Final answer:
To find the molar mass of the solute in a nonelectrolyte solution with a known boiling point elevation, one must first determine the solution's molality and then use the mass of solute dissolved to find the number of moles, allowing the calculation of molar mass.
Step-by-step explanation:
To calculate the molar mass of a solute in a nonelectrolyte solution that boils at 108.27°C after dissolving 50.0 grams of the solute in 50.0 mL water, we need to use the concept of boiling point elevation.
The boiling point elevation (ΔTb) is the difference between the solution's boiling point and the pure solvent's boiling point. We can calculate the molality (m) of the solution using the formula ΔTb = Kb * m, where Kb is the ebullioscopic constant for water, which is 0.512 °C/m. We can then find the number of moles of solute (n) using the formula n = mass of solute / molar mass of solute. Given the mass of the water is 50 grams (which is equivalent to 0.050 kilograms), we can calculate molality.
Once we have the molality of the solution, we can calculate the moles of solute using the equation m = moles of solute / kilograms of solvent. Finally, we can obtain the molar mass of the solute by dividing the mass of the solute by the number of moles of solute.