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A solution made by dissolving 9.81 g of a nonvolatile, nonelectrolyte in 90.0 g of water boiled at 100.37 °C at 760 mm Hg. What is the molar mass of the substance? [kp = 0.51 °c/m]

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Answer:

151 g/mol

Explanation:

In order to solve this problem we need to keep in mind the formula for the boiling point elevation:

  • ΔT = Kb * m * i

Where:

  • ΔT is the temperature difference between the boiling point of the solution and that of pure water. 100.37 °C - 100.00 °C = 0.37 °C.
  • m is the molarity of the solution
  • i is the van't Hoff factor. As the solute is a nonelectrolyte, the factor is 1.

Input the data and calculate m:

  • 0.37 °C = 0.51 °C/m * m * 1
  • m =0.72 m

We now can calculate the number of moles of the substance, using the definition of molarity:

  • molarity = moles of solute / kg of solvent

In this case kg of solvent = 90.0 g / 1000 = 0.090 kg

  • 0.72 m = moles / 0.090 kg
  • moles = 0.065 mol

Finally we calculate the molar mass, using the number of moles and the mass:

  • 9.81 g / 0.065 mol = 151 g/mol

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