The freezing point of a \(5.00 \%\) by mass \(\mathrm{CH}_{3} \mathrm{COOH}\) (aq) solution is \(-1.576^{\circ} \mathrm{C}\). Determine the experimental van't Hoff \(i\) factor for this solution. Account for its value on the basis of your understanding of intermolecular forces.

When a solute is dissolved in a solvent, the freezing point of the solution will be lower than that of the pure solvent; this phenomenon is known as freezing point depression. It occurs because the solute particles disrupt the orderly process by which the solvent molecules arrange themselves into a solid structure, making it harder for the solvent to freeze.

The extent of the freezing point depression depends on the number of solute particles in the solution, not their identity. The equation to quantify this relationship is \( \Delta T_f = i \times K_f \times m \), where \( \Delta T_f \) represents the freezing point depression, \( i \) is the van't Hoff factor which accounts for the number of particles a solute yields upon dissolution, \( K_f \) stands for the molal freezing point depression constant of the solvent, and \( m \) is the molality of the solution.

Molal concentration, or molality, measures the number of moles of solute per kilogram of solvent. Unlike molarity, which depends on the total volume of the solution, molality is only based on the mass of the solvent, making it a more useful concentration unit in scenarios where temperature changes, as volume can vary with temperature.

The formula for calculating molality is expressed as \( m = \frac{moles\ of\ solute}{kilograms\ of\ solvent} \). This unit gives insight into the colligative properties of a solution, such as freezing point depression, which rely on the amount of solute particles rather than the type of particles.

Intermolecular forces are the forces of attraction or repulsion which act between neighboring particles: atoms, molecules, or ions. These forces include hydrogen bonding, dipole-dipole interactions, and dispersion forces (also known as London forces).

In the context of solutions, these forces play a crucial role in determining the physical properties of the solution. Strong intermolecular forces can decrease a substance's solubility and its tendency to dissociate in a solvent. For example, in the case of acetic acid (\( \mathrm{CH}_3\mathrm{COOH} \)) discussed in the exercise, hydrogen bonding between acetic acid molecules and water can influence the extent to which acetic acid dissociates in the water, thus affecting the van't Hoff factor.

Weak acid dissociation refers to the partial ionization of a weak acid in aqueous solutions. Unlike strong acids that dissociate fully in water, weak acids like acetic acid only dissociate to a small extent, establishing an equilibrium between the undissociated acid and its ions.

The van't Hoff factor for weak acids like acetic acid is close to 1, signifying limited production of ions in solution. The dissociation of weak acids can be explained by the acid dissociation constant, \( K_a \), which provides a quantitative measure of the acid's strength in solution. Higher \( K_a \) values indicate stronger acids that dissociate more completely. Understanding both the concept of weak acid dissociation and the role of intermolecular forces helps to rationalize why certain solutions have van't Hoff factors close to, but not exactly, 1.