Problem 10 - A Complete Resource Book in Chemistry for JEE Main

Question

The relative thermal stabilities of alkali metal halides are such that (a) \(\mathrm{CsCl}>\mathrm{RbCl}>\mathrm{KCl}<\mathrm{NaCl}>\mathrm{LiCl}\) (b) \(\mathrm{CsCl}>\mathrm{RbCl}<\mathrm{KCl}>\mathrm{NaCl}<\mathrm{LiCl}\) (c) \(\mathrm{LiCl}>\mathrm{NaCl}>\mathrm{KCl}>\mathrm{RbCl}>\mathrm{CsCl}\) (d) \(\mathrm{CsCl}>\mathrm{RbCl}>\mathrm{KCl}>\mathrm{NaCl}>\mathrm{LiCl}\)

Step-by-Step Solution

Answer

Option (c) is correct: LiCl > NaCl > KCl > RbCl > CsCl.

Step 1: Understanding Thermal Stability

Thermal stability refers to a compound's ability to remain stable at high temperatures. In alkali metal halides, thermal stability often decreases as the size of the metal ion increases, because larger ions result in weaker ionic bonds.

Step 2: Comparing Alkali Metal Sizes

Alkali metals in order from the smallest to largest ionic radii are: Li < Na < K < Rb < Cs. As the size of the cation increases, the lattice energy decreases, thereby reducing thermal stability.

Step 3: Analyzing Halide Sizes

All options use chloride, so the anion size is consistent. Chloride ion size does not contribute to variability in stability for this exercise.

Step 4: Arranging Alkali Metal Halides by Stability

Based on the ionic size, we establish the order of thermal stability of chlorides as LiCl > NaCl > KCl > RbCl > CsCl. Smaller cations like Li+ form stronger bonds and are more thermally stable.

Step 5: Selecting the Correct Option

Review the provided options and select the alignment that matches the established order of thermal stability: LiCl > NaCl > KCl > RbCl > CsCl, which is option (c).

Key Concepts

Thermal Stability in Alkali Metal Halides

Thermal stability is a crucial property for compounds, particularly when it comes to preparing or using materials that must endure high temperatures. In the context of alkali metal halides, this refers to their ability to decompose into their constituent elements as temperatures increase. The general trend observed in alkali metal halides is that smaller cations foster greater thermal stability. This correlation arises because the strength of ionic bonds diminishes as the size of the ionic radius increases.

• Small ions form tighter bonds, hence compounds like ext{LiCl} demonstrate greater stability at elevated temperatures compared to ext{CsCl}.
• In essence, as the ionic character and strength of the electrostatic forces decrease with larger ions, there is a concomitant decrease in thermal stability.

When determining the thermal stability of these halides, it's essential to consider both the size of the metal cation and the nature of the ionic bonding.
Understanding these factors explains why the order of stability follows ext{LiCl} > ext{NaCl} > ext{KCl} > ext{RbCl} > ext{CsCl}. Smaller ions, like ext{Li}^+, exhibit stronger binding which translates into higher thermal resilience.

Significance of Ionic Radii

The size of an ion is significantly influential in dictating a variety of properties, such as ionic bonding strength and thermal stability. Within the realm of alkali metals, the trend of ionic radii increases as we move down the group.

• Starting with ext{Li}^+ as the smallest, the cation size increases from ext{Na}^+, ext{K}^+, ext{Rb}^+, and to ext{Cs}^+ as the largest.
• The size of an ion has a direct effect on lattice energy and, consequently, on bond strength. The larger the ion, the weaker the bond it forms.

This incremental increase in ionic radii affects the compound's ability to maintain its structural integrity at high temperatures.
Smaller ions have a compact structure that enhances lattice energy, thereby improving thermal stability. Conversely, larger ions, having a more expanded structural form, result in decreased lattice energy and thus lower thermal stability. This relationship is critical for chemists and material scientists who design compounds for high-temperature applications.

Understanding Lattice Energy

Lattice energy is a term used to describe the energy required to separate an ionic solid into its gaseous ions. It's a key indicator of the stability of an ionic compound.

• Alkali metal halides like ext{LiCl} tend to have high lattice energies due to the small size of their ions, which allows for stronger attractions and a tighter lattice.
• Lattice energy is inversely related to ionic size; larger ions result in a less compact and therefore less stable lattice.

The trend in lattice energies often mirrors that of thermal stability, where smaller ions like ext{Li}^+ lead to greater lattice energy compared to larger ions like ext{Cs}^+.
Therefore, as the ionic size increases down the group in alkali metals, there's a noticeable decline in lattice energy, contributing to the decreased thermal stability of compounds such as ext{CsCl}. By understanding the relationship between lattice energy and ion size, one can predict the properties of various ionic compounds and determine their potential applications, especially in environments that require high thermal thresholds.
Thus, scientists and engineers often select materials with favorable lattice energies to enhance the performance of materials under thermal stress.