Consider two aqueous solutions, one of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) and the other of nitric acid \(\left(\mathrm{HNO}_{3}\right)\) Both solutions freeze at \(-1.5^{\circ} \mathrm{C}\). What other properties do these solutions have in common?

Freezing point depression is a phenomenon that occurs when a solute is dissolved in a solvent, causing the freezing point of the solution to be lower than that of the pure solvent. This is a colligative property, meaning it depends on the number of particles of solute in the solution, not on the type of particle.
For instance, if sucrose or nitric acid is dissolved in water, the solution's freezing point will drop below the normal 0°C of pure water. The exercise reveals that both solutions freeze at -1.5°C, indicating that the total concentration of solute particles in both solutions is similar, despite the different chemical nature of the solutes. This commonality emphasizes the essence of freezing point depression being independent of the solute's identity, focusing only on the number of solute particles within the solution.

Boiling point elevation is another colligative property which refers to the increase in the boiling point of a solvent upon the addition of a solute. Similar to freezing point depression, boiling point elevation does not depend on the solute's chemical identity but on the number of solute particles.

When solute particles are introduced into a solvent, they disrupt the solvent molecules' ability to escape into a gaseous phase, requiring a higher temperature — a higher boiling point — to allow for the phase transition. Both the sucrose and nitric acid solutions described in the exercise would exhibit a higher boiling point than pure water due to the presence of dissolved solute particles.

The reduction in vapor pressure, when a solute is added to a solvent, is another colligative property known as vapor pressure lowering. It occurs because the solute particles occupy space at the liquid surface, effectively reducing the number of solvent molecules that can escape into the vapor phase.

This result in a lower concentration of solvent molecules above the surface, reducing the system's vapor pressure. Consequently, both sucrose and nitric acid solutions will exhibit a lower vapor pressure compared to pure water, as the dissolved solute particles impede the escape of water molecules, regardless of the solute's nature.

Osmotic pressure is the pressure required to prevent the flow of solvent molecules through a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. This colligative property is significant in many biological and chemical processes.

The osmotic pressure of a solution is directly proportional to the molarity of the solute particles; hence, it is also independent of the solute's type. Both the aqueous sucrose and nitric acid solutions exhibit osmotic pressures which are higher than that of pure water, stemming from the addition of solute molecules in the solvent.

Understanding the difference between electrolytes and non-electrolytes is crucial in predicting a solution's behavior. Electrolytes are substances that, when dissolved in water, dissociate into ions, thus carrying an electric current. Common examples are salts, acids, and bases. Non-electrolytes, on the other hand, do not dissociate into ions in solution and do not conduct electricity.

The nitric acid in the exercise is a strong electrolyte that dissociates completely into hydrogen ions (H+) and nitrate ions (NO3-), which contribute to its electrical conductivity and acidic nature. Sucrose, conversely, is a non-electrolyte; it dissolves as whole molecules, not affecting the water's pH nor conducting electricity. Although the presence of electrolytes and non-electrolytes does not change the fundamental colligative properties of a solution like freezing point depression, their inherent characteristics lead to different effects in electrical conductivity and chemical reactivity of the solution.