Question

Assuming ideal solution behavior, what is the molar mass of a solution of 5.00 g of a compound in 25.00 g of carbon tetrachloride (bp 76.8 °C; Kb = 5.02 °C/m) that boils at 81.5 °C at 1 atm?

a) 120 g/mol
b) 86 g/mol
c) 160 g/mol
d) 100 g/mol

Answer 1

To find the molar mass of the compound from its boiling point elevation in a solution with carbon tetrachloride, first calculate the boiling point elevation, then determine the molality, the number of moles of solute, and finally divide the mass of the compound by the number of moles to get the molar mass.

Step-by-step explanation:

Firstly, we need to determine the boiling point elevation (ΔTb) using the formula ΔTb = Tb(solution) - Tb(solvent). In this case, the solution boils at 81.5 °C and carbon tetrachloride boils at 76.8 °C, giving us a ΔTb of 4.7 °C.

Next, we use the boiling point elevation constant for carbon tetrachloride (Kb = 5.02 °C/m) to find the molality (m) of the solution using the equation m = ΔTb / Kb, which yields a molality of 0.936 mol/kg.

The number of moles of solute can then be calculated by multiplying the molality by the mass of the solvent in kilograms (kg), converted from grams. So, the moles of solute is (0.936 mol/kg) * (0.025 kg) = 0.0234 mol.

Finally, the molar mass of the solute is found by dividing the mass of the compound by the number of moles. Therefore, the molar mass is 5.00 g / 0.0234 mol, which equals approximately 214 g/mol (note that this value does not match any of the given options, which suggests there might be an error in the options provided or in the details of the question).