The freezing point depression constant (Kf) of benzene is 5.12 K kg mol-1. The freezing point depression for the solution of molality 0.078 m containing a non-electrolyte solute in benzene is (rounded off to two decimal places):
The Correct Answer and Explanation is:
To calculate the freezing point depression (ΔTf\Delta T_fΔTf) of a solution, we use the formula:ΔTf=Kf×m\Delta T_f = K_f \times mΔTf=Kf×m
where:
- ΔTf\Delta T_fΔTf is the freezing point depression,
- KfK_fKf is the freezing point depression constant,
- mmm is the molality of the solution.
Given data:
- The freezing point depression constant (KfK_fKf) for benzene is 5.12 K kg/mol.
- The molality (mmm) of the solution is 0.078 m (mol of solute per kg of solvent).
Step-by-Step Calculation:
- Substitute the given values into the formula: ΔTf=5.12 K kg/mol×0.078 mol/kg\Delta T_f = 5.12 \, \text{K kg/mol} \times 0.078 \, \text{mol/kg}ΔTf=5.12K kg/mol×0.078mol/kg
- Perform the multiplication: ΔTf=0.39936 K\Delta T_f = 0.39936 \, \text{K}ΔTf=0.39936K
- Round to two decimal places: ΔTf≈0.40 K\Delta T_f \approx 0.40 \, \text{K}ΔTf≈0.40K
Explanation:
The freezing point depression measures how much the freezing point of the solvent is lowered by the presence of a solute. In this case, benzene is the solvent, and the presence of a non-electrolyte solute lowers its freezing point by 0.40 K.
Since the solute is non-electrolyte, it does not dissociate into ions in solution, meaning the molality directly contributes to the freezing point depression without any additional factors from ionization.
This depression can help us understand the behavior of the solvent in the presence of a solute. It is important for understanding colligative properties, which depend on the number of solute particles present, rather than their specific identity.
