Question

Identify the compound amongst the following of which ${\text{0}}{\text{.1M}}$ solution has the highest boiling point.
A.Glucose
B.Sodium chloride
C.Calcium chloride
D.Ferric chloride

Answer 1

Hint: The boiling point for electrolytes is directly proportional to the number of ions dissociated in solution. For hundred percent dissociation of a solute, the van’t Hoff factor ‘i’ is equal to the number of ions produced from one molecule of the solute.

Complete step by step answer:
Elevation in boiling point refers to the increase in the boiling point of the solution than that of the pure solvent. It has been found that this increase in boiling point depends upon the concentration of the solute dissolved in a solution and hence it is considered a colligative property. For solutions of non – electrolytes, the applicable relation for the colligative property of elevation in boiling point is
$\Delta {{\text{T}}_{\text{b}}}{\text{ = }}{{\text{K}}_{\text{b}}}{{ \times m}}$
Here, $\Delta {{\text{T}}_{\text{b}}}$ represents the elevation in boiling point, \[{{\text{K}}_{\text{b}}}\] represents the molal elevation constant and m represents the molality of the solution.
But electrolytes undergo association or dissociation in the solution and so, the number of particles in the solution increases. Since the value of the colligative property depends on the number of particles of the solute, the experimental value of the colligative property becomes more than the theoretical value.
So, van’t Hoff introduced the factor ‘i’ to calculate the extent of dissociation or association and modified the relation as:
$\Delta {{\text{T}}_{\text{b}}}{\text{ = i}} \times {{\text{K}}_{\text{b}}}{{ \times m}}$
Now, glucose is non-electrolyte and so ‘i’ equals 1.
For electrolytes, ‘i’ equals to the number of ions dissociated.
So, for sodium chloride, ‘i’ equals to 2 as it dissociates as
${\text{NaCl}} \to {\text{N}}{{\text{a}}^ + }{\text{ + C}}{{\text{l}}^ - }$
For calcium chloride, ‘i’ equals to 3 as it dissociates as
${\text{CaC}}{{\text{l}}_2} \to {\text{C}}{{\text{a}}^{2 + }}{\text{ + 2C}}{{\text{l}}^ - }$
For ferric chloride, ‘i’ equals to 4 as it dissociates as
${\text{FeC}}{{\text{l}}_3} \to {\text{F}}{{\text{e}}^{3 + }}{\text{ + 3C}}{{\text{l}}^ - }$
Given that the molarity and the boiling point constant is the same for all the electrolytes. So, the boiling point will be highest for the electrolyte with the highest value of the van't Hoff factor which is ferric chloride.

So, the correct option is D.

Note:
The van’t Hoff factor ‘i’ can be defined as the ratio of the experimental value of the colligative property to the calculated value of the colligative property. Since colligative property is inversely proportional to the molecular mass of the solute, ‘i’ can also be defined as the ratio of the calculated molecular mass to the experimental molecular mass.
If ‘i’ is less than 1, there is association of the solute in the solution and if ‘i’ is greater than 1, there is dissociation of the solute in the solution.