the mass of the water. Finally, the molar mass is obtained by dividing the mass of the solute by the number of moles, yet the resulting value does not match any of the given answer choices.
The righgt answer is b) 60 g/mol
Step-by-step explanation:
Calculating the Molar Mass from Freezing Point Depression
To calculate the molar mass of the dissolved nonelectrolyte, we'll use the colligative property of freezing point depression. The formula we use is ΔTf = Kf * m, where ΔTf is the freezing point depression, Kf is the freezing point depression constant, and m is the molality of the solution.
First, we need to find the molality (m) of the solution with the given freezing point depression (ΔTf = 1.94°C) and the known freezing point depression constant for water (Kf = 1.86°C/m).
m = ΔTf / Kf = (-1.94°C) / (1.86°C/m) = -1.04 m
Since molality is moles of solute per kilogram of solvent, and we have 12.0 g of the solute and 80.0 g (0.0800 kg) of water, we can find the number of moles of solute:
moles = molality * mass of solvent in kilograms = -1.04 m * 0.0800 kg = -0.0832 moles (dropping the negative since moles cannot be negative).
Now we can calculate the molar mass (M) by dividing the mass of the solute by the number of moles:
M = mass of solute / moles = 12.0 g / 0.0832 moles = 144.23 g/mol
However, none of the answer choices correspond to this value, suggesting an error in calculation or given choices. If the calculation is assumed correct, the molar mass would be none of the provided options.
The righgt answer is b) 60 g/mol