Problem 69 - Chemistry The Central Science

Question

(a) Does a 0.10 \(\mathrm{m}\) aqueous solution of NaCl have a higher bolling point, a lower boiling point, or the same boiling point as a 0.10 \(\mathrm{m}\) aqueous solution of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} ?(\mathbf{b})\) The experimental boiling point of the NaCl solution is lower than that calculated assuming that NaCl is completely dissociated in solution. Why is this the case?

Step-by-Step Solution

Answer

(a) A 0.10 M aqueous solution of NaCl will have a higher boiling point than a 0.10 M aqueous solution of C6H12O6, as NaCl has a greater van't Hoff factor (2) than C6H12O6 (1). (b) The lower experimental boiling point for the NaCl solution is due to some Na+ and Cl- ions being associated (ion pairing) in the solution rather than being completely dissociated. This reduces the van't Hoff factor (i) to a value less than 2, leading to a smaller boiling point elevation.

Step 1: Comparing Boiling Points of NaCl and C6H12O6 Solutions

First, let's recall the boiling point elevation equation: \[ΔT_b = i × K_b × m\] Where ΔT_b is the boiling point elevation, i is the van't Hoff factor, K_b is the boiling point elevation constant, and m is the molality. For NaCl, i = 2 (due to its complete dissociation into Na+ and Cl- ions). For C6H12O6, i = 1 (no dissociation, as it is a non-electrolyte). Given that both solutions have the same molality (0.10 M), we can compare their boiling point elevations directly by comparing their van't Hoff factors. Since the van't Hoff factor for NaCl is greater than that for C6H12O6 (2 > 1), the boiling point elevation for the NaCl solution will be higher. Thus, a 0.10 M aqueous solution of NaCl will have a higher boiling point than a 0.10 M aqueous solution of C6H12O6.

Step 2: Explaining the Lower Experimental Boiling Point for NaCl Solution

The assumption that NaCl is completely dissociated in the solution leads to a higher calculated boiling point because the van't Hoff factor (i) will be 2. However, in reality, some Na+ and Cl- ions may be associated (ion pairing) in solution rather than being completely dissociated. This would effectively reduce the van't Hoff factor (i) to a value less than 2. Since the van't Hoff factor (i) in the boiling point elevation equation is directly proportional to the boiling point elevation, a smaller value for i will lead to a smaller value for the boiling point elevation. As a result, the experimental boiling point is lower than what would be calculated assuming complete dissociation of NaCl.

Key Concepts

van't Hoff factor

The van't Hoff factor, represented by the symbol 'i', is significant in understanding boiling point elevation among other colligative properties. It quantifies the number of particles into which a compound dissociates in solution. For instance, NaCl splits into two particles, Na+ and Cl-, giving it a van't Hoff factor of 2. In contrast, glucose (\text{C}_6 \text{H}_{12} \text{O}_6), being a non-electrolyte, does not dissociate, so its factor remains 1.In boiling point elevation, the higher the van't Hoff factor, the more significant the impact on the solution’s boiling point. The factor is included in the formula \[ΔT_b = i × K_b × m\] and helps determine the actual effect of solutes on the solution's boiling point. Real-world scenarios, however, may reflect a lower van't Hoff factor for salts like NaCl due to ion association, which decreases their expected impact on boiling point elevation and explains why experimental data might differ from theoretical calculations.

molality

Molality, denoted as 'm', measures the concentration of a solute in a solvent. Unlike molarity, molality is based on the mass of the solvent, not the volume of the solution, making it temperature-independent. It is defined as the number of moles of solute per kilogram of solvent. In our exercise, the molality of both NaCl and glucose solutions is 0.10 mol/kg.When we delve into boiling point elevation, molality becomes a crucial factor, as it is directly proportional to the increase in boiling point according to the formula \(ΔT_b = i × K_b × m\). Therefore, at the same molality, different substances can affect the boiling point differently due to their respective van’t Hoff factors.

colligative properties

Colligative properties are characteristics of a solution that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the nature of the chemical species present. Boiling point elevation is one such property, along with freezing point depression, vapor pressure lowering, and osmotic pressure.Colligative properties are essential in understanding everyday phenomena, such as why salt is spread on icy roads (to lower the freezing point) or how a car's radiator fluid prevents the engine from overheating (boiling point elevation). Specifically, boiling point elevation is the process where the boiling point of a solvent increases when a solute is dissolved in it. The ability to manipulate the boiling points of solutions through these properties is fundamental in various industries, such as food processing and pharmaceuticals, and also in daily cooking practices.