Question

Which solution will have the highest boiling point?
A. $1\%$ glucose in water.
B. $1\%$ sucrose in water.
C. $1\%$ ${\text{NaCl}}$ in water.
D. $1\%$ ${\text{CaC}}{{\text{l}}_2}$ in water.

Answer 1

The temperature at which the vapour pressure of any liquid becomes equal to the atmospheric pressure is known as the boiling point. The increase in the boiling point of a solvent when a solute is added is known as the elevation in boiling point. The elevation in boiling point can be calculated as the difference between the boiling points of the solution after adding the non-volatile solute and pure solvent.

Complete step by step answer:
In all the four solutions, the solvent is water.
The elevation in boiling point is directly proportional to the van’t Hoff factor. The van’t Hoff factor for any solute is the number of ions a solute dissociates.
We have the equation,
$\Delta {T_{\text{b}}} = i \times {K_{\text{b}}} \times m$
Where $\Delta {T_{\text{b}}}$ is the elevation in boiling point,
$i$ is the van’t Hoff factor,
${K_{\text{b}}}$ is the boiling point elevation constant,
$m$ is the concentration of the solution.
From the given equation,
$\Delta {T_{\text{b}}} \propto i$
As the van’t Hoff factor increases, the boiling point increases.
Glucose is a non-electrolyte and does not dissociate. Thus, the van’t Hoff factor for glucose is $1$.
Sucrose is a non-electrolyte and does not dissociate. Thus, the van’t Hoff factor for sucrose is $1$.
${\text{NaCl}}$ is an electrolyte and dissociates as one ${\text{N}}{{\text{a}}^ + }$ and one ${\text{C}}{{\text{l}}^ - }$ ions. Thus, the van’t Hoff factor for ${\text{NaCl}}$ is $2$.
${\text{CaC}}{{\text{l}}_2}$ is an electrolyte and dissociates as one ${\text{C}}{{\text{a}}^{2 + }}$ and two ${\text{C}}{{\text{l}}^ - }$ ions. Thus, the van’t Hoff factor for ${\text{CaC}}{{\text{l}}_2}$ is $3$.
Thus, ${\text{CaC}}{{\text{l}}_2}$ has the highest van’t Hoff factor. Thus, the solution having the highest boiling point is $1\%$ ${\text{CaC}}{{\text{l}}_2}$ in water.

So, the correct answer is “Option D”.

Note:
The glucose and sucrose are non-electrolytes. Thus, glucose and sucrose do not dissociate into ions and remain as unit molecules in the solution. Thus, the van’t Hoff factor for glucose and sucrose is one.