Problem 67 - Chemistry: The Central Science

Question

List the following aqueous solutions in order of increasing boiling point: \(0.120 \mathrm{~m}\) glucose, \(0.050 \mathrm{~m} \mathrm{LiBr}, 0.050 \mathrm{~m}\) \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}\).

Step-by-Step Solution

Answer

The order of increasing boiling point for the given aqueous solutions is: \(0.120 \mathrm{~m}\) glucose < \(0.050 \mathrm{~m}\) LiBr < \(0.050 \mathrm{~m}\) Zn(NO₃)₂, based on the molality of total solute particles (0.120 m, 0.100 m, and 0.150 m, respectively).

Step 1: Identify the solute particles in each solution

In each solution, we'll determine the solute particles present: 1. 0.120 m glucose (C₆H₁₂O₆): Glucose is a covalent compound, so it stays as a single solute particle. 2. 0.050 m LiBr: LiBr is an ionic compound, which dissolves into Li⁺ and Br⁻ ions. There will be 2 solute particles for each dissolved LiBr unit. 3. 0.050 m Zn(NO₃)₂: Zn(NO₃)₂ is an ionic compound that dissolves into Zn²⁺ and 2 NO₃⁻ ions. There will be 3 solute particles for each dissolved Zn(NO₃)₂ unit.

Step 2: Find the molality of all solute particles in each solution

Now that we've identified the solute particles in each solution, let's find the molality of all particles in each solution: 1. 0.120 m glucose: 1 C₆H₁₂O₆ particle for every 0.120 molality of glucose = 0.120 m of total solute particles. 2. 0.050 m LiBr: As there are 2 solute particles per LiBr unit, we multiply 0.050 m by 2 = 0.100 m of total solute particles. 3. 0.050 m Zn(NO₃)₂: As there are 3 solute particles per Zn(NO₃)₂ unit, we multiply 0.050 m by 3 = 0.150 m of total solute particles.

Step 3: List the solutions in order of increasing boiling point

According to the molality of total solute particles, we can arrange the solutions in order of increasing boiling point: 1. 0.120 m glucose: 0.120 m 2. 0.050 m LiBr: 0.100 m 3. 0.050 m Zn(NO₃)₂: 0.150 m So, the order of increasing boiling point is: 0.120 m glucose < 0.050 m LiBr < 0.050 m Zn(NO₃)₂.

Key Concepts

Colligative Properties

Colligative properties are a set of solution properties that depend only on the ratio of solute particles to solvent particles in a solution, and not on the chemical properties of the solute itself. This means the nature of the solute—whether it's a salt, sugar, or any other substance—does not directly affect colligative properties. Instead, these properties are influenced by the number of particles in solution.

One of the most commonly studied colligative properties is boiling point elevation. When a non-volatile solute is dissolved in a solvent, it causes the solvent's boiling point to increase. This happens because the solute particles disrupt the solvent's ability to enter the gas phase, thereby requiring more energy (higher temperature) to boil.

Boiling point elevation can be calculated using specific formulas and depends on the molality of the solution, as well as the van't Hoff factor, which indicates the number of particles the solute dissociates into.

Molality

Molality is a measure of the concentration of a solution and is defined as the number of moles of solute per kilogram of solvent. It is represented by the symbol 'm' and is calculated using the formula:

\[\begin{equation} \text{Molality} (m) = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \end{equation}\]

Unlike molarity, which is affected by temperature changes due to volume contraction or expansion, molality is temperature-independent since it is based on mass. This characteristic makes molality especially useful in calculations involving boiling point elevation and other colligative properties, where temperature changes are involved.

Ionic Compounds

Ionic compounds are made up of positively and negatively charged ions held together by strong electrostatic forces known as ionic bonds. Common table salt, or sodium chloride (NaCl), is an example of an ionic compound. When these compounds dissolve in water, they dissociate into their respective ions.

For example, LiBr dissolves into Li⁺ and Br⁻ ions, which means the original LiBr formula unit contributes two particles to the solution. This dissociation is crucial when calculating the colligative properties of the solution because each ion counts as a separate solute particle, affecting the extent to which the properties like boiling point are elevated. It's also important to apply the van't Hoff factor, which is the number of particles the compound dissociates into in solution.

Covalent Compounds

Covalent compounds are formed when two or more non-metal atoms share valence electrons in a manner that balances the atoms' needs for additional electrons to achieve a stable electron configuration. This sharing results in a covalent bond.

In solutions, most covalent compounds, such as glucose (C₆H₁₂O₆), do not dissociate into ions. They dissolve as individual molecules, so one formula unit of a covalent compound like glucose contributes only one particle to the solution. This characteristic is significant when predicting the impact of a solute on colligative properties. Since molecular compounds do not dissociate, their effect on properties such as boiling point elevation is often less pronounced than that of ionic compounds, which provide multiple particles per formula unit.