Final answer:
To find the molar mass of the hydrocarbon, we can use the boiling point elevation equation and the molality of the solute. By calculating the change in boiling point caused by the presence of the hydrocarbon in the solution, we can determine the molality of the solute. Using the mass of the solute and the number of moles, we can find the molar mass of the hydrocarbon.
Step-by-step explanation:
To find the molar mass of the hydrocarbon, we need to calculate the change in boiling point caused by the presence of the hydrocarbon in the solution. The boiling point elevation is given by the equation ∆Tb = Kb * m, where ∆Tb is the change in boiling point, Kb is the molal boiling point constant of the solvent, and m is the molality of the solute. In this case, the boiling point of the acetone solution is 56.50°C and the boiling point of the pure solvent acetone is 55.95°C.
Using the equation, we can calculate the molality of the solute:
∆Tb = 56.50 - 55.95 = 0.55°C
m = ∆Tb / Kb = 0.55 / 1.71 = 0.321 mol/kg
The molality is equal to the number of moles of solute divided by the mass of the solvent. Rearranging the equation, we can solve for the number of moles of the solute:
moles of solute = m * mass of solvent = 0.321 * 95 = 30.495 mol
The molar mass of the hydrocarbon is equal to the mass of the solute divided by the number of moles:
molar mass = mass of solute / moles of solute = 3.90 / 30.495 = 0.1276 g/mol
Therefore, the molar mass of the hydrocarbon is approximately 0.1276 g/mol.