The Molar Mass Calculation Puzzle

What is the molar mass of the compound in the given solution?

A solution containing 11.6 g of a molecular compound dissolved in 100.0 g of water has a boiling point of 101.5 °C. Calculate the molar mass of the compound.

Answer:

The molar mass of the compound that caused water's boiling point to elevate to 101.5°C is approximately 39.59 g/mol, as determined using the colligative property of boiling point elevation and the provided data.

Explanation:

The question asks to calculate the molar mass of a molecular compound based on its effect on the boiling point of water. This can be solved using the boiling point elevation concept, which is a colligative property.

The boiling point elevation ΔTb can be calculated as the difference between the solution's boiling point and the pure solvent's boiling point, which is 101.5°C - 100.0°C = 1.5°C for water. Then, using the molal boiling point elevation constant (Kb) for water 0.512°C/m, we can find the molality (m) of the solution:

m = ΔTb / Kb = 1.5°C / 0.512°C/m = 2.93 m

Now, molality is defined as moles of solute per kilogram of solvent. Given that the mass of the solute dissolved is 11.6 g and the mass of the solvent (water) is 100.0 g (0.100 kg), we can find the moles of solute:

moles of solute = molality × mass of solvent = 2.93 m × 0.100 kg = 0.293 moles

Finally, to find the molar mass of the compound, we divide the given mass of the compound by the number of moles obtained:

molar mass = mass of solute / moles of solute = 11.6 g / 0.293 moles = 39.59 g/mol

Therefore, the molar mass of the compound is approximately 39.59 g/mol.