Problem 23 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The freezing point of equimolal aqueous solutions will be highest for : (a) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3} \mathrm{Cl}\) (aniline hydrochloride) (b) \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) (c) \(\mathrm{La}\left(\mathrm{NO}_{3}\right)_{3}\) (d) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (glucose)

Step-by-Step Solution

Answer

Glucose (\(\text{C}_6\text{H}_{12}\text{O}_6\)) has the highest freezing point.

Step 1: Understand the Concept of Freezing Point Depression

The freezing point of a solution is lowered compared to that of the pure solvent due to the presence of solute particles. The extent of this depression is directly proportional to the number of dissolved particles in the solution. For an equimolal solution, the concentration of solute particles, given as molality, is the same for all dissolved substances.

Step 2: Determine the Number of Dissociated Ions or Particles

The key to solving the problem is to determine how many ions or particles each compound dissociates into when dissolved in water. More particles result in a greater depression of the freezing point.For each compound:- \(\text{C}_6\text{H}_5\text{NH}_3\text{Cl}\) dissociates into two ions: \(\text{C}_6\text{H}_5\text{NH}_3^+\) and \(\text{Cl}^-\).- \( \text{Ca(NO}_3)_2 \) dissociates into three ions: \(\text{Ca}^{2+}\) and two \(\text{NO}_3^-\).- \(\text{La(NO}_3)_3\) dissociates into four ions: \(\text{La}^{3+}\) and three \(\text{NO}_3^-\).- \( \text{C}_6\text{H}_{12}\text{O}_6 \) (glucose) does not dissociate into ions.

Step 3: Compare the Number of Particles in Solution for Each Compound

Since the freezing point is inversely related to the number of particles, the solution with the least dissociation will have the highest freezing point.- \(\text{C}_6\text{H}_5\text{NH}_3\text{Cl}\): 2 particles- \(\text{Ca(NO}_3)_2\): 3 particles- \(\text{La(NO}_3)_3\): 4 particles- \(\text{C}_6\text{H}_{12}\text{O}_6\): 1 particle (non-dissociative)

Key Concepts

Colligative Properties

Colligative properties are delightful to learn because they showcase how the behavior of solutions depends on the quantity of dissolved solute particles. Unlike most chemical properties, which depend on the type of chemical species, colligative properties are unique as they depend solely on how many particles are present in the solution.
These properties include important phenomena like boiling point elevation, vapor pressure reduction, and in our case, freezing point depression. When we add solute to a solvent, the freezing point of that solution drops compared to the pure solvent. This happens because adding solute particles disrupts the structure and stability of the liquid phase of the solvent, making it more difficult for the solvent to organize into a solid form at its original freezing point.
Hence, the more particles you place into a solution, the lower the freezing point. This is the pivotal point in the exercise, where the number of dissociated particles in a solution directly influences how much the freezing point will drop.

Ion Dissociation

Ion dissociation is a crucial concept that comes into play when determining how freezing point depression works. Upon dissolution in water, ionic compounds break apart into ions. This process is called dissociation, and this very step results in more particles present in the solution, contributing to the colligative properties.
Imagine dissolving \( ext{Ca(NO}_3)_2\) in water. It breaks down into three ions: \[ \text{Ca}^{2+} \]\ and two \[\text{NO}_3^-\; ext{ions}\]. The more ions present after dissolving, the greater the impact on the freezing point depression due to an increase in particle concentration.
Different substances dissociate into different numbers of ions: \( ext{C}_6 ext{H}_5 ext{NH}_3 ext{Cl}\) dissociates into two ions, whereas \( ext{La(NO}_3)_3\) dissociates into four. These dissociation numbers are vital because the more the dissociation, the larger the effect on the solution's freezing point, leading to greater freezing point depression. Non-electrolytes like glucose do not dissociate into ions; they stay as single molecules, resulting in the least effect on freezing point depression.

Molality

Molality is an essential concentration unit in colligative properties, defined as moles of solute per kilogram of solvent. Unlike molarity, which depends on the volume of solution, molality is solely concerned with the mass of the solvent, making it particularly useful when temperature changes are involved.
This independence from temperature fluctuations ensures more accurate measurements, especially in cases of freezing point depression. By using molality, scientists can be certain that the changes in freezing points are due to the number of particles added rather than the expansion or contraction of the solution volume with temperature changes.
In the given exercise, the solutions are equimolal, meaning each solution has the same molality or concentration of solute particles. This equal concentration simplifies analysis as we can directly compare their effect on the freezing points based solely on the number and type of particles each solute delivers into the solution upon dissolution.