A solution containing 3.24 g of sulfur in 40 g of benzene boils 0.81 °C above the boiling point of pure benzene.Determine the number of S atoms in one molecule of dissolved sulfur.K_b for benzene is 2.53 °C m^-1.

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The boiling point elevation ($\Delta T_b$) can be calculated using the formula $\Delta T_b = i \cdot K_b \cdot m$, where $i$ is the van't Hoff factor (which is 1 for molecular substances), $K_b$ is the ebullioscopic constant of the solvent, and $m$ is the molality of the solution. Given $\Delta T_b = 0.81$ °C and $K_b = 2.53$ °C kg/mol for benzene, we can solve for $m$, the molality of the solution. First, calculate the molality ($m$) of the solution: $$m = \frac{\Delta T_b}{K_b} = \frac{0.81}{2.53} = 0.32 \, \text{mol/kg}$$Next, calculate the moles of sulfur ($n$) in the solution:$$n = m \times \text{mass of solvent in kg} = 0.32 \, \text{mol/kg} \times 0.04 \, \text{kg} = 0.0128 \, \text{mol}$$Given the mass of sulfur is 3.24 g, calculate the molar mass ($M$) of the sulfur in the solution:$$M = \frac{\text{mass}}{\text{moles}} = \frac{3.24 \, \text{g}}{0.0128 \, \text{mol}} = 253.125 \, \text{g/mol}$$The atomic mass of sulfur (S) is approximately 32 g/mol, so the number of sulfur atoms in one molecule of dissolved sulfur can be determined by dividing the molar mass of the dissolved sulfur by the atomic mass of sulfur:$$\frac{253.125 \, \text{g/mol}}{32 \, \text{g/mol/atom}} = 7.91 \approx 8$$Therefore, there are 8 sulfur atoms in one molecule of dissolved sulfur, which corresponds to $S_8$, a common allotrope of sulfur.

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