A solution of 0.250 g of naphthalene (mothballs) in 35.00 g of camphor lowers the freezing point by 2.10 °C. What is the molar mass of naphthalene? The freezing-point-depression constant for camphor is 37.7 °C kg/mol.

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Identify the formula for freezing point depression: \( \Delta T_f = i \cdot K_f \cdot m \), where \( \Delta T_f \) is the change in freezing point, \( i \) is the van't Hoff factor (which is 1 for naphthalene as it does not ionize), \( K_f \) is the freezing-point-depression constant, and \( m \) is the molality of the solution.

Rearrange the formula to solve for molality \( m \): \( m = \frac{\Delta T_f}{K_f} \). Substitute the given values: \( \Delta T_f = 2.10 \text{ °C} \) and \( K_f = 37.7 \text{ °C kg/mol} \).

Calculate the molality \( m \) using the rearranged formula.

Use the definition of molality: \( m = \frac{\text{moles of solute}}{\text{kg of solvent}} \). Here, the mass of camphor is 35.00 g, which is 0.035 kg.

Solve for the moles of naphthalene using the calculated molality and the mass of camphor. Then, use the relationship \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \) to find the molar mass of naphthalene, given the mass of naphthalene is 0.250 g.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Freezing Point Depression

Freezing point depression is a colligative property that describes the decrease in the freezing point of a solvent when a solute is added. The extent of this depression is directly proportional to the molality of the solute and the freezing-point-depression constant of the solvent. This relationship is expressed by the formula ΔTf = Kf * m, where ΔTf is the change in freezing point, Kf is the freezing-point-depression constant, and m is the molality of the solution.

Molality

Molality (m) is a measure of concentration defined as the number of moles of solute per kilogram of solvent. It is particularly useful in colligative properties because it accounts for the mass of the solvent rather than the volume, which can change with temperature. In this problem, calculating molality is essential for determining how much the freezing point is lowered due to the addition of naphthalene to camphor.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the molar mass of naphthalene in this scenario, one must first determine the number of moles of naphthalene using the freezing point depression data and the known mass of naphthalene. The molar mass can then be calculated by dividing the mass of naphthalene by the number of moles derived from the freezing point depression equation.

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