Question

The value of ${{K}_{f}}$ for water is 1.86${}^\circ C$,calculated from the glucose solution. The value of ${{K}_{f}}$ for water calculated for $NaCl$ solution will be:
(A) =1.86
(B) <1.86
(C) >1.86
(D) zero

Answer 1

Hint: The freezing point depression is a colligative property and freezing point depression constant is a constant that we can derive from the relation of depression in freezing point. This constant will be a characteristic constant for a given solvent.

Complete step by step answer:
- A substance can have three states to change into. They are solid, liquid and gas. As we know every substance is in one of these three phases at certain temperatures. The conditions of temperature and pressure at which the substance will change its phase depend on the intermolecular forces of atoms and molecules.

- As we know, the freezing point is the temperature at which a substance in liquid phase is changed to solid phase. Adding solutes to an ideal solution results in a positive $\Delta S$, an increase in entropy. As a result of this addition, the newly formed solution’s chemical and physical properties will also change.

-Here comes the idea of colligative properties. It’s the properties that undergo changes due to the addition of solutes to a solvent. The factor which these properties depend on is the number of solutes added. The one example we can provide for colligative properties is depression in freezing point.
The extent to which changes can occur to freezing point on addition of a pure solvent to solution can be given by the following equation
$\Delta {{T}_{f}}={{K}_{f}}\times m\times i$
 Where ,
 $\Delta {{T}_{f}}$ is the change in freezing point
  ${{K}_{f}}$ is the proportionality constant for freezing
 $m$ is the molality
 $i$ is the Van't Hoff Factor

- As we can see the ${{K}_{f}}$ (freezing point depression constant) is a proportionality constant. We can describe it as depression in freezing point produced when one mole of solute dissolved in one kg of solvent. Hence its value would be a constant for a solvent.
-The water will have the same freezing point depression constant in both glucose solution and $NaCl$ solution and its value is 1.86${}^\circ C$.
So, the correct answer is “Option A”.

Note: It should be noted that, when a solute is added to a solvent, its freezing point changes. The change occurs in such a way that the solution will have a lower freezing point than a pure solvent. The reason is that, when a substance is added to a solvent (such as water), the solute-solvent interactions will prevent the solvent from going into the solid phase and as a result the solute-solvent interactions require to decrease the temperature further in order to solidify the solution.