Final answer:
To calculate the molar mass of the unknown nonelectrolyte, use the boiling point elevation to find the molality, then calculate the number of moles, and finally divide the mass of the solute by the number of moles.
Step-by-step explanation:
The student is asking to calculate the molar mass of an unknown nonelectrolyte based on the boiling point elevation after dissolving in water. Boiling point elevation is a colligative property related to the number of solute particles in a solution and can be calculated using the formula ΔTb = i * Kb * m, where ΔTb is the boiling point elevation, i is the van't Hoff factor (which is 1 for nonelectrolytes), Kb is the ebullioscopic constant of the solvent (water in this case), and m is the molality of the solution.
To find the molar mass, we follow these steps:
Calculate the molality (m) of the unknown solute using ΔTb = Kb * m, which gives m = ΔTb / Kb.
Using the molality and the mass of the solvent (water), calculate the number of moles of solute.
Calculate the molar mass by dividing the mass of the solute by the number of moles.
For the given problem:
The molality of the solution is m = 0.634°C / 0.512°C/m = 1.238 mol/kg.
The number of moles of solute is (76.6 g / molar mass) = (379.6 g water / 1000 g/kg) * 1.238 mol/kg.
The molar mass of the solute is found to be Molar Mass = 76.6 g / moles.
Detailed calculations would yield the actual value for the molar mass.