Problem 76 - Chemistry The Science in Context

Question

Which aqueous solution has the highest boiling point: \(0.5 \mathrm{m}\) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right), 0.5 \mathrm{m} \mathrm{KI},\) or \(0.5 \mathrm{m} \mathrm{Na}_{2} \mathrm{SO}_{4} ?\)

Step-by-Step Solution

Answer

1) 0.5 m CH3OH 2) 0.5 m KI 3) 0.5 m Na2SO4 Answer: The 0.5 m Na2SO4 aqueous solution has the highest boiling point.

Step 1: Identify the van 't Hoff factors

Determine the number of particles each solute dissociates into when dissolved in water. Methanol (CH3OH): It doesn't dissociate in water, so i = 1. Potassium iodide (KI): It dissociates into K+ and I- ions, so i = 2. Sodium sulfate (Na2SO4): It dissociates into 2 Na+ ions and 1 SO42- ion, so i = 3.

Step 2: Calculate the boiling point elevations for each solution

Use the boiling point elevation formula (ΔT = K_b * m * i) to calculate the boiling point elevation for each solution, using the given molality (0.5 m). For methanol: ΔT_methanol = (0.5 mol/kg) * K_b * 1 For potassium iodide: ΔT_KI = (0.5 mol/kg) * K_b * 2 For sodium sulfate: ΔT_Na2SO4 = (0.5 mol/kg) * K_b * 3 Note that K_b remains constant for all solutions because it only depends on the solvent, which is water in all cases. To compare the boiling points, we do not need to know the exact value of K_b, since it is the same factor for all three solutions.

Step 3: Compare the boiling point elevations

The higher the boiling point elevation, the higher the boiling point of the aqueous solution. From the calculations, we see that: ΔT_Na2SO4 > ΔT_KI > ΔT_methanol Thus, the 0.5 m Na2SO4 aqueous solution has the highest boiling point.

Key Concepts

van 't Hoff factor

The van 't Hoff factor is a key concept in understanding boiling point elevation and other colligative properties. It measures how many particles a single solute formula unit disassociates into when dissolved in a solvent, such as water. This factor is denoted by the symbol \( i \) and can vary depending on the chemical nature of the solute. For instance:

• Methanol (CH₃OH) does not dissociate into particles in solution, so its van 't Hoff factor \( i \) is 1.
• Potassium iodide (KI) dissociates into two ions: \( K^+ \) and \( I^- \), thus its \( i \) is 2.
• Sodium sulfate (Na₂SO₄) breaks into three ions: two \( Na^+ \) ions and one \( SO₄^{2-} \) ion, giving it an \( i \) of 3.

So, the greater the van 't Hoff factor, the more it impacts the solution’s boiling and freezing points. This is why ionic compounds like Na₂SO₄ can significantly elevate boiling points more than non-ionizing compounds like methanol.

aqueous solution

An aqueous solution is a solution where water serves as the solvent. Being a universal solvent, water can dissolve a variety of substances, including ionic, non-ionic, and polar molecules. When substances dissolve in water:

• Solutes like salts, acids, and bases often dissociate into ions.
• Molecules, depending on their structure, might interact with water but not dissociate, like methanol.

This interaction between solutes and the water solvent affects physical properties such as boiling points. When comparing boiling point elevations, we examine how these solutes affect the water's ability to vaporize. In the presence of solutes that form ions, such as Na₂SO₄ in the problem, strong ionic interactions mean higher boiling point elevations.

molality

Molality is a concentration term used in chemistry defined as the number of moles of solute per kilogram of solvent. It is represented by the symbol \( m \) and calculated using the formula:

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

Unlike molarity, which depends on the volume of the solution, molality is solely based on mass, making it independent of temperature changes. This is an advantage when studying colligative properties like boiling point elevation. In the exercise, each solution has a molality of 0.5 m, meaning 0.5 moles of each solute are dissolved in one kilogram of water. This ensures consistency, allowing changes in boiling point to be attributed to solute dissociation, as indicated by their respective van 't Hoff factors.