Answer:
The molar mass of the unknown solute can be calculated using the formula for boiling point elevation:
ΔT = Kb * m
Where:
- ΔT is the change in boiling point (i.e., the boiling point of the solution minus the boiling point of the pure solvent)
- Kb is the ebullioscopic constant (also known as the boiling point elevation constant) of the solvent
- m is the molality of the solution (i.e., moles of solute per kilogram of solvent)
From your question, I can gather that:
- The boiling point of the solution is 98.01°C.
- The boiling point of the pure solvent is 94.00°C.
- The molality is unknown, but we can calculate it once we find the number of moles of solute.
- The mass of the solvent is 1479 g, which is 1.479 kg.
First, let's calculate the change in boiling point, ΔT:
ΔT = 98.01°C - 94.00°C = 4.01°C
Now we can rearrange the equation to solve for molality:
m = ΔT / Kb
However, we need the value of Kb, which is given in cm, not °C. We need to convert Kb from cm to °C. The conversion factor is 1 cm = 1°C. So:
Kb = 463 cm = 463 °C
Substituting the values into the equation, we get:
m = 4.01°C / 463 °C/kg mol = 0.00866 mol/kg
Now, molality is defined as the number of moles of solute per kilogram of solvent. We can rearrange the equation to solve for the number of moles of solute:
moles of solute = molality * mass of solvent = 0.00866 mol/kg * 1.479 kg = 0.0128 mol
Now, knowing that the molar mass is the mass of the solute divided by the number of moles, we can calculate the molar mass of the solute:
Molar mass = mass of solute / moles of solute = 21.1 g / 0.0128 mol = 1648.4 g/mol
Therefore, the molar mass of the unknown nonelectrolyte is approximately 1648.4 g/mol.