QJEEM23Che9a1: JEE Main 2023 Chemistry - Class 12 JEEM23Che9a1 Solution: If the degree of dissociation of aqueous solution of weak…

The degree of dissociation, often represented as $\alpha$ , is the fraction of a mole of a substance that has dissociated into ions in solution. For a weak monobasic acid, this degree of dissociation can increase the number of particles in solution, which can in turn affect colligative properties such as the freezing point.

In this case, a weak monobasic acid, when it dissociates, produces two particles: one $H^{+}$ ion and one anion. So if the degree of dissociation is 0.3 ( $\alpha = 0.3$ ), the average number of particles per molecule of the acid ( $i$ ), also known as the van't Hoff factor, will be $1 + \alpha = 1 + 0.3 = 1.3$ .

The decrease in freezing point ( $\Delta T_{f}$ ) is given by the formula $\Delta T_{f} = i \cdot m \cdot K_{f}$ , where $m$ is the molality of the solution and $K_{f}$ is the cryoscopic constant of the solvent. Therefore, the observed freezing point depression will be 1.3 times the theoretical freezing point depression for a non-dissociating solute (where $i = 1$ ).

So, the observed freezing point will be 30% higher than the theoretical freezing point, given the degree of dissociation of 0.3.