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 of which freeze at \(-1.5^{\circ} \mathrm{C}\). What other properties do these solutions have in common?

Freezing point depression refers to the phenomenon where the addition of a solute to a solvent results in the lowering of the freezing point of the solvent. This is a colligative property, meaning it depends solely on the number of solute particles in a solution, and not on their chemical identity.

In the given exercise, both sucrose and nitric acid solutions freeze at -1.5°C, which is lower than the freezing temperature of pure water at 0°C. This indicates that the solute particles interfere with the formation of ice crystals, thereby requiring a colder temperature to freeze. The magnitude of freezing point depression is calculated using the formula:

where is the freezing point depression, i is the van 't Hoff factor (which represents the number of particles the solute breaks down into), k_f is the cryoscopic constant (a property of the solvent) and m is the molality of the solution. As both solutions have the same freezing point depression, this step-by-step analysis demonstrates that the solutions must have an equivalent molality of solute particles.

Molality is a measure of the concentration of a solute in a solution. Defined as the number of moles of solute per kilogram of solvent ( ), it is a way to express the concentration without concern for volume changes due to temperature.

It's crucial to distinguish molality from molarity, which is the number of moles per liter of solution. Unlike molarity, molality is not affected by temperature because mass remains constant with temperature changes. From the exercise, we learn that the molalities of the sucrose and nitric acid solutions must be the same, for they cause an identical freezing point depression. This also suggests that, by knowing the molality and the freezing point depression, we could determine other properties of the solutions using various colligative property equations.

Solution conductivity is a measure of a solution's ability to conduct electricity. It is contingent on the presence of ions, which are charged particles. Ionic compounds, such as salts and acids, often dissolve in water to form ions, making the solution conductive.

In the context of the exercise, the sucrose solution does not conduct electricity because sucrose does not ionize in solution. Conversely, nitric acid dissociates into and ions, allowing for electrical conductivity. While the freezing point depression and molality of both solutions are the same, their electrical conductivity differs markedly due to the distinct properties of the dissolved substances.

The pH of a solution is a numeric scale used to specify the acidity or basicity of an aqueous solution. It is defined as the negative logarithm of the hydrogen ion concentration ( ) in moles per liter.

Although sucrose and nitric acid solutions share the same freezing point depression and molality, their pH values differ greatly. Sucrose solution is neutral, meaning it has a pH close to 7, because it does not release hydrogen ions in water. Nitric acid, however, ionizes to release ions, resulting in a low pH, indicating a high level of acidity. This difference highlights the significance of understanding both colligative properties and the specific characteristics of solutes when analyzing solution properties.