What is the molecular weight of sulfur if 35.5 grams of sulfur dissolve in 100.0 grams of CS2 to produce a solution that has a boiling point of 49.48°C?
The molecular mass of sulfur is 256 u.
As you might have guessed, this is a boiling point elevation problem. The formula for boiling point elevation is
##ΔT_”b” = K_”b”m##
We need to look up the values of ##T_”b”^”o”## and ##K_”b”## for CS₂. They are
##T_”b”^”o”## = 46.2 °C and ##K_”b”## = 2.37 °C·kg/mol
##ΔT_”b” = T_”b”^”o” – T_”b”## = (49.48 – 46.2) °C = 3.28 °C
We can use this information to calculate the ##m## of the solution.
##m = (ΔT_”b”)/K_”b” = (3.28″ °C”)/(2.37″ °C·kg·mol⁻¹”)## = 1.38 mol·kg⁻¹
We have 100.0 g or 0.1000 kg of CS₂. So we can calculate the moles of sulfur.
Molality = ##”moles of [solute](http://socratic.org/chemistry/solutions-and-their-behavior/solute)”/”kilograms of [solvent](http://socratic.org/chemistry/solutions-and-their-behavior/solvent)”##
Moles of solute = molality× kilograms of solvent = 1.38 mol·kg⁻¹ × 0.1000 kg = 0.138 mol
So 35.5 g of sulfur = 0.138 mol
∴ Molar mass of sulfur = ##(35.5″ g”)/(0.138″ mol”)## = 257 g/mol
∴ The experimental molecular mass of sulfur is 257 u (The actual molecular mass of S₈ is 256 u).
