Calculate the freezing point and boiling point of a solution containing 10.0 g of naphthalene (C10H8) in 100.0 mL of benzene. Benzene has a density of 0.877 g/cm³.

Verified step by step guidance

1. Calculate the molality of the solution: First, determine the moles of naphthalene (C_{10}H_{8}) using its molar mass. Then, find the mass of benzene using its density and volume, and convert this mass to kilograms. Finally, use the formula for molality: \( \text{molality} = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \).
2. Determine the freezing point depression: Use the formula \( \Delta T_f = i \cdot K_f \cdot m \), where \( i \) is the van't Hoff factor (which is 1 for naphthalene, a non-electrolyte), \( K_f \) is the freezing point depression constant for benzene, and \( m \) is the molality calculated in the previous step. Subtract \( \Delta T_f \) from the normal freezing point of benzene to find the new freezing point.
3. Determine the boiling point elevation: Use the formula \( \Delta T_b = i \cdot K_b \cdot m \), where \( i \) is the van't Hoff factor (1 for naphthalene), \( K_b \) is the boiling point elevation constant for benzene, and \( m \) is the molality. Add \( \Delta T_b \) to the normal boiling point of benzene to find the new boiling point.
4. Identify the constants: Look up the values for the freezing point depression constant \( K_f \) and the boiling point elevation constant \( K_b \) for benzene, as well as its normal freezing and boiling points.
5. Combine the results: Use the calculated \( \Delta T_f \) and \( \Delta T_b \) to determine the final freezing and boiling points of the solution.