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

Options

A. `K_2CO_3`
B. `Li_2CO_3`
C. `(NH_4)_2CO_3`
D. `Na_2CO_3`

Answer

To determine which carbonate salt is soluble due to high entropy change, we will analyze the given options step by step.

### Step 1: Identify the Options
The options provided are:
1. Potassium carbonate (K2CO3)
2. Lithium carbonate (Li2CO3)
3. Ammonium carbonate ((NH4)2CO3)
4. Sodium carbonate (Na2CO3)

### Step 2: Understand the Factors Affecting Solubility
Solubility of salts is influenced by:
- **Lattice Energy**: The energy required to separate the ions in a solid.
- **Enthalpy of Solvation (or Hydration)**: The energy released when ions are surrounded by solvent molecules.
- **Entropy Change (ΔS)**: The change in disorder when a solid dissolves.

### Step 3: Analyze Metal Carbonates
The first three options (potassium carbonate, lithium carbonate, and sodium carbonate) are metal carbonates. The solubility of these salts is primarily influenced by lattice energy and enthalpy of solvation.

- For metal carbonates, the lattice energy tends to be high, which means they are less soluble. The enthalpy of solvation does not compensate enough for the lattice energy to make these salts soluble.

### Step 4: Analyze Ammonium Carbonate
Ammonium carbonate is different from the metal carbonates. Its formula is (NH4)2CO3.

- When ammonium carbonate dissolves, the enthalpy of solution (ΔH_solution) is positive, indicating that energy is absorbed.
- However, the dissolution of ammonium carbonate leads to a significant increase in disorder (high positive entropy change, ΔS).

### Step 5: Apply Gibbs Free Energy Equation
Using the Gibbs Free Energy equation:
\[ \Delta G = \Delta H - T \Delta S \]

- Since ΔH is positive for ammonium carbonate and ΔS is also positive (and likely large), the term \( T \Delta S \) can outweigh ΔH, leading to a negative ΔG.
- A negative ΔG indicates that the process is spontaneous, which means ammonium carbonate is soluble.

### Conclusion
Therefore, the carbonate salt that is soluble due to high entropy change is **Ammonium Carbonate (NH4)2CO3**.

### Final Answer
**Ammonium Carbonate (NH4)2CO3 is the correct answer.**

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