Final answer:
To calculate the freezing point of a solution, the freezing point depression formula ΔTf = Kfm is used. First, determine the change in freezing point by subtracting the freezing point of pure benzene from the observed freezing point. Then, calculate the molal concentration and use it along with the mass of solute and solvent to find the molar mass.
Step-by-step explanation:
Calculate the Freezing Point of a Solution
To calculate the freezing point of a solution, we need to apply the concept of freezing point depression. The freezing point depression is directly proportional to the molal concentration of the solution and can be given by the equation ΔTf = Kfm, where ΔTf is the change in freezing point, Kf is the freezing point depression constant, and m is the molality.
Step 1: Determine the Change in Freezing Point
The change in freezing point (ΔT) can be found by subtracting the freezing point of pure benzene from the observed freezing point. Using the information provided, we find ΔT = 5.5 °C - 2.32 °C = 3.2 °C.
Step 2: Determine the Molal Concentration
Next, we determine the molal concentration by rearranging the equation to m = ΔTf / Kf. Substituting the values, we get m = 3.2 °C / 5.12 °C/m.
The molar mass of the solute can be determined if the amount of solute and solvent used is known, along with the observed freezing point depression. By applying the same principles used to find the molality, we can calculate the molar mass, which in turn can be used to deduce the molecular formula if the solute consists of a single element represented by X.