JEE Main 2023 — Solutions Question with Solution

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.