Question

A \(0.10-m\) NaCl aqueous solution has a higher boiling point than a \(0.10-m \mathrm{MgSO}_{4}\) aqueous solution. Explain why.

Short answer

A 0.10 m NaCl aqueous solution has a higher boiling point than a 0.10 m MgSO₄ aqueous solution because NaCl dissociates more completely into ions than MgSO₄. Both solutions have the same molality and van't Hoff factor (2), however, the higher dissociation of NaCl leads to a greater effective concentration of solute particles, resulting in a higher boiling point elevation.

Step-by-step solution

Understanding boiling point elevation

Boiling point elevation is a colligative property, which means it depends on the number of solute particles in a solution, and not their specific nature. The boiling point elevation can be calculated using the following formula: \[ΔT_b = i K_b molality \]Where ΔTb is the elevation in boiling point, i is the van't Hoff factor (number of solute particles formed per formula unit of solute), Kb is the boiling point elevation constant, and molality is the number of moles of solute per kilogram of solvent.

Calculate the van't Hoff factor for each solution

The van't Hoff factor (i) represents the number of particles formed when a solute dissociates in a solvent. For NaCl, when it dissolves in water, it dissociates into Na+ and Cl- ions. Therefore, the van't Hoff factor for NaCl is 2. For MgSO4, when it dissolves in water, it dissociates into Mg2+ and SO42- ions. Therefore, the van't Hoff factor for MgSO4 is also 2.

Conclusion and explanation

Both NaCl and MgSO4 solutions have the same molality (0.10 m) and van't Hoff factor (2). However, NaCl has a higher boiling point elevation than MgSO4. This can be explained by the fact that dissociation of MgSO4 is not complete, i.e., some MgSO4 molecules don't dissociate into ions in the solution, leading to a lower effective concentration of particles contributing to the boiling point elevation. In the case of NaCl, there is almost complete dissociation, so the effective concentration of particles is higher, leading to a higher boiling point elevation. Thus, a 0.10 m NaCl aqueous solution has a higher boiling point than a 0.10 m MgSO4 aqueous solution because NaCl dissociates more completely into ions than MgSO4, leading to a greater effective concentration of solute particles and a higher boiling point elevation.

Key concepts

Boiling Point Elevation

Boiling point elevation is a fascinating concept in chemistry that deals with how the presence of a solute affects the boiling point of a solvent. It's a perfect example of a colligative property, meaning it depends on the number of particles in a solution, not their identity. When you add a solute to a solvent, it raises the boiling point of the solution compared to the pure solvent. This happens because the solute particles make it harder for solvent molecules to escape into the vapor phase, requiring more heat to reach boiling point.

The boiling point elevation can be quantified with the formula \[ΔT_b = i K_b ext{ molality} \]where:

• ΔTb is the change in boiling point,
• i is the van't Hoff factor,
• Kb is the boiling point elevation constant specific to the solvent,
• molality is the concentration of the solution in moles of solute per kilogram of solvent.

Understanding this can help explain why salt is added to water when cooking at high altitudes where water boils at lower temperatures.

Van't Hoff Factor

The van't Hoff factor, often symbolized as \(i\), is essential in understanding colligative properties like boiling point elevation. It represents how many particles a solute breaks into when it dissolves in a solvent. For instance, when NaCl is dissolved in water, it dissociates into Na\(^+\) and Cl\(^-\), resulting in a van't Hoff factor of 2.

This factor is crucial because it directly influences properties like boiling point elevation, freezing point depression, and osmotic pressure. The higher the van't Hoff factor, the greater the effect on these properties, due to an increase in the number of dissolved particles.

While the theoretical van't Hoff factor can be determined by counting the ions produced by the solute, in reality, some compounds might not dissociate completely. For instance, MgSO\( _4 \) may have a van't Hoff factor of 2 theoretically, but partial dissociation in solution can lower its effective value.

Solute Dissociation

Solute dissociation is the process where a solute breaks down into its constituent ions or molecules when dissolved in a solvent, like water. This process is significant for ionic compounds, such as salts. Complete dissociation results in a high number of individual particles in the solution, significantly impacting colligative properties.

NaCl dissociates almost completely into Na\(^+\) and Cl\(^-\) ions in water. This means nearly all the NaCl initially added contributes to increasing the effective concentration of particles, enhancing the boiling point elevation effect.

On the other hand, MgSO\( _4 \) might not dissociate completely in water, leaving some intact molecules without breaking into ions. This partial dissociation results in a lower number of effective particles, reducing its influence on boiling point elevation, despite having a similar van't Hoff factor as NaCl. This incomplete dissociation accounts for the differences observed in boiling point elevation between solutions of MgSO\( _4 \) and NaCl.