Final answer:
The formula of the sulfur molecule dissolved in carbon disulfide, given the boiling point elevation of 0.107 °C, is determined to be S8. Therefore, the answer is a) S₈.
Step-by-step explanation:
To determine the formula of a sulfur molecule in carbon disulfide, we need to use the boiling point elevation formula ΔTb = Kb * m, where ΔTb is the boiling point elevation, Kb is the ebullioscopic constant of the solvent (carbon disulfide), and m is the molality of the solution. First, we calculate the molality (m) of the sulfur in the solution:
m = moles of solute / kilograms of solvent
Given the boiling point elevation (ΔTb) is 0.107 °C and the Kb for carbon disulfide (CS₂) is 2.34 °C/m, we have:
0.107 °C = 2.34 °C/m * m
m = 0.107 °C / 2.34 °C/m = 0.0457 m
The number of moles of sulfur is calculated by:
moles of sulfur = molality (m) * kilograms of solvent
moles of sulfur = 0.0457 m * 0.0178 kg = 0.00081346 mol
Next, we calculate the molar mass (M) of sulfur:
M = mass of solute / moles of solute
M = 0.210 g / 0.00081346 mol = 258.2 g/mol
The molar mass of atomic sulfur (S) is 32 g/mol, so we divide the molar mass of sulfur in the solution by the molar mass of atomic sulfur to find the number of sulfur atoms per molecule:
258.2 g/mol / 32 g/mol = 8.07 ≈ 8
Since we can only have whole atoms in a molecule, the sulfur molecule is most likely to have 8 atoms, forming an S8 molecule. Therefore, the answer is a) S₈.