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.

Key Concepts

Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. These properties include boiling point elevation and freezing point depression, which are crucial for calculating the changes in freezing and boiling points when a solute is added to a solvent.

Molar Mass and Mole Calculation

To calculate the effects of a solute on the freezing and boiling points, it is essential to determine the molar mass of the solute and convert grams to moles. For naphthalene (C10H8), the molar mass is approximately 128.17 g/mol, which allows for the calculation of the number of moles present in the solution, a key step in applying colligative property formulas.

Freezing Point Depression and Boiling Point Elevation Formulas

The freezing point depression and boiling point elevation can be calculated using the formulas ΔTf = i * Kf * m and ΔTb = i * Kb * m, where ΔTf and ΔTb are the changes in freezing and boiling points, respectively, i is the van 't Hoff factor (which is 1 for naphthalene), Kf and Kb are the solvent's freezing and boiling point constants, and m is the molality of the solution. These formulas are essential for determining the new freezing and boiling points of the solution.