Understanding Boiling Point Elevation in Solutions

Boiling point elevation is a colligative property, meaning it depends on the concentration of solute particles in a solution, not on the identity of the solute itself. When a non-volatile solute is added to a solvent, the boiling point of the solvent increases. This increase in boiling point, denoted as $\Delta T_b$, is directly proportional to the molal concentration of the solute particles.

The formula for boiling point elevation is given by:

$$ \Delta T_b = i \cdot K_b \cdot m $$

Where:

• $\Delta T_b$ is the elevation in boiling point.
• $i$ is the van't Hoff factor, which represents the number of particles the solute dissociates into in the solution. For non-electrolytes, $i=1$. For electrolytes, $i$ is greater than 1.
• $K_b$ is the molal boiling point elevation constant, which is a property of the solvent (in this case, water).
• $m$ is the molality of the solution (moles of solute per kilogram of solvent).

In this problem, all solutions are 1M aqueous solutions. For dilute aqueous solutions, molality ($m$) is approximately equal to molarity (M). Since the solvent (water) is the same, $K_b$ is constant for all solutions. The concentration ($m$) is also effectively the same (1 molal, approximately). Therefore, the boiling point elevation ($\Delta T_b$) is primarily dependent on the van't Hoff factor ($i$). A higher van't Hoff factor means more particles are present in the solution, leading to a greater elevation in the boiling point.

Determining the van't Hoff Factor (\(i\)) for Each Compound

Let's determine the van't Hoff factor ($i$) for each of the given compounds, assuming complete dissociation for ionic compounds:

• A. C6H12O6 (Glucose): Glucose is a covalent compound and a non-electrolyte. It does not dissociate in water.

  C6H12O6(s) → C6H12O6(aq)

  Number of particles = 1. So, $i = 1$.

• B. NaCl (Sodium Chloride): Sodium chloride is an ionic compound that dissociates into one sodium ion and one chloride ion.

  NaCl(s) → Na⁺(aq) + Cl^-(aq)

  Number of particles = 1 + 1 = 2. So, $i = 2$.

• C. MgCl2 (Magnesium Chloride): Magnesium chloride is an ionic compound that dissociates into one magnesium ion and two chloride ions.

  MgCl₂(s) → Mg²⁺(aq) + 2Cl^-(aq)

  Number of particles = 1 + 2 = 3. So, $i = 3$.

• D. AlCl3 (Aluminum Chloride): Aluminum chloride is an ionic compound that dissociates into one aluminum ion and three chloride ions.

  AlCl₃(s) → Al³⁺(aq) + 3Cl^-(aq)

  Number of particles = 1 + 3 = 4. So, $i = 4$.

• E. Al2(SO4)3 (Aluminum Sulfate): Aluminum sulfate is an ionic compound that dissociates into two aluminum ions and three sulfate ions.

  Al₂(SO₄)₃(s) → 2Al³⁺(aq) + 3SO₄^2-(aq)

  Number of particles = 2 + 3 = 5. So, $i = 5$.

Comparing van't Hoff Factors and Boiling Point Elevation

We can now list the van't Hoff factors for each compound:

Since $\Delta T_b$ is directly proportional to $i$ (when $K_b$ and $m$ are constant), the order of increasing boiling point elevation will be the same as the order of increasing van't Hoff factors:

Order of $i$: 1 < 2 < 3 < 4 < 5

Corresponding order of compounds:

A ($i=1$) < B ($i=2$) < C ($i=3$) < D ($i=4$) < E ($i=5$).

Final Arrangement by Increasing Boiling Point Elevation

Arranging the solutions in the increasing order of their elevation in boiling points based on their van't Hoff factors, we get:

C₆H₁₂O₆ < NaCl < MgCl₂ < AlCl₃ < Al₂(SO₄)₃

Which corresponds to the order:

A < B < C < D < E

Boiling Point Elevation Revision

Additional Information on Colligative Properties and Solutions

Colligative properties are crucial for understanding the behavior of solutions. Besides boiling point elevation, other colligative properties include freezing point depression, osmotic pressure, and vapor pressure lowering. All these properties are directly proportional to the concentration of solute particles.

Types of Solutes:

• Non-electrolytes: These compounds (like glucose, sucrose, urea) do not dissociate into ions when dissolved in water. The number of particles remains the same as the number of molecules dissolved, so $i=1$.
• Electrolytes: These compounds dissociate into ions when dissolved in water.
  • Strong Electrolytes: These dissociate completely (or nearly completely) into ions. Ionic compounds (salts, strong acids, strong bases) are typically strong electrolytes. The van't Hoff factor ($i$) for strong electrolytes is equal to the number of ions formed per formula unit upon complete dissociation.
  • Weak Electrolytes: These dissociate only partially into ions. Weak acids and weak bases are weak electrolytes. For weak electrolytes, the actual van't Hoff factor is between 1 and the theoretical number of ions formed by complete dissociation, depending on the degree of dissociation. In this problem, we assumed strong electrolytes dissociate completely.

The van't Hoff factor allows us to account for the increased number of particles in solutions of electrolytes compared to solutions of non-electrolytes of the same molar concentration. This explains why a 1M solution of NaCl has a greater boiling point elevation than a 1M solution of glucose, and why solutions of salts with more ions (like Al2(SO4)3) have even higher boiling point elevations at the same concentration.