what is the cryoscopic constant Kc of water at 25 ° C
The Correct Answer and Explanation is:
The cryoscopic constant (Kc) is a property of a solvent that represents the freezing point depression per molal concentration of solute. For water, this constant at 25 °C is approximately 1.86 °C·kg/mol.
Explanation:
The cryoscopic constant is related to how much the freezing point of a solvent decreases when a solute is added. The formula for the freezing point depression is given by: ΔTf=Kf⋅m\Delta T_f = K_f \cdot mΔTf=Kf⋅m
Where:
- ΔTf\Delta T_fΔTf is the freezing point depression,
- KfK_fKf (or Kc in some texts) is the cryoscopic constant of the solvent,
- mmm is the molality of the solution, which is defined as moles of solute per kilogram of solvent.
For water, the freezing point at standard pressure is 0 °C, and when a solute is added, the freezing point decreases (i.e., the solution freezes at a lower temperature). The cryoscopic constant KfK_fKf for water is experimentally determined to be about 1.86 °C·kg/mol at 25 °C.
This means that for every 1 mole of solute dissolved in 1 kilogram of water, the freezing point of the solution will decrease by 1.86 °C.
The value of Kf for different solvents varies, depending on their molecular properties. For example, solvents with higher Kf values experience a greater decrease in freezing point for the same concentration of solute. The cryoscopic constant is widely used in applications like determining the molar mass of a solute by measuring the freezing point depression of a solution.
