Problem 79 - Chemistry The Science in Context

Question

Arrange the following aqueous solutions in order of increasing boiling point: a. \(0.06 \mathrm{m} \mathrm{FeCl}_{3}(i=3.4)\) b. \(0.10 m \mathrm{MgCl}_{2}(i=2.7)\) c. \(0.20 \mathrm{m} \mathrm{KCl}(i=1.9)\)

Step-by-Step Solution

Answer

Question: Arrange the following aqueous solutions in order of increasing boiling point: a. 0.06 m FeCl3 (i=3.4), b. 0.10 m MgCl2 (i=2.7), c. 0.20 m KCl (i=1.9). Answer: The aqueous solutions arranged in order of increasing boiling point are a. 0.06 m FeCl3 (i=3.4), b. 0.10 m MgCl2 (i=2.7), and c. 0.20 m KCl (i=1.9).

Step 1: (Step 1: Calculate the product of m and i for each solution)

For each solution, multiply the given molality (m) by the given van't Hoff factor (i). a. \(0.06\,\mathrm{m}\,\mathrm{FeCl_3}(i=3.4)\) Product: \(0.06\,\mathrm{m} \cdot 3.4 = 0.204\) b. \(0.10\,\mathrm{m}\,\mathrm{MgCl_2}(i=2.7)\) Product: \(0.10\,\mathrm{m} \cdot 2.7 = 0.27\) c. \(0.20\,\mathrm{m}\,\mathrm{KCl}(i=1.9)\) Product: \(0.20\,\mathrm{m} \cdot 1.9 = 0.38\)

Step 2: (Step 2: Arrange the solutions in order of increasing boiling point elevation)

Compare the product of molality and van't Hoff factor and arrange the solutions. We have the products: a. \(0.204\) b. \(0.27\) c. \(0.38\) Thus, the order of increasing boiling point elevation is: a < b < c.

Step 3: (Step 3: Give the final answer)

Based on the calculations, the aqueous solutions arranged in order of increasing boiling point are: a. \(0.06\,\mathrm{m}\,\mathrm{FeCl_3}(i=3.4)\) b. \(0.10\,\mathrm{m}\,\mathrm{MgCl_2}(i=2.7)\) c. \(0.20\,\mathrm{m}\,\mathrm{KCl}(i=1.9)\)

Key Concepts

Molality

Molality is a measure of the concentration of a solution defined in terms of the amount of solute per kilogram of solvent. It is expressed in units of molal (m), which is shorthand for moles of solute per kilogram of solvent. Molality is particularly useful when dealing with phenomena that depend on the temperature, such as boiling point elevation, because it is independent of the volume of the solution, which can change with temperature.
Molality is calculated as:

• molality (m) = \( \frac{\text{moles of solute}}{\text{kilograms of solvent}} \)

An example of this is in solutions like the ones in the exercise, where salts like FeCl₃, MgCl₂, and KCl are dissolved in water.
These compounds are ionic, meaning they dissociate into ions in aqueous solutions, providing an important factor for calculating their effect on boiling point elevation.

Van't Hoff Factor

The van't Hoff factor, denoted as \(i\), is crucial in determining the effect of solute particles on colligative properties, such as boiling point elevation. It represents the number of particles a solute forms in solution relative to the number of formula units dissolved.
For example:

• FeCl₃ dissociates into four particles: one Fe³⁺ ion and three Cl^- ions resulting in \(i \approx 3.4\).
• MgCl₂ breaks down into three particles: one Mg²⁺ ion and two Cl^- ions indicating \(i \approx 2.7\).
• KCl dissociates into two particles: one K⁺ ion and one Cl^- ion giving \(i \approx 1.9\).

The van't Hoff factor helps in adjusting the concentration of particles in calculations of colligative properties by considering the dissociation in solution, reflecting how many effective particles are present in the solution compared to pure solute.

Solution Concentration

Solution concentration is the measure of how much solute is present in a given amount of solvent. It is essential for determining the physical properties of solutions, including boiling point elevation.
Two common ways to express concentration are:

• Molality (as discussed previously).
• Molarity, which is moles of solute per liter of solution.

For boiling point elevation calculations like those in the exercise, molality is favored because it stays constant with temperature changes, unlike molarity.
Understanding solution concentration is key to predicting and comparing the properties of different solutions, such as which will have a higher boiling point, by applying the relationship between concentration and colligative properties.

Aqueous Solutions

Aqueous solutions are mixtures where water is the solvent.
They are incredibly significant in both chemistry and everyday life, as water is a universal solvent with the ability to dissolve many substances, particularly ionic compounds like salts.
In the context of the boiling point elevation exercise, an aqueous solution means that substances like FeCl₃, MgCl₂, and KCl are all dissolved in water, which is the solvent.
The dissolved ions interact with water molecules, affecting how the solvent's properties change, such as increasing the boiling point.

• This change is due to the disruption of hydrogen bonding between water molecules caused by the presence of solute particles.
• The more ions present, the greater the effect on boiling point elevation, which highlights the importance of the van't Hoff factor and molality.

Understanding how aqueous solutions work helps us to predict the behavior of solutions under various conditions, like temperature changes.