Question

Arrange the following aqueous solutions in order of decreasing freezing point, and explain your reasoning: \(0.50 \mathrm{~m} \mathrm{HCl}, 0.50 \mathrm{~m}\) glucose, \(0.50 \mathrm{~m}\) acetic acid.

Short answer

Arrange: 0.50 m glucose > 0.50 m acetic acid > 0.50 m HCl.

Step-by-step solution

Understanding Colligative Properties

Colligative properties depend on the number of solute particles in a solution, not on their identity. Freezing point depression is one of these properties, meaning the addition of solute lowers the freezing point of a solvent. For solutions, the greater the number of solute particles, the lower the freezing point.

Identifying Solute Particles

First, glucose (\(\text{C}_6\text{H}_{12}\text{O}_6\)) is a non-electrolyte and does not ionize in water, contributing 1 particle per molecule to the solution. Acetic acid (\(\text{CH}_3\text{COOH}\)) is a weak electrolyte, partially ionizing in water to form \(\text{CH}_3\text{COO}^-\) and \(\text{H}^+\), providing slightly more than 1 particle per molecule, revealing it partly dissociates but not completely. HCl is a strong electrolyte, fully ionizing into \(\text{H}^+\) and \(\text{Cl}^-\), which accounts for 2 particles per molecule.

Comparing Freezing Point Depressions

For equal molal concentrations, the depression in freezing point increases with the number of particles formed by solute molecules. Glucose contributes only 1 particle, acetic acid slightly more than 1 due to partial ionization, and HCl provides the maximum of 2 particles. Therefore, in order of decreasing freezing points, the list goes: glucose (least depression), acetic acid (medium depression), and HCl (most depression).

Arranging the Solutions

Based on the above analysis, arrange the solutions in order of decreasing freezing point: 0.50 m glucose, 0.50 m acetic acid, and 0.50 m HCl.

Key concepts

Colligative Properties

Colligative properties are unique characteristics of solutions that depend primarily on the number of solute particles, rather than their chemical identity. A well-known example of this is freezing point depression. When a solute is added to a solvent, it disrupts the solvent's ability to form a solid structure as its temperature lowers, which effectively reduces the freezing point of the solution. This is why, during winter, salt is spread on icy roads; the salt disrupts the water molecules and helps to prevent ice formation.
The relationship between the number of solute particles and the extent of freezing point depression is a direct one: the more particles that dissolve in the solution, the lower the freezing point becomes. This principle is crucial in determining how different substances, when dissolved, will affect the freezing point of a solvent. It’s important to remember that this property doesn’t rely on what the solute is, but on how many particles it splits into when it dissolves. This is why colligative properties are a topic of interest in studying electrolytes and nonelectrolytes.

Electrolytes

Electrolytes are substances that, when dissolved in water, break apart into ions and thus conduct electricity. When thinking about colligative properties, electrolytes play a crucial role in the number of particles they provide to a solution. Electrolytes can be classified into two categories based on their ability to dissociate in a solution: strong electrolytes and weak electrolytes.
- **Strong Electrolytes**: These compounds completely ionize in a solution. For instance, hydrochloric acid (HCl) dissociates fully into hydrogen ions ( \( ext{H}^+ \) ) and chloride ions ( \( ext{Cl}^- \) ), contributing significantly more particles to the solution compared to non-electrolytes. With 0.50 m HCl, there are 2 times the number of initial molecules since it splits entirely into two different ions.- **Weak Electrolytes**: Such as acetic acid, only partially dissociate, producing fewer ions compared to strong electrolytes. For instance, acetic acid in water exists more as whole molecules with some dissociation into acetate ions ( \( ext{CH}_3 ext{COO}^- \) ) and hydrogen ions ( \( ext{H}^+ \) ). Thus, acetic acid will cause less freezing point depression than HCl but more than a non-electrolyte like glucose.In conclusion, knowing whether a solute is a strong or weak electrolyte helps predict how it affects the colligative properties of a solution.

Solutions

A solution is a homogeneous mixture consisting of two or more substances. In this context, it often involves a solvent (like water) and one or more solutes (like glucose, acetic acid, or HCl). Understanding the various factors that influence solutions helps to explain many natural and artificial processes. Colligative properties, including freezing point depression, highlight the collective nature of solutions.
Solutions can be categorized based on the properties of the solutes they contain: - **Non-Electrolyte Solutions**: These contain solutes that do not ionize in water. Glucose is an example, which remains as individual molecules without breaking into ions. It results in a single particle contribution per molecule to the solution, hence causing the least disruption to the freezing point. - **Electrolyte Solutions**: When these solutes are added, they may split into ions. Like the case of HCl, it can significantly alter the number of particles added to the solution, enhancing the colligative impact drastically compared to non-electrolytes. Knowing whether a substance is an electrolyte or non-electrolyte and understanding how many particles it forms can help predict its impact on the freezing point of the solution. So, when arranging solutions like 0.50 m solutions of HCl, glucose, and acetic acid based on their freezing points, it's the particle count from the dissolution process that sets the order.