Arrange the following solutions according to their increasing boiling point.

A. 0.1 M Glucose

B. 0.1 M \(NaCl\)

C. 0.1 M \(K_4[Fe(CN)_6]\)

D. 0.1 M \(MgCl_2\)

E. 0.1 M \(AlCl_3\)

Choose the correct answer from the options given below:

A < B < D < E < C

The correct answer is option 2. A < B < D < E < C.

Boiling point elevation is a colligative property, meaning it depends on the number of solute particles (ions or molecules) in a solution, not the type of particles. When a solute dissolves in a solvent (such as water), it increases the boiling point of the solution. The more particles the solute dissociates into, the higher the boiling point will be.

The boiling point elevation (\(\Delta T_b\)) is given by:

\(\Delta T_b = i \cdot K_b \cdot m\)

where:

\(i\) is the van’t Hoff factor, representing the number of particles the solute dissociates into.

\(K_b\) is the ebullioscopic constant of the solvent (water in this case).

\(m\) is the molality of the solution.

Step-by-step Dissociation and Analysis of Each Compound:

A. 0.1 M Glucose

Glucose is a non-electrolyte, meaning it does not dissociate into ions when dissolved in water. Therefore, the van’t Hoff factor \(i = 1\). Since glucose does not break apart into multiple particles, it has the least effect on the boiling point elevation.

van't Hoff factor \(i = 1\).

Contributes the least to boiling point elevation.

B. 0.1 M NaCl (B)

Sodium chloride (NaCl) is a strong electrolyte and dissociates completely into two ions: \(Na^+\) and \(Cl^-\) in water. Therefore, the van’t Hoff factor \(i = 2\).

van't Hoff factor \(i = 2\).

Contributes more to boiling point elevation than glucose but less than compounds that produce more ions.

D. 0.1 M \(MgCl_2\)

Magnesium chloride (MgCl₂) dissociates completely into three ions: one \(Mg^{2+}\) ion and two \(Cl^-\) ions. Therefore, the van’t Hoff factor \(i = 3\).

van't Hoff factor \(i = 3\).

Contributes more to boiling point elevation than both glucose and NaCl because it dissociates into three ions.

E. 0.1 M \(AlCl_3\)

Aluminum chloride (AlCl₃) dissociates into four ions: one \(Al^{3+}\) ion and three \(Cl^-\) ions. Therefore, the van’t Hoff factor \(i = 4\).

van't Hoff factor \(i = 4\).

Contributes more to boiling point elevation than MgCl₂, NaCl, and glucose, as it dissociates into four ions.

C. 0.1 M \(K_4[Fe(CN)_6\)

Potassium ferrocyanide (\(K_4[Fe(CN)_6\)) dissociates into five ions: four \(K^+\) ions and one \(Fe(CN)_6^{4-}\) ion. Therefore, the van’t Hoff factor \(i = 5\).

van't Hoff factor \(i = 5\).

Contributes the most to boiling point elevation, as it dissociates into five ions.

Boiling Point Elevation Ranking:
Since boiling point elevation increases with the number of particles in solution, the order of increasing boiling points will follow the order of the van't Hoff factors:

1. A (Glucose): Lowest boiling point because \(i = 1\).

2. B (NaCl): Higher than glucose, with \(i = 2\).

3. D (MgCl₂): Higher than NaCl, with \(i = 3\).

4. E (AlCl₃): Higher than MgCl₂, with \(i = 4\).

5. C (\(K_4[Fe(CN)_6\)): Highest boiling point because \(i = 5\).

Thus, the correct order of increasing boiling points is: A (Glucose) < B (NaCl) < D (MgCl₂) < E (AlCl₃) < C (\(K_4[Fe(CN)_6\))

This matches option 2: A < B < D < E < C.