Problem 47 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Match the following if the molecular weights of \(X, Y\) and \(Z\) are same. $$ \begin{array}{cll} \hline & \text { Boiling Point } & \boldsymbol{K}_{b} \\ \hline X & 100 & 0.63 \\ \hline Y & 27 & 0.53 \\ \hline Z & 253 & 0.98 \end{array} $$

Step-by-Step Solution

Answer

X is water, Y is a low-boiling solvent, Z is a high-boiling solvent.

Step 1: Understanding the Problem

We are given three substances, X, Y, and Z, with the same molecular weight. We need to match their boiling points and boiling point elevation constants ( K_b ). Generally, a higher boiling point implies a stronger intermolecular force, and a higher K_b suggests that the solvent is more effective at elevating the boiling point when a solute is added.

Step 2: Analyze the Boiling Points

Examine the boiling points of X, Y, and Z: X has 100°C, Y has 27°C, and Z has 253°C. Z has the highest boiling point, indicating the strongest intermolecular forces, while Y has the lowest, indicating the weakest intermolecular forces.

Step 3: Analyze the Boiling Point Elevation Constants

Consider the boiling point elevation constants ( K_b ): X is 0.63, Y is 0.53, and Z is 0.98. Z has the highest K_b , which means that adding a solute to Z raises its boiling point the most, suggesting it is the most effective solvent.

Step 4: Matching the Characteristics

We'll match the characteristics based on both boiling point and K_b . X, with a boiling point of 100°C, and a K_b of 0.63, is most likely water because its properties are close to that of pure water. Y, with the lowest boiling point (27°C) and the lowest K_b (0.53), may be a low-boiling-point liquid like some alcohol. Z, with the highest boiling point (253°C) and the highest K_b (0.98), could be a high-boiling-point solvent like glycerol or an oil.

Key Concepts

Boiling Point

The boiling point of a liquid is the temperature at which its vapor pressure is equal to the atmospheric pressure. At this point, the liquid turns into vapor. The boiling point can give insights into the strength of the intermolecular forces present in a substance. For example, a substance with a high boiling point features strong intermolecular attractions, as more energy is necessary to overcome these forces and allow the molecules to escape as gas.

In the original exercise, Z has a boiling point of 253°C, much higher than X at 100°C, and especially higher than Y at 27°C. This suggests that Z has the strongest intermolecular forces among the three. Y, with the lowest boiling point, indicates it has the weakest intermolecular forces. Therefore, the boiling point is quite informative when assessing the nature of a liquid and its intermolecular interactions.

Elevation Constant (K_b)

The elevation constant, denoted as \(K_b\), is a measure of a solvent's effectiveness in raising its boiling point upon the addition of a solute. When a solute is dissolved in a solvent, the boiling point of the solution becomes higher than that of the pure solvent. This phenomenon is known as boiling point elevation.

\(K_b\) is unique to each solvent and is defined as the degree to which the boiling point increases per mole of solute added. A higher \(K_b\) indicates a more significant increase in boiling point for the same amount of solute. In our exercise, Z has the highest \(K_b\) of 0.98, showing it is the most effective solvent for increasing boiling points, while Y has the lowest \(K_b\) of 0.53, demonstrating its lesser efficacy as a solvent in this regard.

Intermolecular Forces

Intermolecular forces are the attractions between molecules that determine many physical properties, such as boiling point, melting point, and solubility. There are several types of intermolecular forces, such as hydrogen bonds, dipole-dipole interactions, and London dispersion forces, ranging from very strong to relatively weak.

A higher boiling point, as noted in the exercise for substance Z, suggests strong intermolecular forces, possibly hydrogen bonding or strong dipole-dipole interactions, which necessitate more energy to break. Conversely, Y's low boiling point reflects weak intermolecular forces, like London dispersion forces, which require less energy to overcome.

Understanding intermolecular forces is crucial for predicting and explaining the behavior of substances under different conditions. These forces significantly influence how substances interact, dissolve, and change state, thus being a central concept in the study of chemistry.