Question

The freezing point of \(0.20 \mathrm{~m}\) 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: HF is primarily nonionized in the solution.

Step-by-step solution

Calculate the observed freezing point depression

ΔTf(observed) is given as -0.38°C. Since the freezing point of pure water is 0°C, we have: ΔTf(observed) = 0°C - (-0.38°C) = 0.38°C

Calculate the theoretical freezing point depression

To calculate the theoretical freezing point depression, (ΔTf(theoretical)), we need 0.20 m as molality (m) and the Kf value for water as 1.86°C/m: ΔTf(theoretical) = Kf * m * i Assuming complete dissociation, i = 2 ΔTf(theoretical) = 1.86°C/m * 0.20 m * 2 = 0.744°C

Evaluate the observed and theoretical freezing point depressions

Now, we compare the observed and theoretical freezing point depressions to determine whether HF is primarily nonionized or dissociated. ΔTf(observed) = 0.38°C ΔTf(theoretical) = 0.744°C Since ΔTf(observed) is much smaller than ΔTf(theoretical), it indicates that HF is primarily nonionized in this solution. The difference between observed and theoretical values suggests HF molecules, rather than complete dissociation into H+ and F- ions.

Key concepts

Colligative Properties

Understanding colligative properties is essential when figuring out the behaviors of solutions. Colligative properties are characteristics of solutions that depend on the number of particles in a given volume of solvent and not on the nature of the chemical species itself. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

When a non-volatile solute is added to a solvent, it disrupts the solvent's normal freezing and boiling behaviors. For instance, the freezing point of the solvent will drop, which is known as freezing point depression. This process happens because the solute particles interfere with the solvent molecules' ability to form a solid structure, therefore requiring a lower temperature to achieve the structured solid phase (ice).

Freezing point depression can be quantified by the formula \( \Delta T_f = K_f \times m \times i \), where \( \Delta T_f \) represents the freezing point depression, \( K_f \) is the freezing point depression constant unique to each solvent, \( m \) is the molality of the solution, and \( i \) is the van't Hoff factor, which signifies the number of particles the solute splits into or forms when dissolved. This equation is pivotal in understanding why the freezing point of a solution is lowered and by how much.

Dissociation of Electrolytes

The process by which compounds split into ions when dissolved in a solvent is delineated as the dissociation of electrolytes. Electrolytes are substances that produce ions in solution, thus carrying an electric current. They can be classified as strong or weak electrolytes based on their ability to dissociate.

Strong Electrolytes

• Dissociate completely in solution into their constituent ions.
• Include strong acids like HCl, strong bases like NaOH, and salts like NaCl.

Weak Electrolytes

• Dissociate partially, with most of the substance remaining in its molecular form.
• Include weak acids such as acetic acid (CH\(_3\)COOH) and weak bases like ammonia (NH\(_3\)).

The degree of dissociation of an electrolyte affects colligative properties. The aforementioned exercise involves hydrogen fluoride (HF), a weak electrolyte that does not fully dissociate in solution. Therefore, when calculating freezing point depression or other colligative effects for a solution of HF, we must take into account that it does not completely split into ions, implying a lower van't Hoff factor (i) than would be expected for a strong electrolyte.

Molality

The concentration of a solution can be expressed in various ways, one of them being molality. Molality is a measure of the amount of solute per kilogram of solvent, not depending on the volume changes due to temperature like molarity does. It's calculated by the formula: \( m = \frac{{\text{{moles of solute}}}}{{\text{{kilograms of solvent}}}} \).

Molality is particularly useful in colligative properties equations because these properties depend on the quantity of solute particles rather than their volume or mass. Since in the freezing point depression formula \( \Delta T_f = K_f \times m \times i \), \( m \) represents molality, it must be carefully calculated to yield accurate results. In our exercise, the given molality of HF is \(0.20 \, \text{{m}}}\), meaning that for every kilogram of water, there are 0.20 moles of HF. This information, combined with the freezing point depression constant and the van't Hoff factor, guides us in predicting the extent to which the solution's freezing point will be depressed.