Calculate the molar mass of an unknown molecular (nonelectrolyte) compound in an aqueous solution containing 35.9 g of the compound in 150.0 g of water with a freezing point of -1.3 °C.

Verified step by step guidance

1. Identify the freezing point depression formula: \( \Delta T_f = i \cdot K_f \cdot m \), where \( i \) is the van't Hoff factor (1 for nonelectrolytes), \( K_f \) is the freezing point depression constant for water (1.86 °C kg/mol), and \( m \) is the molality.
2. Calculate the freezing point depression \( \Delta T_f \) by subtracting the observed freezing point from the normal freezing point of water (0 °C): \( \Delta T_f = 0 - (-1.3) = 1.3 \) °C.
3. Rearrange the formula to solve for molality \( m \): \( m = \frac{\Delta T_f}{i \cdot K_f} \). Substitute \( \Delta T_f = 1.3 \) °C, \( i = 1 \), and \( K_f = 1.86 \) °C kg/mol.
4. Calculate the molality \( m \) using the values from the previous step.
5. Use the definition of molality \( m = \frac{\text{moles of solute}}{\text{kg of solvent}} \) to find the moles of solute, then use the mass of the solute to calculate the molar mass: \( \text{Molar mass} = \frac{\text{mass of solute (g)}}{\text{moles of solute}} \).