Problem 117 - A Complete Resource Book in Chemistry for JEE Main

Question

The following compounds are to be arranged in order of their increasing thermal stabilities. Identify the correct order. 1\. \(\mathrm{K}_{2} \mathrm{CO}_{3}\) 2\. \(\mathrm{MgCO}_{3}\) 3. \(\mathrm{CaCO}_{3}\) 4\. \(\mathrm{BeCO}_{3}\) (a) \(1<2<3<4\) (b) \(4<2<3<1\) (c) \(4<2<1<3\) (d) \(2<4<3<1\)

Step-by-Step Solution

Answer

The order is (b) 4<2<3<1.

Step 1: Understanding Thermal Stability

Thermal stability refers to the resistance of a compound to decomposition upon heating. In the case of carbonates ( ext{XCO}_3), thermal stability typically increases with the charge density of the cation  ext{X}. Cations like Be, Mg, and Ca are alkaline earth metals, while K is an alkali metal.

Step 2: Determine Cations and Their Sizes

The cations in the compounds are Be, Mg, Ca, and K. Be is the smallest cation (smallest radius and largest charge density), while K is the largest. The order of ionic radii from largest to smallest is  ext{K}^{+} > ext{Ca}^{2+} > ext{Mg}^{2+} > ext{Be}^{2+}.

Step 3: Evaluating Stability: Polarizing Power and Charge

The stability of carbonates  ext{MCO}_3 inversely depends on the cation's ability to distort the electron cloud (polarizing power). Higher polarizing power destabilizes carbonate. Smaller, more highly charged cations (Be)> exert more polarizing power than larger, less charged ones (K). Consequently, the trend for stability is K > Ca > Mg > Be.

Step 4: Arranging Based on Cation Influence

Given the most stable carbonate results from the least polarizing power,  ext{KCO}_3 is most stable and  ext{BeCO}_3 is least, the correct order is 4 < 2 < 3 < 1.

Key Concepts

Carbonate Stability

When we talk about thermal stability, especially with compounds like carbonates, we refer to how well these compounds resist breaking down when exposed to heat. Carbonates are compounds that contain the carbonate ion,  ext{CO}_3^{2-}. Their stability upon heating depends significantly on the metallic cation they are paired with.

To understand this better, let's focus on a few examples: potassium carbonate ( ext{K}_2 ext{CO}_3), magnesium carbonate ( ext{MgCO}_3), calcium carbonate ( ext{CaCO}_3), and beryllium carbonate ( ext{BeCO}_3). These compounds decompose to release carbon dioxide when heated, and their resistance to this decomposition among the alkaline and alkali metals varies.

• Alkali metals like potassium form more stable carbonates compared to alkaline earth metals.
• The nature of the bond and the size of the cation are important factors in determining thermal stability.
• Smaller, more charged cations such as  ext{Be}^{2+} exert greater destabilizing effects than larger and less charged ones like  ext{K}^{+}.

Understanding the order of stability helps in predicting how these materials behave under heat, which is useful in both chemical reactions and industrial processes.

Charge Density and Ionic Radii

Charge density refers to how much electric charge is concentrated in a given amount of space for an ion. It's influenced by two main factors: the charge of the ion and its size, often described as the ionic radius.

Ions with high charge and small size have high charge density. For instance,  ext{Be}^{2+} is a small ion with a significant charge, thus it has a very high charge density. On the other hand,  ext{K}^{+} is larger with a lower charge density due to its single positive charge and larger ionic radius.

Here's how charge density affects stability:

• Smaller, highly charged ions polarize the carbonate ion more effectively. This phenomenon influences the compound's decomposition temperature.
• Larger ions with smaller charge density, like potassium ions, do not polarize the carbonate ion as much, resulting in higher stability.

In summary, ionic size and charge directly affect a compound's structure and stability. Smaller, more charged ions lead to less stable carbonates while larger ions enhance stability.

Polarizing Power of Cations

Polarizing power is a measure of an ion's ability to distort the electron cloud of another ion. It is largely a characteristic of the cation in the compound.

The potential to distort increases with:

• Higher positive charge on the cation.
• Smaller radius of the cation.

Cation's polarizing power is crucial because it determines how tightly the compound's ions are held together. For example,  ext{Be}^{2+} is small and highly charged. It has high polarizing power which leads to greater electron cloud distortion. This disrupts the carbonate bond, making  ext{BeCO}_3 less stable.

Conversely, ions like  ext{K}^{+}, which are larger and less charged, exhibit lower polarizing power, making their compounds more robust against thermal decomposition. Thus, understanding polarizing power helps predict and control material behaviors in various chemical settings.