Problem 20 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The following compounds have been arranged in order of their increasing thermal stabilities. Identify the correct order. \(\mathrm{K}_{2} \mathrm{CO}_{3}\) (I) \(\mathrm{MgCO}_{3}\) (II) \(\mathrm{CaCO}_{3}\) (III) \(\mathrm{BeCO}_{3}(\mathrm{IV})\) (a) \(1<\|<1\|\) < IV (b) \(\mathrm{IV}<\|<\| \|<1\) (c) \(I \mathrm{IV}<\mathrm{Il}<\mathrm{I}<\mathrm{III}\) (d) \(\mathrm{II}<\mathrm{IV}<\mathrm{III}<\mathrm{I}\)

Step-by-Step Solution

Answer

(b) IV < II < III < I

Step 1: Understand Thermal Stability

To solve this problem, we first need to understand how thermal stability relates to the decomposition of carbonates. Thermal stability increases as the cation's ionic radius and the lattice energy of the carbonate increase. This is because larger cations destabilize the carbonate ion by weakening its bond with the metal, leading to it's easier decomposition on heating.

Step 2: Identify Trends in Periodic Table

Cations from Group 2 (alkaline earth metals) show increasing thermal stability from top to bottom. Therefore, BeCO₃ is less stable compared to MgCO₃ and CaCO₃ because beryllium has a smaller ionic radius than magnesium and calcium, making BeCO₃ less thermally stable.

Step 3: Consider Alkali Metal Carbonates

Potassium (K⁺) is an alkali metal ion, and alkali metal carbonates are generally more stable than alkaline earth metal carbonates of lower group metals. As a result, K₂CO₃ should be more thermally stable than MgCO₃, CaCO₃, and BeCO₃.

Step 4: Arrange in Order of Increasing Stability

Based on the trends and explanations given: BeCO₃ has the lowest thermal stability followed by MgCO₃, and then by CaCO₃. Finally, K₂CO₃ has the highest thermal stability, which leads us to the order: BeCO₃ < MgCO₃ < CaCO₃ < K₂CO₃.

Step 5: Select the Correct Answer From Options

According to the insights gathered, the correct order of increasing thermal stabilities is IV (BeCO₃) < II (MgCO₃) < III (CaCO₃) < I (K₂CO₃). Comparing this with provided options, it matches with option (b).

Key Concepts

Carbonates Decomposition

In the world of inorganic chemistry, carbonates are compounds that contain the carbonate ion, \\( \text{CO}_3^{2-} \), typically bonded to a metal. These compounds can decompose when exposed to heat, a process known as **thermal decomposition.** This decomposition is a chemical change where the carbonate breaks down into a metal oxide and carbon dioxide gas. For example:

• \( \text{MgCO}_3 \rightarrow \text{MgO} + \text{CO}_2 \)
• \( \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \)

The ability of a carbonate to resist decomposition when heated is referred to as its **thermal stability.** Generally, thermal stability of carbonates increases with factors like larger cation size and greater lattice energy. These factors stabilize the lattice structure, thereby requiring more energy to break it down during decomposition. Understanding the trends in the decomposition of different metal carbonates is crucial in predicting their thermal stability.

Cation Ionic Radius

The cation ionic radius significantly affects the thermal stability of metal carbonates. Larger cations tend to increase thermal stability compared to smaller ones. This happens because larger cations decrease the charge density around the carbonate ion. With less charge concentration, the bonds between the carbonate and the metal cation are less strained and more stable.
This can be observed within a group in the periodic table such as the alkali metals and alkaline earth metals. For instance, in Group 2 elements like Be, Mg, and Ca, the ionic radius increases as we move down the group which in turn increases the thermal stability.
In our example, beryllium has a much smaller cationic ionic radius compared to magnesium and calcium. Thus, \\( \text{BeCO}_3 \) is less stable thermally than \\( \text{MgCO}_3 \) or \\( \text{CaCO}_3 \). The trend manifests as **\( \text{Be} < \text{Mg} < \text{Ca} \)** in terms of thermal stability due to the variations in the cationic sizes.

Lattice Energy

Lattice energy is another vital factor influencing the thermal stability of carbonates. It is a measure of the strength of forces holding the ions together in a crystalline ionic compound. The higher the lattice energy, the more stable the compound is thermally, as it indicates stronger bonds between the ions.
In the case of carbonates, the bond between the metal cation and the carbonate ion tends to be stronger with higher lattice energies. This is due to the stronger electrostatic attraction requiring more energy for thermal decomposition.

• Alkali metal carbonates such as \\( \text{K}_2\text{CO}_3 \) usually have higher lattice energy than some alkaline earth metal carbonates like \\( \text{MgCO}_3 \) or \\( \text{CaCO}_3 \).
• This leads to \\( \text{K}_2\text{CO}_3 \) being more thermally stable than its Group 2 counterparts.

Recognizing how lattice energy impacts thermal decomposition can help you comprehend why certain carbonates withstand decomposing better than others.