Problem 71 - Chemistry: The Central Science in SI Units, Global Edition

Question

List the following aqueous solutions in order of increasing boiling point: \(0.080 \mathrm{~m} \mathrm{KBr}, 0.130 \mathrm{~m}\) urea \(\left(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\right)\), \(0.080 \mathrm{~m} \mathrm{Mg}\left(\mathrm{NO}_{2}\right)_{2}\) \(0.030 \mathrm{~m}\) phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\)

Step-by-Step Solution

Answer

The aqueous solutions listed in order of increasing boiling point are: Phenol, Urea, KBr, and Mg(NO_2)_2.

Step 1: Identify the van't Hoff factors for all solutes

Determine the number of ions or particles that each solute dissociates into when dissolved in water: 1. KBr: This is an ionic compound that dissociates into K+ and Br- ions. The van't Hoff factor, i, for KBr is 2. 2. Urea (CO(NH_2)_2): This is a covalent compound that does not dissociate in water. The van't Hoff factor, i, for urea is 1. 3. Mg(NO_2)_2: This ionic compound dissociates into one Mg2+ ion and two NO_2- ions. The van't Hoff factor, i, for this compound is 3. 4. Phenol (C_6H_5OH): This is a covalent compound that does not dissociate in water. The van't Hoff factor, i, for phenol is 1.

Step 2: Calculate the change in boiling point for each solution

Using the boiling point elevation formula, we can determine the change in boiling points for each solution: \[\Delta T_b = iK_bm\] Since we only need to arrange the solutions in order of boiling points and the boiling-point elevation constant, \(K_b\), is the same for all solutes in water, we can compare the product of \(i\) and \(m\) for each solution to determine their order. 1. KBr solution: \((i \times m) = 2 \times 0.080 = 0.16\) 2. Urea solution: \((i \times m) = 1 \times 0.130 = 0.13\) 3. Mg(NO_2)_2 solution: \((i \times m) = 3 \times 0.080 = 0.24\) 4. Phenol solution: \((i \times m) = 1 \times 0.030 = 0.03\)

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

Now that we have the product of van't Hoff factor and molality for each solution, we can list them in order of increasing boiling points: 1. Phenol solution (\(i \times m = 0.03\)) 2. Urea solution (\(i \times m = 0.13\)) 3. KBr solution (\(i \times m = 0.16\)) 4. Mg(NO_2)_2 solution (\(i \times m = 0.24\)) In conclusion, the aqueous solutions can be listed in order of increasing boiling points as follows: Phenol, Urea, KBr, and Mg(NO_2)_2.

Key Concepts

Van't Hoff Factor

The van't Hoff factor, denoted as \( i \), plays a crucial role in solutions, particularly when examining properties like boiling point elevation. This factor represents the number of particles a solute dissociates into when dissolved in a solvent.

For example, KBr, a typical ionic compound, separates into two ions \( K^+ \) and \( Br^- \). Thus, it has a van't Hoff factor of 2. Conversely, covalent compounds like urea and phenol do not dissociate in water, resulting in a van't Hoff factor of 1 for both.

Understanding \( i \) helps in predicting how a solute will affect the solution properties, such as boiling points. For a solute that dissociates into more ions, like \( \text{Mg(NO}_2\text{)}_2 \), which splits into three ions (one \( \text{Mg}^{2+} \) and two \( \text{NO}_2^- \)), the van't Hoff factor is 3. Such differences directly impact how solutions react and change properties.

Dissociation of Compounds

When compounds dissolve, they may do so by dissociating into ions, transforming solutions in unique ways. The dissociation changes the number of particles in a solution, directly influencing colligative properties like boiling point and freezing point, affected by the number and not the type of particles.

Ionic compounds like \( \text{Mg(NO}_2\text{)}_2 \) upon dissolving break into \( \text{Mg}^{2+} \) and \( \text{NO}_2^- \) ions. This dissociation increases the number of solute particles in the solution, altering the boiling point significantly, more so than non-dissociating compounds.

Covalent compounds like urea and phenol do not dissociate and therefore introduce lesser number of particles into the solution, thus impacting boiling points differently than their ionic counterparts.

Molality in Solutions

Molality, represented by \( m \), is a way to measure the concentration of a solution. It is expressed as moles of solute per kilogram of solvent. Unlike molarity, which depends on the volume of a solution, molality is independent of temperature changes since it's based on mass, not volume.

In terms of boiling point elevation, molality helps determine the extent of boiling point increase a solution experiences when a solute is added. For instance, evaluating molality alongside the van't Hoff factor allows you to predict how much boiling point elevation will occur due to the number of particles in the solution.

While evaluating solutions such as the \( 0.130 \text{ m} \) urea and \( 0.080 \text{ m} \) \( \text{Mg(NO}_2\text{)}_2 \), despite their different concentrations, understanding their molality gives insight into how significantly each solution’s boiling point will elevate. The higher the product of molality and van't Hoff factor, the greater the boiling point elevation.