Problem 109 - Chemistry The Molecular Science

Question

Arrange these aqueous solutions in order of increasing boiling point. (Assume theoretical values for \(i\).) (a) \(0.20 \mathrm{~mol}\) ethylene \(\mathrm{glycol} / \mathrm{kg}\) (b) \(0.12 \mathrm{~mol} \mathrm{~K}_{2} \mathrm{SO}_{4} / \mathrm{kg}\) (c) \(0.10 \mathrm{~mol} \mathrm{BaCl}_{2} / \mathrm{kg}\) (d) \(0.12 \mathrm{~mol} \mathrm{KBr} / \mathrm{kg}\)

Step-by-Step Solution

Answer

(a) < (d) < (c) < (b) in order of increasing boiling point.

Step 1: Understand the Problem

The problem asks us to arrange solutions based on their boiling points. Each solution has a solute dissolved in water, which affects the boiling point due to boiling point elevation, a colligative property related to the number of solute particles in the solution.

Step 2: Determine the Van't Hoff Factor (i)

The Van't Hoff factor, denoted as \(i\), represents the number of particles a solute dissociates into in solution:- Ethylene glycol (a non-electrolyte): \(i = 1\).- \(\mathrm{K}_2\mathrm{SO}_4\) (dissociates into 3 ions): \(i = 3\).- \(\mathrm{BaCl}_2\) (dissociates into 3 ions): \(i = 3\).- \(\mathrm{KBr}\) (dissociates into 2 ions): \(i = 2\).

Step 3: Calculate the Effective Molality

The effective molality is the product of the actual molality and the Van't Hoff factor since boiling point elevation depends on the number of particles:- Ethylene glycol: \(0.20 \, \text{mol/kg} \times 1 = 0.20\).- \(\mathrm{K}_2\mathrm{SO}_4\): \(0.12 \, \text{mol/kg} \times 3 = 0.36\).- \(\mathrm{BaCl}_2\): \(0.10 \, \text{mol/kg} \times 3 = 0.30\).- \(\mathrm{KBr}\): \(0.12 \, \text{mol/kg} \times 2 = 0.24\).

Step 4: Rank the Solutions

The boiling point increases with higher effective molality. Arrange the solutions by effective molality from lowest to highest:1. Ethylene glycol: 0.20.2. \(\mathrm{KBr}\): 0.24.3. \(\mathrm{BaCl}_2\): 0.30.4. \(\mathrm{K}_2\mathrm{SO}_4\): 0.36.

Key Concepts

Colligative Properties

Colligative properties are fascinating because they depend solely on the number of solute particles in a solution, not their identity. This means that what matters is how many particles are in the solution, regardless of what those particles are made of. Some common colligative properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

Among these properties, boiling point elevation is important for understanding how solutions' properties differ from pure solvents. When a solute is added to a solvent, the boiling point of the resulting solution is higher than that of the pure solvent. Why does this happen? It's because the solute particles make it harder for solvent molecules to enter the gaseous phase as they're heated up. Therefore, more heat (or energy) is required to boil the solution.

• Boiling point elevation is directly proportional to the number of solute particles.
• The greater the number of particles, the higher the boiling point elevation.

This dependency on the number of particles brings us to another key concept: the Van't Hoff factor.

Van't Hoff Factor

The Van't Hoff factor, denoted as \( i \), is a concept used to quantify the effect of solute particles in a solution. Essentially, it tells us how many particles the solute dissociates into when dissolved in a solvent. This is important because the more particles there are in a solution, the greater the change in colligative properties.

Here's how it works in some common cases:

• A non-electrolyte, like ethylene glycol, does not dissociate into ions, so \( i = 1 \).
• For ionic compounds such as \( \text{K}_2\text{SO}_4 \) and \( \text{BaCl}_2 \), which dissociate into multiple ions, \( i = 3 \).
• Other ionic compounds like \( \text{KBr} \) dissociate into two ions, giving \( i = 2 \).

The Van't Hoff factor plays a critical role in calculating the effective molality, which is what we will explore next.

Effective Molality

Effective molality helps quantify the total concentration of solute particles present in a solution. This measure is crucial in determining various colligative properties, including boiling point elevation. To compute effective molality, we multiply the actual molality of the solute (moles of solute per kilogram of solvent) by the Van't Hoff factor \( i \).

Let's take an example and see how this works into practical use. Consider ethylene glycol with a molality of 0.20 mol/kg. Since it's a non-electrolyte, its effective molality is simply:
\[0.20 \, \text{mol/kg} \times 1 = 0.20\]\

• For \( \text{K}_2\text{SO}_4 \), the effective molality is:
  \[0.12 \, \text{mol/kg} \times 3 = 0.36\]
• For \( \text{BaCl}_2 \), the calculation becomes:
  \[0.10 \, \text{mol/kg} \times 3 = 0.30\]
• Finally, for \( \text{KBr} \):
  \[0.12 \, \text{mol/kg} \times 2 = 0.24\]

These effective molalities then allow us to determine which solution has the greatest impact on the boiling point — the higher the effective molality, the greater the boiling point elevation.