The molecular weights determined by using colligative properties of substances which associate or dissociate will be abnormal and are called abnormal molecular weights. Ionic substances like NaCl, BaCl₂, AlCl₃, etc., ionize in solutions. Their colligative properties are high due to increase in number of particles when compared with solutions of non-electrolytes like glucose having equal molecular mass. When molecules of substance like acetic acid in benzene associate as dimers, trimers or polymers, the number of particles decreases and their colligative properties also decrease. The ratio of the observed colligative property and calculated colligative property is called Van’t Hoff factor i.

\[\text{i = }\frac{\text{observed colligative property}}{\text{calculated colligative property}}\]

\[\text{or, i = }\frac{\text{calculated molecular mass}}{\text{observed molecular mass}}\]

The value of Van’t Hoff factor i is greater than 1 for ionic substances while it has lower value than 1 for associated substances.

\[\frac{\text{calculated molecular mass}}{\text{observed molecular mass}} = \frac{\text{Normal number of solute particles}}{\text{Number of solute particles after dissociation or association}}\]

Which of the following solutions will have the maximum lowering of vapour pressure at 300 K?

1 M BaCl₂

The correct answer is option 1 M BaCl₂.

The phenomenon of lowering of vapor pressure in a solution, known as Raoult's Law, occurs due to the presence of solute particles in the solution. According to Raoult's Law, the vapor pressure of a solvent above a solution is proportional to the mole fraction of the solvent in the solution.

When a solute is dissolved in a solvent, the vapor pressure of the resulting solution decreases compared to the pure solvent. This is because the solute particles disrupt the normal escape of solvent molecules into the vapor phase, leading to a decrease in the number of solvent molecules in the vapor phase.

The degree of lowering of vapor pressure depends on the number of solute particles present in the solution. More solute particles result in a greater reduction in vapor pressure. This is because each solute particle effectively "occupies space" at the surface of the solvent, reducing the number of solvent molecules able to escape into the vapor phase.

Now, let's consider the options given:

1. 1 M \(BaCl_2\) (Barium Chloride): \(BaCl_2\) dissociates into three ions in solution: one barium ion (\(Ba^{2+}\)) and two chloride ions (\(2Cl^-\)). Therefore, it contributes three particles to the solution.

2. 1 M NaCl (Sodium Chloride): NaCl dissociates into two ions in solution: one sodium ion (\(Na^+\)) and one chloride ion (\(Cl^-\)). Therefore, it contributes two particles to the solution.

3. 1 M Phenol: Phenol does not dissociate into ions in solution. It remains as intact molecules. Therefore, it contributes one particle to the solution.

4. 1 M Sucrose: Sucrose does not dissociate into ions in solution. It remains as intact molecules. Therefore, it contributes one particle to the solution.

Since \(BaCl_2\) contributes the highest number of particles to the solution (three particles), it will result in the maximum lowering of vapor pressure among the given options.

Therefore, 1 M \(BaCl_2\) solution will have the maximum lowering of vapor pressure at 300 K.