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Question: Elevation in the boiling point for 1 molal solution of glucose is 2 K. The depression in the freezin...

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 Kb{K_b} and Kf{K_f} is :
a.) Kb{K_b}= 0.5 Kf{K_f}
b.) Kb{K_b}= 2 Kf{K_f}
c.) Kb{K_b}= 1.5 Kf{K_f}
d.) Kb{K_b}= Kf{K_f}

Explanation

Solution

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-
ΔTb\Delta {T_b}= Kb×m{K_b} \times m
While depression in freezing point describes the lowering of the freezing point of the compound. Its formula is given as-
ΔTf\Delta {T_f}= Kf×m{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 Kb{K_b}and Kf{K_f}
We have the formula to calculate elevation boiling point as-
ΔTb\Delta {T_b}= Kb×m{K_b} \times m
Where ΔTb\Delta {T_b} is the elevation in boiling point
Kb{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-
ΔTf\Delta {T_f}= Kf×m{K_f} \times m
Where ΔTf\Delta {T_f}is the depression in freezing point
Kf{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,
ΔTbΔTf\dfrac{{\Delta {T_b}}}{{\Delta {T_f}}}= m×Kbm×Kf\dfrac{{m \times {K_b}}}{{m \times {K_f}}}
22\dfrac{2}{2}= 1×Kb2×Kf\dfrac{{1 \times {K_b}}}{{2 \times {K_f}}}
Kb{K_b}= 2Kf{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.