Question

List the following aqueous solutions in order of decreasing freezing point: \(0.040 \mathrm{~m}\) glycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right), 0.020 \mathrm{~m} \mathrm{KBr}\),

Short answer

The order of decreasing freezing point for the given aqueous solutions is: Sodium acetate \((0.010 \mathrm{~m}\)) > Glycerin \((0.040 \mathrm{~m})\) = KBr \((0.020 \mathrm{~m})\).

Step-by-step solution

Calculate the van't Hoff factor for each solute

The van't Hoff factor (i) for glycerin, a non-electrolyte, is 1 because it does not dissociate into ions in solution. For KBr, a strong electrolyte, the van't Hoff factor is 2, as it dissociates into one K+ and one Br- ion. For sodium acetate, a strong electrolyte, the van't Hoff factor is 2, as it dissociates into one Na+ and one \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^-\) ion.

Calculate freezing point depression for each solution

We can use the formula ΔTf = Kf * m * i to find the freezing point depression for each of the solutions. For simplicity, we'll assume Kf is the same for all three solutions since we are only comparing the relative decrease in freezing point. For glycerin: ΔTf = Kf * 0.040 m * 1 = 0.040 Kf For KBr: ΔTf = Kf * 0.020 m * 2 = 0.040 Kf For sodium acetate: ΔTf = Kf * 0.010 m * 2 = 0.020 Kf

List the solutions in order of decreasing freezing point

The solution with the highest freezing point depression will have the lowest freezing point. Based on the calculations above, - Sodium acetate has the lowest ΔTf (0.020 Kf), so it has the highest freezing point. - Glycerin and KBr have the same ΔTf (0.040 Kf), so they would have the same freezing point, which is lower than sodium acetate. So, the order of decreasing freezing point is sodium acetate > glycerin = KBr.

Key concepts

Van't Hoff Factor

In the realm of chemistry, the van't Hoff factor, denoted as \( i \), is pivotal when discussing the behavior of solutions, especially in determining colligative properties like freezing point depression. This factor indicates the number of particles a compound dissociates into in a solution. For substances that do not dissociate, known as non-electrolytes, the van't Hoff factor is 1. This means they do not split into ions, retaining their molecular structure.

Conversely, electrolytes dissociate in aqueous solutions, splitting into ions. Strong electrolytes, like potassium bromide (KBr) and sodium acetate, completely dissociate, resulting in a van't Hoff factor greater than 1. For instance, KBr dissociates into two ions: K\(^+\) and Br\(^-\), which makes its van't Hoff factor 2. Similarly, sodium acetate splits into sodium (Na\(^+\)) and acetate (\(\text{C}_2\text{H}_3\text{O}_2^-\)).

Understanding the van't Hoff factor helps predict how a solute in solution will affect properties such as boiling point, osmotic pressure, and indeed, freezing point. It effectively tells us how many times the solute concentration appears increased purely by dissociation.

Aqueous Solutions

Aqueous solutions are an integral part of chemistry, formed when a solute dissolves in water, which acts as the solvent. Water, due to its polar nature, is excellent at dissolving a wide range of substances, making it a universal solvent.

In many chemical processes and reactions, aqueous solutions are crucial because ionic compounds often dissolve in water to form ions, which are free to interact and react. Because the solvent is water, these solutions exhibit properties that are crucial for calculations involving colligative properties. Such properties include boiling point elevation and freezing point depression, which depend on the concentration of dissolved particles, rather than the identity of the solute itself.

In understanding the behavior of aqueous solutions, we pay careful attention to how substances like electrolytes and non-electrolytes dissolve, as this influences the number of particles that interface with each other and with the solvent. It's these interactions that affect the solution's macroscopic properties.

Electrolytes and Non-electrolytes

When solutes dissolve in water to form an aqueous solution, they can be classified into two broad categories: electrolytes and non-electrolytes based on their ability to conduct electricity.

**Electrolytes** are substances that dissociate into ions in water, thus enabling the solution to conduct electricity. They can be further categorized into strong and weak electrolytes. Strong electrolytes, like KBr and sodium acetate, completely dissociate in solution, which is why their van't Hoff factors are typically greater than 1. These complete dissociations are the reason such solutions are good conductors of electricity. Weak electrolytes only partially dissociate, resulting in fewer ions in solution.

On the other hand, **non-electrolytes** do not dissociate into ions when dissolved. For example, glycerin remains intact as molecules in solution. Non-electrolytes do not conduct electricity because they do not produce charged particles. Their property of staying intact contributes to a van't Hoff factor of 1, and they have different implications for colligative properties when compared with electrolytes.

Recognizing whether a compound is an electrolyte or a non-electrolyte helps predict its impact on the freezing point of solutions and other physical properties.