Which of the following has lowest thermal stability ?

Options

A. `Li_(2)CO_(3)`
B. `Na_(2)CO_(3)`
C. `K_(2)CO_(3)`
D. `Rb_(2)CO_(3)`

Explanation

To determine which carbonate has the lowest thermal stability among the given options, we need to analyze the charge density of the metal cations associated with each carbonate. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Thermal Stability
Thermal stability of a compound refers to its ability to withstand heat without decomposing. In the case of carbonates, the stability can be influenced by the cation present.

**Hint:** Remember that higher charge density in cations can lead to greater distortion of the carbonate anion, resulting in lower thermal stability.

### Step 2: Identify the Cations
The question involves carbonates of alkali metals, specifically Li⁺, Na⁺, K⁺, and Rb⁺.

**Hint:** List out the cations and their corresponding carbonates to visualize the problem better.

### Step 3: Determine Charge Density
Charge density is defined as the charge of the ion divided by its size (ionic radius). For the alkali metals, the charge is the same (+1) for all, but the size varies.

**Hint:** Recall that as you move down the group in the periodic table, the ionic size increases.

### Step 4: Compare Ionic Sizes
The order of ionic sizes for the given cations is:
- Li⁺ (smallest)
- Na⁺
- K⁺
- Rb⁺ (largest)

**Hint:** Remember that smaller cations have higher charge density because the charge is concentrated in a smaller volume.

### Step 5: Calculate Charge Densities
Since all cations have the same charge (+1), the charge density will be inversely related to the size:
- Li⁺ has the highest charge density.
- Na⁺ has a lower charge density than Li⁺.
- K⁺ has a lower charge density than Na⁺.
- Rb⁺ has the lowest charge density.

**Hint:** Think about how the size of the cation affects the charge density.

### Step 6: Relate Charge Density to Thermal Stability
The cation with the highest charge density (Li⁺) will distort the carbonate anion the most, leading to the least thermal stability. Therefore, the carbonate associated with Li⁺ will have the lowest thermal stability.

**Hint:** Connect the dots between charge density and the stability of the carbonate.

### Conclusion
Based on the analysis, the carbonate with the lowest thermal stability is that of lithium (Li₂CO₃).

**Final Answer:** The carbonate with the lowest thermal stability is Li₂CO₃.