Understanding Boiling Point Elevation and Colligative Properties

This question asks us to identify the solution among four given options that will have the highest boiling point. The boiling point of a solution is a colligative property, meaning it depends on the concentration of solute particles, not on the identity of the solute itself. Adding a non-volatile solute to a solvent increases the boiling point of the solvent. This phenomenon is called boiling point elevation.

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

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

Where:

• \(\Delta T_b\) is the increase in boiling point compared to the pure solvent.
• \(i\) is the van't Hoff factor, which represents the number of particles the solute dissociates into when dissolved in the solvent.
• \(K_b\) is the molal boiling point elevation constant, which is a property of the solvent.
• \(m\) is the molal concentration of the solution.

In this problem, all solutions have the same molar concentration (1M), and we assume they are all in the same solvent (likely water, as it's a common solvent for these solutes). For dilute solutions, molarity is approximately proportional to molality, so we can compare based on molarity. The constant \(K_b\) is the same for all solutions since the solvent is the same. Therefore, the boiling point elevation, and thus the boiling point, will be highest for the solution with the largest van't Hoff factor (\(i\)).

Analyzing the Solutions and Van't Hoff Factor

We need to determine the van't Hoff factor (\(i\)) for each of the given solutes. Ionic compounds dissociate into ions when dissolved, while non-ionic (molecular) compounds generally do not dissociate. The van't Hoff factor for an ionic compound is approximately equal to the number of ions formed per formula unit.

• 1M BaCl₂ solution: Barium chloride (BaCl₂) is an ionic compound. When it dissolves in water, it dissociates into one barium ion (Ba²⁺) and two chloride ions (Cl^-).

  BaCl\(_2\)\((aq)\) \(\rightarrow\) Ba\(^{2+}\)\((aq)\) + 2Cl\(^-\)\((aq)\)

  Total number of particles = 1 cation + 2 anions = 3 particles.

  Assuming complete dissociation, the van't Hoff factor \(i\) for BaCl₂ is 3.

• 1M NaCl solution: Sodium chloride (NaCl) is an ionic compound. When it dissolves, it dissociates into one sodium ion (Na⁺) and one chloride ion (Cl^-).

  NaCl\((aq)\) \(\rightarrow\) Na\(^+\)\((aq)\) + Cl\(^-\)\((aq)\)

  Total number of particles = 1 cation + 1 anion = 2 particles.

  Assuming complete dissociation, the van't Hoff factor \(i\) for NaCl is 2.

• 1M C₆H₁₂O₆ solution: Glucose (C₆H₁₂O₆) is a molecular compound (sugar). It does not dissociate into ions when dissolved in water.

  The van't Hoff factor \(i\) for glucose is 1.

• 1M (NH₂)₂CO solution: Urea ((NH₂)₂CO) is a molecular compound. It does not dissociate into ions when dissolved in water.

  The van't Hoff factor \(i\) for urea is 1.

Comparing the van't Hoff factors:

• BaCl₂: \(i = 3\)
• NaCl: \(i = 2\)
• C₆H₁₂O₆: \(i = 1\)
• (NH₂)₂CO: \(i = 1\)

The highest van't Hoff factor is 3, which corresponds to the 1M BaCl₂ solution.

Conclusion on Boiling Point Elevation

Since boiling point elevation is directly proportional to the van't Hoff factor \(i\) (for solutions of the same molar concentration and solvent), the solution with the highest \(i\) will have the greatest boiling point elevation. A greater boiling point elevation means a higher boiling point.

The 1M BaCl₂ solution has the highest van't Hoff factor (\(i=3\)), therefore it will have the highest boiling point among the given options.

Revision Table: Colligative Properties Summary

Additional Information on Colligative Properties

Colligative properties are fascinating because they highlight how the mere presence of solute particles affects the physical properties of the solvent, regardless of what the particles actually are (their chemical identity). These properties are crucial in many applications, such as determining molar masses of unknown substances, desalination of water (using osmotic pressure), and creating anti-freeze solutions (using freezing point depression).

While we assumed complete dissociation for ionic compounds here, in reality, dissociation may not be 100%, especially in concentrated solutions. This can lead to the actual van't Hoff factor being slightly less than the theoretical integer value. However, for dilute solutions like 1M, the assumption of complete dissociation provides a good approximation for comparing the relative effects.