Calculate the molar mass of an unknown compound given that an aqueous solution containing 17.5 g of the compound in 100.0 g of water has a freezing point of -1.8 °C.

Verified step by step guidance

1. <Step 1: Understand the concept of freezing point depression. The freezing point of a solution is lower than that of the pure solvent. The change in freezing point (\( \Delta T_f \)) is related to the molality (\( m \)) of the solution and the freezing point depression constant (\( K_f \)) of the solvent.>
2. <Step 2: Use the formula for freezing point depression: \( \Delta T_f = i \cdot K_f \cdot m \), where \( i \) is the van't Hoff factor (assumed to be 1 for non-electrolytes), \( K_f \) is the freezing point depression constant for water (1.86 °C kg/mol), and \( m \) is the molality of the solution.>
3. <Step 3: Calculate the change in freezing point: \( \Delta T_f = 0 - (-1.8) = 1.8 \) °C.>
4. <Step 4: Rearrange the formula to solve for molality: \( m = \frac{\Delta T_f}{i \cdot K_f} = \frac{1.8}{1 \cdot 1.86} \) mol/kg.>
5. <Step 5: Use the definition of molality (moles of solute per kilogram of solvent) to find the molar mass of the compound. Calculate the moles of solute using the molality and the mass of the solvent (0.1 kg), then use the mass of the solute (17.5 g) to find the molar mass: \( \text{Molar mass} = \frac{\text{mass of solute}}{\text{moles of solute}} \).>