Caryophyllene, a nonelectrolyte, is one of the compounds responsible for the flavor of cloves. A 207 mg sample of caryophyllene was dissolved in 1.00 g of chloroform (K_b = 3.63 $\circ$ C/m), increasing the boiling point of chloroform by 3.68 $\circ$ C. What is the molar mass of caryophyllene? A)204 g/mol B)156 g/mol C)164 g/mol D)193 g/mol E)219 g/mol

Question

Quizplus · Accepted Answer

The boiling point elevation formula is $\Delta T_b = iK_b m$, where $i$ is the van't Hoff factor (1 for nonelectrolytes), $K_b$ is the ebullioscopic constant of the solvent, and $m$ is the molality of the solution. Given $\Delta T_b = 3.68^\circ C$, $K_b = 3.63^\circ C/m$, and the mass of caryophyllene (207 mg = 0.207 g) dissolved in 1.00 g of chloroform, we can find the molar mass of caryophyllene. First, calculate the molality: $m = \frac{\Delta T_b}{K_b} = \frac{3.68}{3.63} m = 1.014 m$. Then, use the definition of molality ($m = \frac{\text{moles of solute}}{\text{kg of solvent}}$) to find the moles of caryophyllene: $1.014 m = \frac{\text{moles of caryophyllene}}{0.001 kg}$. Solving for moles gives $0.001014 \text{ moles}$. Finally, calculate the molar mass: $M = \frac{\text{mass}}{\text{moles}} = \frac{0.207 g}{0.001014 \text{ moles}} = 204 g/mol$.

Caryophyllene, a Nonelectrolyte, Is One of the Compounds Responsible for the Flavor