An aqueous solution of a certain organic compound has a density of 1.063 g/mL, an osmotic pressure of 12.16 atm at 25.0 °C, and a freezing point of -1.03 °C. The compound is known not to dissociate in water. What is the molar mass of the compound?

Verified step by step guidance

1. Step 1: Use the osmotic pressure formula \( \Pi = iMRT \) to find the molarity (M) of the solution. Since the compound does not dissociate, the van't Hoff factor \( i = 1 \). Rearrange the formula to solve for M: \( M = \frac{\Pi}{RT} \), where \( R = 0.0821 \text{ L atm/mol K} \) and \( T = 298.15 \text{ K} \) (25.0 °C in Kelvin).
2. Step 2: Calculate the molality (m) of the solution using the freezing point depression formula \( \Delta T_f = iK_f m \). Since the compound does not dissociate, \( i = 1 \). Rearrange the formula to solve for m: \( m = \frac{\Delta T_f}{K_f} \), where \( \Delta T_f = 1.03 \text{ °C} \) and \( K_f \) is the cryoscopic constant for water (1.86 °C kg/mol).
3. Step 3: Use the density of the solution to find the mass of the solvent. Assume 1 L of solution for simplicity, which has a mass of 1063 g (since density = 1.063 g/mL). Subtract the mass of the solute (found from molality) to find the mass of the solvent.
4. Step 4: Convert the molality to moles of solute using the mass of the solvent in kg. Use the relationship \( m = \frac{\text{moles of solute}}{\text{kg of solvent}} \) to find the moles of solute.
5. Step 5: Calculate the molar mass of the compound by dividing the mass of the solute (from the density and volume of solution) by the moles of solute (from the molality calculation). Use the formula \( \text{Molar mass} = \frac{\text{mass of solute}}{\text{moles of solute}} \).