The osmotic pressures of equimolar solutions of urea, \(\mathrm{BaCl}_{2}\) and \(\mathrm{AlCl}_{3}\) will be in the order : (a) \(\mathrm{AlCl}_{3}>\mathrm{BaCl}_{2}>\) urea (b) \(\mathrm{BaCl}_{2}>\mathrm{AlCl}_{3}>\) urea (c) urea \(>\mathrm{BaCl}_{2}>\mathrm{AlCl}_{3}\) (d) \(\mathrm{BaCl}_{2}>\) urea \(>\mathrm{AlCl}_{3}\)

Understanding the Van't Hoff factor is crucial for grasping the behavior of solutions in various conditions, such as osmotic pressure scenarios covered in the Joint Entrance Exam (JEE) Chemistry syllabus. The Van't Hoff factor, denoted by the symbol 'i', is a dimensionless quantity that indicates the number of particles a compound forms when it dissolves in a solution. For non-electrolytes, substances that do not produce ions in solution, the Van't Hoff factor is typically 1. This is because they do not dissociate upon dissolving.

For electrolytes, the factor differs depending on the degree of dissociation. Strong electrolytes fully dissociate into ions, resulting in a Van't Hoff factor equal to the total number of ions produced. For example, common table salt (NaCl) would have a factor of 2. Weak electrolytes only partially dissociate, and their Van't Hoff factors are usually between 1 and the total number of ions that could be formed.

Calculation of the Van't Hoff factor is essential when predicting properties such as boiling point elevation, freezing point depression, and osmotic pressure, all of which are influenced by the number of solute particles in the solution. In osmotic pressure, for instance, a solution with a higher Van't Hoff factor will have a higher osmotic pressure, assuming the solutions are equimolar.

Dissociation is the process where ionic compounds separate into their constituent ions when dissolved in a solvent, like water. This process is vital for JEE Chemistry students to comprehend as it affects the properties of solutions, such as conductivity and reactivity, along with osmotic pressure. In the given example, \(\mathrm{BaCl}_{2}\) and \(\mathrm{AlCl}_{3}\) are both electrolytes, and they dissociate in water to a different extent because of their structure and the nature of their ionic bonds.

The dissociation of \(\mathrm{BaCl}_{2}\) results in one \(\mathrm{Ba}^{2+}\) ion and two \(\mathrm{Cl}^{-}\) ions, while \(\mathrm{AlCl}_{3}\) yields one \(\mathrm{Al}^{3+}\) ion and three \(\mathrm{Cl}^{-}\) ions. The total number of particles that result from this process determines the osmotic pressure of the solution, thus directly linking the concept of dissociation with osmotic pressure.

The properties of solutions play a significant role in different analytical aspects of Chemistry, such as physical states, concentrations, and interactions between solutes and solvents. One important property is osmotic pressure, which can be influenced by factors like temperature, concentration, and the nature of the solute.

For a solution to exert osmotic pressure, it must be separated by a semipermeable membrane from pure solvent or a less concentrated solution. Osmotic pressure drives the solvent across the membrane into the more concentrated solution, seeking to equalize the concentrations on both sides of the membrane.

Colligative Properties

Additionally, osmotic pressure is a colligative property - a property that depends on the number of solute particles in a solvent, regardless of their identity. Hence, for equimolar solutions of different substances, the one with the higher Van't Hoff factor will exhibit a higher osmotic pressure because it releases more particles into the solution.

The study of these properties helps chemists to predict how substances will behave in various situations, enabling them to engineer solutions with desired properties for industrial, pharmaceutical, or environmental applications.