Question

The freezing point of \(0.20 \mathrm{~m} \mathrm{HF}\) is \(-0.38^{\circ} \mathrm{C}\). Is HF primarily nonionized in this solution (HF molecules), or is it dissociated to \(\mathrm{H}^{+}\) and \(\mathrm{F}^{-}\) ions?

Short answer

Answer: Based on the comparison of the calculated and given freezing point depressions, it can be concluded that HF is primarily nonionized in this 0.20 m solution.

Step-by-step solution

Recall the freezing point depression formula

The formula for freezing point depression is given by: ΔTf = Kf * m * i where ΔTf is the freezing point depression, Kf is the cryoscopic constant of the solvent (water, in this case), m is the molality of the solution, and i is the van't Hoff factor, representing the number of ions formed by the solute per formula unit.

Use the cryoscopic constant of water

For water, the cryoscopic constant Kf is equal to 1.86 °C/m.

Calculate the expected freezing point depression for nonionized HF

If HF is nonionized in the solution, then i = 1. The expected freezing point depression will be: ΔTf,expected = Kf * m * i = 1.86°C/m * 0.20m * 1 = 0.372°C

Compare the calculated and given freezing point depressions

The calculated freezing point depression for nonionized HF is 0.372°C, while the given freezing point depression is -0.38°C. Since the freezing point depression is very close for nonionized HF, we can infer that the substance is primarily nonionized (existing as HF molecules) in the solution. Therefore, based on the comparison of the calculated and given freezing point depressions, it can be concluded that HF is primarily nonionized in this 0.20 m solution.

Key concepts

Colligative Properties

Colligative properties are unique characteristics of solutions that depend on the ratio of solute particles to solvent molecules, rather than the type of chemical species present. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

Freezing point depression is a colligative property that describes how the presence of a solute lowers the freezing point of a solvent. When a non-volatile solute is dissolved in a solvent, it disrupts the formation of the solid phase (ice in the case of water), requiring a colder temperature to freeze the solution than the pure solvent alone. It's important to note that the degree of freezing point depression is proportional to the number of particles of solute in the solution — a concept directly related to the van't Hoff factor, which we'll discuss later.

Understanding Freezing Point Depression

Through this concept, students learn why adding salt to ice on roads can help prevent the formation of ice. The added salt acts as a solute, which lowers the freezing point of the water on the surface, thus reducing ice formation. In the classroom, this property is commonly demonstrated with saltwater solutions.

Cryoscopic Constant

The cryoscopic constant, symbolized as Kf, is a property specific to each solvent, reflecting how susceptible its freezing point is to the presence of a solute. It is defined as the freezing point depression expected for a one molal solution of a non-volatile, non-ionizing solute.

Every solvent has its unique cryoscopic constant value. For water, this value is typically 1.86 °C/m. This means that adding one mole of a non-volatile, non-ionizing solute to one kilogram of water would lower the freezing point of water by approximately 1.86 °C.

Practical Application of Cryoscopic Constant

In our exercise, we utilized the cryoscopic constant of water to calculate the expected freezing point depression of a hydrofluoric acid (HF) solution. This calculation is essential in various practical applications such as formulating antifreeze solutions for vehicles or in making ice creams where control over the freezing process is crucial.

Van't Hoff Factor

The van't Hoff factor, represented by the symbol i, expresses the number of particles a solute yields in solution. Simple, non-electrolyte compounds that do not dissociate in solution have a van't Hoff factor of 1, since one formula unit of the solute gives one particle in solution. However, electrolytes can dissociate into ions, and thus have van't Hoff factors greater than 1.

For instance, common table salt (NaCl) dissociates into two ions, Na+ and Cl-, and therefore its van't Hoff factor is approximately 2. In the provided exercise, if hydrofluoric acid (HF) were to fully dissociate, it would separate into H+ and F- ions, resulting in a van't Hoff factor of 2. Yet, the calculation using a factor of 1 suggests that HF primarily remains nonionized in the solution.

Importance in Solutions

The van't Hoff factor plays a vital role in determining the extent of freezing point depression, among other colligative properties. Understanding this factor helps predict how a solute will affect a solvent's physical properties, which is very valuable in chemical manufacturing, food processing, and even in pharmaceuticals where solution concentration must be controlled precisely.