Kf and Kb for benzene are 5.07 K kg/mol and 2.53 K kg/mol respectively. A solution of a non-volatile solute in benzene showed an elevation of 0.50 K. What should be the depression of the freezing point of this solution?
The Correct Answer and Explanation is:
To solve this, we can use the following relationship between freezing point depression and boiling point elevation, which is governed by the formula:ΔT=K×m\Delta T = K \times mΔT=K×m
Where:
- ΔT\Delta TΔT is the change in temperature (either freezing point depression or boiling point elevation),
- KKK is the cryoscopic constant (for freezing point depression) or the ebullioscopic constant (for boiling point elevation),
- mmm is the molality of the solution.
Given that:
- The elevation of the boiling point ΔTb\Delta T_bΔTb is 0.50 K, and
- Kb=2.53 K kg/molK_b = 2.53 \, \text{K kg/mol}Kb=2.53K kg/mol for benzene.
We can first calculate the molality mmm of the solution using the boiling point elevation formula:ΔTb=Kb×m\Delta T_b = K_b \times mΔTb=Kb×m
Substituting the known values:0.50=2.53×m0.50 = 2.53 \times m0.50=2.53×m
Solving for mmm:m=0.502.53≈0.197 mol/kgm = \frac{0.50}{2.53} \approx 0.197 \, \text{mol/kg}m=2.530.50≈0.197mol/kg
Now that we know the molality, we can use it to find the freezing point depression ΔTf\Delta T_fΔTf using the formula for freezing point depression:ΔTf=Kf×m\Delta T_f = K_f \times mΔTf=Kf×m
Substitute the known values (Kf=5.07 K kg/molK_f = 5.07 \, \text{K kg/mol}Kf=5.07K kg/mol and m=0.197 mol/kgm = 0.197 \, \text{mol/kg}m=0.197mol/kg):ΔTf=5.07×0.197≈1.00 K\Delta T_f = 5.07 \times 0.197 \approx 1.00 \, \text{K}ΔTf=5.07×0.197≈1.00K
Thus, the depression of the freezing point of the solution is 1.00 K.
Explanation:
The change in temperature for both freezing point depression and boiling point elevation depends on the molality of the solution and the specific constants for the solvent. The key concept here is that the amount by which the boiling point increases or the freezing point decreases is directly proportional to the molality of the solute. By first calculating the molality from the known boiling point elevation and then using it to calculate the freezing point depression, we can determine how much the freezing point of the solution will decrease.
