Calculate the molecular mass of sulphur if 35 gram of sulphur dissolves in 100 gram of CS2 to produce a solution that has a boiling point of 49.48°C
To calculate the molecular mass of sulfur, we can use the concept of the elevation of boiling point and the formula for calculating the molecular mass.
The elevation of boiling point (∆Tb) is the difference between the boiling point of the solution and the boiling point of the pure solvent. In this case, the boiling point of the pure solvent CS2 is not given, so we need to assume it is 0°C, which is the normal boiling point of CS2.
The formula to calculate the molecular mass is:
Molecular mass = (molar weight of CS2 * ∆Tb) / (molality of solute)
To find the molality of the solute (sulfur), we need to determine the number of moles of sulfur and the mass of the solvent (CS2) used.
Given:
Mass of sulfur (solute) = 35 grams
Mass of CS2 (solvent) = 100 grams
Boiling point elevation (∆Tb) = 49.48°C
Step 1: Convert the temperature to Kelvin.
∆Tb = 49.48°C = 49.48 + 273.15 = 322.63 K
Step 2: Calculate the molality of sulfur.
Molality = Moles of solute / Mass of solvent (in kg)
Moles of sulfur = Mass of sulfur / Molar mass of sulfur
The molar mass of sulfur is 32 g/mol.
Moles of sulfur = 35 g / 32 g/mol = 1.09 mol
Mass of solvent (CS2) in kg = Mass of solvent (CS2) / 1000
Mass of solvent (CS2) = 100 g
Mass of solvent (CS2) in kg = 100 g / 1000 = 0.1 kg
Molality = 1.09 mol / 0.1 kg = 10.9 mol/kg
Step 3: Calculate the molecular mass of sulfur.
Molecular Mass = (Molar weight of CS2 * ∆Tb) / Molality
The molar weight of CS2 is 76.14 g/mol.
Molecular Mass = (76.14 g/mol * 322.63 K) / 10.9 mol/kg
Molecular Mass = 2255.70 g/mol
Therefore, the molecular mass of sulfur is approximately 2255.70 g/mol.