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 correct order is (b) \(4<2<3<1\).

Step 1: Understanding Thermal Stability

Thermal stability refers to the ability of a compound to resist decomposition at high temperatures. In carbonates, the stability increases with the increased size of the metal cation in the carbonate. This is because larger cations are less polarizing and thus destabilize the carbonate ion less.

Step 2: Identifying Cation Sizes

Examine the cation sizes from the given compounds: 1. Potassium (K^+) is largest. 2. Calcium (Ca^2+) is large. 3. Magnesium (Mg^2+) is smaller. 4. Beryllium (Be^2+) is the smallest. Thus, cation sizes in decreasing order are: K > Ca > Mg > Be.

Step 3: Arranging Thermal Stabilities

Based on cation size, the thermal stability will increase with increasing cation size. Hence, the order of increasing thermal stability is: 1. BeCO_3 < MgCO_3 < CaCO_3 < K_2CO_3. This order corresponds to option (b).

Key Concepts

Cation Size Effect

When discussing the thermal stability of carbonate compounds, cation size plays a crucial role. Cations are the positively charged ions in a compound, and their size can greatly influence how stable a compound is when exposed to heat.

Here's why size matters:

• Larger cations have a lower charge density. This means they have a lesser ability to polarize the oxygen atoms in the carbonate ion.
• The less polarization there is, the more stable the carbonate compound. The carbonate ion feels less 'distorted' by the presence of the cation, which means it's more resistant to breaking down under high temperatures.
• In comparison, smaller cations like \( \text{Be}^{2+} \) are highly polarizing. This can destabilize the carbonate ion, making the compound more likely to decompose when heated.

Understanding the link between cation size and polarization helps explain the pattern seen in carbonate stability. With the compounds provided, we see that potassium \( \text{(K}^{+}) \) is the largest and beryllium \( \text{(Be}^{2+}) \) is the smallest, affecting their respective compound's thermal properties.

Decomposition of Compounds

Decomposition is a chemical process where a compound breaks down into simpler substances when subjected to heat.

In the context of carbonates:

• When a carbonate decomposes, it typically forms an oxide and releases carbon dioxide gas. For example, magnesium carbonate \( \text{MgCO}_3 \) would decompose to form magnesium oxide \( \text{MgO} \) and carbon dioxide \( \text{CO}_2 \).
• The easier it is for a compound to decompose, the less thermally stable it is considered to be.
• Thermal stability is linked directly with the nature of the cation present within the compound. Cations with smaller sizes and higher charge densities promote decomposition.

Understanding decomposition helps us to rank the stability of different metal carbonates. The process of decomposition is key to identifying which compounds will retain their structure and which will break apart under heat.

Metal Carbonates Stability

The stability of metal carbonates can differ significantly based on the metal cation present. This stability is fundamental to predicting their behavior when heated.

Key facts about carbonate stability:

• Large cations (like \( \text{K}^+ \)) tend to form carbonates that are more stable. Potassium carbonate (\( \text{K}_2\text{CO}_3 \)) has one of the highest stabilities due to the large size and low polarizing power of the potassium cation.
• As cation size decreases (as seen with magnesium \( \text{Mg}^{2+} \) and beryllium \( \text{Be}^{2+} \)), the stability of the carbonate decreases. This is due to an increase in polarizing power, which distorts the carbonate ion and leads to easier decomposition.
• Calcium carbonate (\( \text{CaCO}_3 \)) is more stable than magnesium carbonate but less stable than potassium carbonate, clearly showing the impact of cation size and charge on stability.

By understanding these concepts, students can predict which metal carbonates will hold up better under thermal stress, based on the size and charge of the metal cations involved.