Question

What is the correct sequence of osmotic pressure of \(0.01 \mathrm{M}\) aq. solution of : (1) \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) (2) \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) (3) \(\mathrm{BaCl}_{2}\) (4) Glucose (a) \(\pi_{4}>\pi_{2}>\pi_{3}>\pi_{1}\) (b) \(\pi_{3}>\pi_{4}>\pi_{2}>\pi_{1}\) (c) \(\pi_{3}>\pi_{4}>\pi_{1}>\pi_{2}\) (d) \(\pi_{1}>\pi_{2}>\pi_{3}>\pi_{4}\)

Short answer

\( \pi_{1} > \pi_{2} > \pi_{3} > \pi_{4} \) (Option d)

Step-by-step solution

Determine the van't Hoff factor for each compound

The van't Hoff factor (i) is the number of particles a compound dissociates into in solution. For each compound, this factor is: (1) \( \mathrm{Al}_{2}(\mathrm{SO}_{4})_{3} \): i = 5 (it dissociates into 2 Al^3+ and 3 SO4^2-). (2) \( \mathrm{Na}_{3} \mathrm{PO}_{4} \): i = 4 (it dissociates into 3 Na+ and 1 PO4^3-). (3) \( \mathrm{BaCl}_{2} \): i = 3 (it dissociates into 1 Ba^2+ and 2 Cl-). (4) Glucose: i = 1 (it does not dissociate as it is a non-electrolyte).

Apply the formula for osmotic pressure

The osmotic pressure \( \pi \) can be calculated using the formula \( \pi = i M R T \), where i is the van't Hoff factor, M is the molar concentration, R is the universal gas constant, and T is the temperature in Kelvin. Since M, R, and T are constant for all solutions as per the question, the osmotic pressure is directly proportional to the van't Hoff factor i.

Compare the osmotic pressures

Since the osmotic pressure is directly proportional to i, the compound with the highest value of i will have the highest osmotic pressure and vice versa. Comparing the i values for each compound, we get: \( \pi_{1} > \pi_{2} > \pi_{3} > \pi_{4} \).

Key concepts

van't Hoff factor

The van't Hoff factor, represented by the symbol 'i', is immensely crucial when studying solutions in chemistry, especially in the context of osmotic pressure for the JEE Chemistry examination. It indicates the number of particles into which a compound dissociates in a solution. For instance, a substance like table salt (NaCl) that breaks down into two separate ions (Na+ and Cl-) when dissolved in water would have a van't Hoff factor of 2.

Understanding this factor is essential because it affects colligative properties, which are the physical changes in a solution that depend on the quantity, not the identity, of dissolved solute particles. The van't Hoff factor is also used to correct the observed values of colligative properties for ionic compounds, which can dissociate to form more than one particle per formula unit in a solution. Thus, a higher value of 'i' means a greater effect on the solution's colligative properties, such as osmotic pressure, which is a pertinent point for JEE aspirants to note.

colligative properties

Colligative properties are those properties of solutions that depend on the number of solute particles in a given volume of solvent and not on the chemical nature of the solute itself. These include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure—core topics within JEE Chemistry.

For JEE students, it's important to comprehend that the improvement in boiling point, the depression in freezing point, or the osmotic pressure of the solution increases as the number of dissolved particles in the solution increases. These changes are colligative properties because they can be calculated solely based on the number of solute particles, which is directly related to the van't Hoff factor. This makes understanding the dissociation in solutions and the type of electrolytes present crucial for predicting and calculating these properties.

dissociation in solution

Dissociation in solution describes the process by which a compound breaks apart into its constituent ions when it is dissolved in a solvent, like water. This concept is imperative for JEE Chemistry aspirants to grasp as it impacts the colligative properties of a solution.

For example, strong electrolytes like salts, strong acids, and bases dissociate completely, producing a greater number of ions, which in turn increases the van't Hoff factor ('i') for the solution. On the other hand, weak electrolytes only partially dissociate, resulting in fewer ions. Non-electrolytes do not dissociate at all in a solution. Therefore, the degree of dissociation affects the calculation of osmotic pressure and other colligative properties, as clearly illustrated by the exercise provided. Recognizing this will enable students to predict the behavior of solutions and their properties accurately.

electrolytes and non-electrolytes

In JEE Chemistry, understanding the difference between electrolytes and non-electrolytes is pivotal. Electrolytes are substances that produce ions when dissolved in water and consequently conduct electricity. They are classified as strong or weak depending on their ability to dissociate completely or partially respectively.

Non-electrolytes, like glucose, do not dissociate in water; thus, they don't conduct electricity and their van't Hoff factor is 1. This distinction has direct implications on studying osmotic pressure as electrolytes with higher dissociation will result in higher osmotic pressure in a solution. As exhibited in the exercise, glucose, being a non-electrolyte, results in the lowest osmotic pressure, while the compound with the highest dissociation (Al2(SO4)3) demonstrates the highest osmotic pressure. JEE aspirants must be adept at identifying these types of solutes to excel in their understanding of colligative properties.