Question

Which of the following solutions will have maximum osmotic pressure? Assume \(90 \%\) dissociation of each salt: (a) decinormal aluminium sulphate (b) decinormal barium chloride solution (c) decinormal sodium sulphate solution (d) solution of equal volumes of decinormal barium chloride and decinormal sodium sulphate solutions

Short answer

The decinormal aluminium sulphate solution will have the maximum osmotic pressure due to the highest number of ions in solution (7.2 after accounting for the 90% dissociation).

Step-by-step solution

Understand Osmotic Pressure

Osmotic pressure is directly proportional to the molarity of the solution and the number of particles into which a compound dissociates. Since all the solutions are decinormal (0.1N), their osmotic pressure will primarily depend on the extent of dissociation into ions.

Calculate the Degree of Dissociation

Given that each salt is 90% dissociated, calculate the effective number of particles released from each salt in solution. For a 90% dissociation: aluminium sulphate \( Al_2(SO_4)_3 \) dissociates into 2 Al^3+ and 3 SO4^2- ions, barium chloride \( BaCl_2 \) into 1 Ba^2+ and 2 Cl- ions, sodium sulphate \( Na_2SO_4 \) into 2 Na+ and 1 SO4^2- ions. For the mixture, total ions will be the sum of ions from each.

Determine Number of Ions Produced by Each Solution

- For aluminium sulphate: 2 Al^3+ + 3(2) SO4^2- = 2 + 6 = 8 ions- For barium chloride: 1 Ba^2+ + 2 Cl- = 1 + 2 = 3 ions- For sodium sulphate: 2 Na+ + 1 SO4^2- = 2 + 1 = 3 ionsThe number of ions produced in the mixed solution will be the sum of barium chloride and sodium sulphate, which is 3 + 3 = 6 ions.

Account for the Dissociation Percentage

Since each salt dissociates by 90%, multiply the number of ions calculated by 0.9 for the actual number of ions in the solution:- Aluminium sulphate: 8 * 0.9 = 7.2 ions- Barium chloride: 3 * 0.9 = 2.7 ions- Sodium sulphate: 3 * 0.9 = 2.7 ions- Mixture: 6 * 0.9 = 5.4 ions

Compare the Number of Ions for Osmotic Pressure

Compare the effective number of ions to find the maximum osmotic pressure. The solution with the highest number will have the highest osmotic pressure.

Key concepts

Dissociation of Salts

Understanding the dissociation of salts is essential in chemistry, particularly when discussing properties such as osmotic pressure. Dissociation is the process by which an ionic compound separates into its ions when it dissolves in water. For example, aluminium sulphate \( Al_2(SO_4)_3 \) dissociates into two aluminium ions \( Al^{3+} \) and three sulfate ions \( SO4^{2-} \) when dissolved in water.

However, not all salts dissociate completely. The degree of dissociation, usually expressed as a percentage, indicates the extent to which a salt separates into ions in a solution. If we are told that a salt dissociates 90%, we understand that only 90% of the dissolved salt actually separates into its constituent ions. This is critical because the osmotic pressure of a solution is influenced by the total number of dissolved particles, including ions, in the solution.

Molarity and Osmolarity

Molarity is a measure of the concentration of a solute in a solution, usually defined as the number of moles of solute per liter of solution \( (mol/L) \). When we move from molarity to osmolarity, we are considering the total concentration of all solute particles that contribute to the osmotic pressure in a solution.

In the case of salts that dissociate, osmolarity takes into account all the individual ions present in the solution. For instance, if you have a decinormal \( (0.1N) \) sodium sulphate solution, the molarity would account for the sodium sulphate formula units, whereas the osmolarity would account for the separate sodium \( (Na^+) \) and sulfate \( (SO4^{2-}) \) ions that result from the dissociation of the salt.

van't Hoff Factor

The van't Hoff factor \(i\) is a useful concept when dealing with properties of solutions that depend on the number of particles in solution, such as osmotic pressure, boiling point elevation, and freezing point depression. It represents the number of particles a compound forms when it dissociates in solution.

For non-electrolytes that do not dissociate, the van't Hoff factor is 1. For electrolytes like salts, \(i\) can be greater than 1, depending on how many ions one formula unit produces on dissociation. In the exercise we're examining, the assumption of a 90% dissociation rate directly affects the van't Hoff factor of each salt. Therefore, the van't Hoff factor is not only determined by the salt's formula but also by its degree of dissociation in the particular solution.

To apply the van't Hoff factor properly, you multiply the molarity of the solution by \(i\), the adjusted number that accounts for partial dissociation, to calculate the effective osmolarity contributing to osmotic pressure. This reflects the importance of considering both the dissociation rate and the van't Hoff factor when comparing osmotic pressures of different solutions.