Which of the following carbonate salt is soluble due to high entropy change?

Options

A. `K_(2)CO_(3)`
B. `Li_(2)CO_(3)`
C. `(NH_(4))_(2)CO_(3)`
D. `Na_(2)CO_(3)`

Explanation

To determine which carbonate salt is soluble due to high entropy change, we can follow these steps:

### Step 1: Understand the Concept of Solubility and Entropy
Solubility of a salt in water can be influenced by the changes in entropy (ΔS) during the dissolution process. A positive change in entropy generally favors solubility.

**Hint:** Remember that entropy is a measure of disorder; higher disorder often leads to higher solubility.

### Step 2: Analyze the Given Carbonate Salts
The options provided are:
1. K2CO3 (Potassium carbonate)
2. Li2CO3 (Lithium carbonate)
3. NH4CO3 (Ammonium carbonate)
4. Na2CO3 (Sodium carbonate)

**Hint:** Consider the structure and stability of each salt when dissolved in water.

### Step 3: Consider the Role of Lattice Energy and Hydration Energy
The solubility of salts is influenced by lattice energy (energy required to separate the ions) and hydration energy (energy released when ions are surrounded by water molecules). A high hydration energy compared to lattice energy usually indicates good solubility.

**Hint:** Compare the lattice energy and hydration energy of each salt to assess their solubility.

### Step 4: Evaluate the Entropy Change for Each Salt
- For **NH4CO3**, the dissolution leads to a significant increase in disorder because the ammonium ions and carbonate ions become solvated by water molecules. This results in a high positive entropy change.
- For **K2CO3**, **Li2CO3**, and **Na2CO3**, while they are also soluble, their solubility is more dependent on the balance between lattice energy and hydration energy rather than a significant increase in entropy.

**Hint:** Focus on the ammonium carbonate as it is known for its high positive entropy change upon dissolution.

### Step 5: Conclusion
Based on the analysis, **NH4CO3 (Ammonium carbonate)** is the carbonate salt that is soluble due to a high entropy change. The dissolution process leads to a significant increase in disorder, making it more favorable.

**Final Answer:** The soluble carbonate salt due to high entropy change is **NH4CO3** (Option 3).