Problem 95 - A Complete Resource Book in Chemistry for JEE Main

Question

Thermal stability of \(\mathrm{BaCO}_{3}, \mathrm{CaCO}_{3}\) and \(\mathrm{MgCO}_{3}\) is (a) \(\mathrm{BaCO}_{3}>\mathrm{CaCO}_{3}>\mathrm{MgCO}_{3}\) (b) \(\mathrm{BaCO}_{3}>\mathrm{MgCO}_{3}>\mathrm{CaCO}_{3}\) (c) \(\mathrm{MgCO}_{3}>\mathrm{CaCO}_{3}>\mathrm{BaCO}_{3}\) (d) \(\mathrm{CaCO}_{3}>\mathrm{MgCO}_{3}>\mathrm{BaCO}_{3}^{3}\)

Step-by-Step Solution

Answer

The thermal stability order is \( \mathrm{BaCO}_{3} > \mathrm{CaCO}_{3} > \mathrm{MgCO}_{3} \).

Step 1: Understanding Thermal Stability

Thermal stability refers to a compound's ability to remain unchanged at high temperatures. In carbonates like \( \text{BaCO}_3 \), \( \text{CaCO}_3 \), and \( \text{MgCO}_3 \), this stability is influenced by the metal cation's ability to stabilize the carbonate ion through lattice energy and polarizing power.

Step 2: Analyzing Ionic Size

Check the ionic size of the metal cations. Larger cations like Ba\(^2+\) result in weaker lattice energies compared to smaller cations like Mg\(^2+\). Weaker lattice energies indicate higher thermal stability as the carbonate decomposes less readily.

Step 3: Evaluating Polarizing Power

Assess the polarizing power, which is inversely related to cation size. Smaller cations like Mg\(^2+\) have higher polarizing power and thus destabilize the carbonate ion more, making \( \text{MgCO}_3 \) less thermally stable compared to \( \text{CaCO}_3 \) and \( \text{BaCO}_3 \).

Step 4: Determining Stability Order

Combine both ionic size and polarizing power insights. Larger cations with smaller polarizing power contribute to higher thermal stability in carbonates. Therefore, the thermal stability order is \( \text{BaCO}_3 > \text{CaCO}_3 > \text{MgCO}_3 \).

Key Concepts

Ionic Size

Ionic size is a key factor affecting thermal stability. In the context of metal carbonates like \( \text{BaCO}_3 \), \( \text{CaCO}_3 \), and \( \text{MgCO}_3 \), the ionic size refers to the size of the metal cation involved. Larger cations generally lead to weaker lattice energies. This is because the larger the cation, the further apart the ions in the lattice are, making the attractive forces between the ions weaker. Consider the metal cations in these compounds:

• \( \text{Ba}^{2+} \)
• \( \text{Ca}^{2+} \)
• \( \text{Mg}^{2+} \)

Among these, \( \text{Ba}^{2+} \) has the largest ionic size, followed by \( \text{Ca}^{2+} \), and \( \text{Mg}^{2+} \) is the smallest. Larger \( \text{Ba}^{2+} \) ions mean the lattice is less tightly bound, allowing \( \text{BaCO}_3 \) to maintain stability at higher temperatures. As the ionic size decreases, the lattice becomes more compact, which may increase lattice energy but decreases thermal stability.

Polarizing Power

Polarizing power plays a significant role in determining a compound's thermal stability. It describes the ability of a cation to distort the electron cloud of an adjacent anion. This power is inversely related to the ionic size, meaning that smaller cations have higher polarizing power. When metal cations, such as \( \text{Mg}^{2+} \), have greater polarizing power, they can significantly distort the \( \text{CO}_3^{2-} \) ion, weakening the overall ionic bonds within the lattice structure, leading to decreased thermal stability. Here's the breakdown of their polarizing power:

• \( \text{Mg}^{2+} \) > \( \text{Ca}^{2+} \) > \( \text{Ba}^{2+} \)

While high polarizing power indicates stronger distortion, it also results in higher instability for the carbonate ion. Thus, \( \text{MgCO}_3 \) with its high polarizing power becomes less thermally stable versus \( \text{CaCO}_3 \) and \( \text{BaCO}_3 \), due to greater disruption within its lattice.

Lattice Energy

Lattice energy is the energy released when ions come together to form a solid. It is a measure of the strength of the forces holding the ions together in a crystal lattice. This energy is influenced by both ionic size and polarizing power. In simpler terms, the smaller the ionic size, the stronger the lattice energy due to the ions being close and tightly packed. Conversely, larger ions have weaker lattice energies. But here's the trick: weaker lattice energy may mean higher thermal stability in certain contexts. With carbonates like \( \text{BaCO}_3 \), \( \text{CaCO}_3 \), and \( \text{MgCO}_3 \), this means:

• \( \text{BaCO}_3 \) has weaker lattice energy but more thermal stability due to its larger cation.
• \( \text{MgCO}_3 \) with smaller cations has stronger lattice energy but is less thermally stable because the high polarizing power disrupts the stability.

Thus, understanding lattice energy helps us predict the thermal behavior of these carbonates under heating.