Question

Thermal stability of \(\mathrm{BaCO}_{3}, \mathrm{CaCO}_{3}\) and \(\mathrm{MgCO}_{3}\) is (1) \(\mathrm{CaCO}_{3}>\mathrm{MgCO}_{3}>\mathrm{BaCO}_{3}\) (2) \(\mathrm{MgCO}_{3}>\mathrm{CaCO}_{3}>\mathrm{BaCO}_{3}\) (3) \(\mathrm{BaCO}_{3}>\mathrm{MgCO}_{3}>\mathrm{CaCO}_{3}\) (4) \(\mathrm{BaCO}_{3}>\mathrm{CaCO}_{3}>\mathrm{MgCO}_{3}\)

Short answer

Option (2): MgCO₃ > CaCO₃ > BaCO₃.

Step-by-step solution

- Understanding Thermal Stability

Thermal stability refers to the ability of a compound to resist decomposition when heated. In carbonates, this is influenced by the cation present (Ba, Ca, or Mg), which affects the lattice energy and the ease with which the compound decomposes.

- Analyzing Cations

Consider the position of Ba, Ca, and Mg in the periodic table. As we move down the group from Mg to Ba, the size of the cation increases. Larger cations result in weaker lattice energies, making it easier for the compound to decompose.

- Trend in Thermal Stability

Smaller cations like Mg will have stronger lattice energies and thus higher thermal stability compared to larger cations like Ca and Ba. Therefore, thermal stability generally decreases going from MgCO₃ to CaCO₃ to BaCO₃.

- Determining the Correct Order

Based on the analysis, the correct order of increasing thermal stability is: BaCO₃ < CaCO₃ < MgCO₃.

- Matching with Given Options

Compare the correct order with the provided options: (1) CaCO₃ > MgCO₃ > BaCO₃, (2) MgCO₃ > CaCO₃ > BaCO₃, (3) BaCO₃ > MgCO₃ > CaCO₃, and (4) BaCO₃ > CaCO₃ > MgCO₃. The correct match is option (2): MgCO₃ > CaCO₃ > BaCO₃.

Key concepts

Thermal Stability

Thermal stability is a key concept when discussing the decomposition of substances under heat. It specifically refers to the resistance of a compound against breaking down when exposed to high temperatures.

For metal carbonates like \(\text{BaCO}_3\), \(\text{CaCO}_3\), and \(\text{MgCO}_3\), thermal stability is largely influenced by the nature of the cation present.

The underlying principle here is the lattice energy— the energy required to break the ionic bonds in a solid. When the lattice energy is high, more energy is needed to decompose the compound, thus making it thermally stable.

In summary, compounds with higher lattice energies exhibit greater thermal stability, meaning they decompose at higher temperatures.

Carbonates Decomposition

When we talk about carbonates decomposition, we mean the process where carbonates (\text{CO}_3^{2-}) break down into their constituent elements when heated. This reaction generally produces metal oxides and carbon dioxide.

For example:

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

The ease of this decomposition depends on the strength of the bonds within the crystal lattice of the carbonate. Stronger bonds equate to higher thermal stability.

In our case, \text{MgCO}_3 decomposes at a higher temperature than \text{CaCO}_3 and \text{BaCO}_3, due to stronger ionic bonds resulting from the smaller size and higher charge density of the \(\text{Mg}^{2+}\) ion.

Cation Effect

The cation effect is crucial in determining the thermal stability of metal carbonates. The cation's size and charge density play significant roles in this context.

Here's what happens:

• As you go down Group 2 in the periodic table, the cation size increases (from \(\text{Mg}^{2+}\) to \(\text{Ba}^{2+}\)).
• Larger cations, such as \(\text{Ba}^{2+}\), have lower charge density and result in weaker electrostatic attractions in the crystal lattice.
• This leads to lower lattice energy and, hence, lower thermal stability.

So, the trend in thermal stability for carbonates of Mg, Ca, and Ba is: \(\text{MgCO}_3 > \text{CaCO}_3 > \text{BaCO}_3\). Smaller cations like \(\text{Mg}^{2+}\) lead to higher lattice energies and greater stability against heat-induced decomposition.