# Elevation in the boiling point for 1 molal solution of glucose is 2 K. The depression in the freezing point of 2 molal solution of glucose in the same solvent is 2 K. The relation between ${K_b}$ and ${K_f}$ is :

a.) ${K_b}$= 0.5 ${K_f}$

b.) ${K_b}$= 2 ${K_f}$

c.) ${K_b}$= 1.5 ${K_f}$

d.) ${K_b}$= ${K_f}$

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**Hint:**The elevation in boiling point describes that when a compound is added to another compound, its boiling point rises and the added compound is impure. Its formula can be given as-

$\Delta {T_b}$= ${K_b} \times m$

While depression in freezing point describes the lowering of the freezing point of the compound. Its formula is given as-

$\Delta {T_f}$= ${K_f} \times m$

On filling the values and by dividing, we can get the answer.

**Complete step by step answer :**

Let us start by writing what is given to us and what we need to find.

Thus, Given :

Molality of the solution A = 1 molal

Elevation in the boiling point of A = 2 K

Molality of the solution B = 1 molal

Depression in the freezing point of B = 2 K

To find : Relation between ${K_b}$and ${K_f}$

We have the formula to calculate elevation boiling point as-

$\Delta {T_b}$= ${K_b} \times m$

Where $\Delta {T_b}$ is the elevation in boiling point

${K_b}$is the boiling point elevation constant

‘m’ is the molality of the solution

Further, we have the expression for depression in freezing point as-

$\Delta {T_f}$= ${K_f} \times m$

Where $\Delta {T_f}$is the depression in freezing point

${K_f}$ is the cryoscopic constant or molal depression constant

‘m’ is the molality of solution.

On dividing the elevation in boiling point by depression in freezing point

We have,

$\dfrac{{\Delta {T_b}}}{{\Delta {T_f}}}$= $\dfrac{{m \times {K_b}}}{{m \times {K_f}}}$

$\dfrac{2}{2}$= $\dfrac{{1 \times {K_b}}}{{2 \times {K_f}}}$

${K_b}$= 2${K_f}$

**So, the option b.) is the correct answer.**

**Note:**It must be noted that the elevation in boiling point and depression in freezing point are colligative properties. These depend on the number of solute particles present in the solution.