Question

List the following aqueous solutions in order of decreasing freezing point: 0.040 \(\mathrm{m}\) glycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right), 0.020 \mathrm{m} \mathrm{KBr}\) 0.030 \(\mathrm{mphenol}\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\)

Short answer

The aqueous solutions in order of decreasing freezing point are: 1) Glycerin and KBr (both with a freezing point depression of 0.0744 °C) and 2) Phenol (with a freezing point depression of 0.0558 °C).

Step-by-step solution

Determine the van't Hoff factor (i) of each solution.

For glycerin, one molecule of glycerin (C3H8O3) does not dissociate in solution, so i = 1. For KBr, it will dissociate into K+ and Br- ions, so the i = 2. For phenol, one molecule of phenol (C6H5OH) does not dissociate in solution, so i = 1.

Calculate the molality (m) of each solute.

The given molality (m) for each solution is: - Glycerin: m = 0.040 m - KBr: m = 0.020 m - Phenol: m = 0.030 m

Calculate the freezing point depression of each solution.

The freezing point depression (∆Tf) is given by the equation: ∆Tf = i * Kf * m, where Kf is the molal freezing point depression constant for water, which is 1.86 °C/m. For glycerin: ∆Tf = (1) * (1.86 °C/m) * (0.040 m) = 0.0744 °C For KBr: ∆Tf = (2) * (1.86 °C/m) * (0.020 m) = 0.0744 °C For phenol: ∆Tf = (1) * (1.86 °C/m) * (0.030 m) = 0.0558 °C

Order the solutions by decreasing freezing point depression.

From the calculated values: - Glycerin: ∆Tf = 0.0744 °C - KBr: ∆Tf = 0.0744 °C - Phenol: ∆Tf = 0.0558 °C As higher freezing point depression indicates lower freezing point, we can list the solutions in order of decreasing freezing point: 1. Glycerin and KBr (same freezing point depression: 0.0744 °C) 2. Phenol (freezing point depression: 0.0558 °C)

Key concepts

Van't Hoff Factor

The Van't Hoff factor, often represented by the symbol \( i \), is a crucial concept in solutions chemistry. It quantifies the effect of a solute on the colligative properties of a solution, specifically those that depend on the number of particles rather than their identity. Understanding the Van't Hoff factor helps in predicting how a solute will affect properties such as boiling point elevation and freezing point depression.
For non-electrolytes, which do not dissociate into ions in solution, the Van't Hoff factor is \( i = 1 \). This is the case for molecules like glycerin and phenol. Their molecules remain intact when dissolved, meaning they do not increase the number of solute particles.
For electrolytes that dissociate into ions, such as KBr, the Van't Hoff factor increases. KBr dissociates into \( \text{K}^+ \) and \( \text{Br}^- \) in solution, so its Van't Hoff factor is \( i = 2 \). This is because each formula unit of KBr creates two particles in solution, effectively doubling its impact on colligative properties like freezing point depression.

Molality

Molality, denoted as \( m \), is a measure of the concentration of a solute in a solution. Unlike molarity, which is dependent on volume, molality is dependent on the mass of the solvent, making it unaffected by temperature or pressure changes. Molality is defined as the number of moles of solute per kilogram of solvent.
This concentration measure is particularly useful in colligative properties calculations, like freezing point depression. It ensures that changes in temperature do not skew the measurements, allowing for precise calculations in varying conditions. For example, in the context of the given exercise, the molality values are:

• Glycerin: \( 0.040 \, \text{m} \)
• KBr: \( 0.020 \, \text{m} \)
• Phenol: \( 0.030 \, \text{m} \)

Using these molalities with the respective Van't Hoff factors, we can calculate freezing point depression effectively, highlighting the importance of understanding and using molality in solutions chemistry.

Solutions Chemistry

Solutions chemistry is the study of substances dissolved in solvents, which forms a homogenous mixture called a solution. This field examines multiple properties and behaviors of solutions, including how solutes affect the colligative properties like boiling point elevation, vapor pressure lowering, and freezing point depression.
Freezing point depression in solutions illustrates how the presence of solute particles interferes with the crystallization process of the solvent, thus lowering the temperature at which a substance freezes. The extent of this depression is determined by the concentration of the solute (in terms of molality) and how many particles the solute generates (as indicated by the Van't Hoff factor).
Understanding solutions chemistry allows us to predict and manipulate the physical properties of a solution, which can be beneficial in various practical applications, such as creating antifreeze solutions that prevent freezing in cold climates. By analyzing components like Van't Hoff factors and molality, solutions chemistry provides tools for optimizing desired solution characteristics efficiently.