Final answer:
To find the molar mass of substance Z, we used the principle of freezing point depression and calculated the molality of the urea solution. Using the same molality for the Z solution, we calculated the moles of Z and then used this to find the molar mass. Our calculation resulted in a molar mass of 342.27 g/mol, which does not match any of the given options.
Step-by-step explanation:
To calculate the molar mass of substance Z, we will use the principle of freezing point depression in colligative properties. Both solutions have the same freezing point depression, so they must have the same molality (moles of solute per kilogram of solvent) because they freeze at the same temperature.
We know the mass of urea is 7.5 g, and its molar mass (from the molecular formula CO(NH2)2) is 60.06 g/mol. We can calculate the moles of urea as follows:
Moles of urea = Mass of urea / Molar mass of urea = 7.5 g / 60.06 g/mol = 0.1249 moles
This gives us the molality of the urea solution:
Molality (urea solution) = Moles of urea / Mass of water (kg) = 0.1249 moles / 0.100 kg = 1.249 m
Since substance Z has the same freezing point depression, it should also have the same molality. Now we calculate the moles of Z:
Moles of Z = Molality (Z solution) x Mass of water (kg) = 1.249 m x 0.100 kg = 0.1249 moles
Now we can find the molar mass of Z:
Molar mass of Z = Mass of Z / Moles of Z = 42.75 g / 0.1249 moles = 342.27 g/mol
However, none of the options match our calculated molar mass, meaning that there might be a mistake in the given options or a misinterpretation in the question.