`k_(2)CO_(3)` cannot be prepared by solvay process because

Explanation

To understand why \( K_2CO_3 \) cannot be prepared by the Solvay process, we need to analyze the steps involved in the process and the properties of the compounds formed.

### Step-by-Step Solution:

1. **Understanding the Solvay Process**:
- The Solvay process is used to produce sodium carbonate (\( Na_2CO_3 \)) from sodium chloride (\( NaCl \)). It involves the reaction of carbon dioxide (\( CO_2 \)) with ammonia (\( NH_3 \)) and water to form ammonium bicarbonate (\( NH_4HCO_3 \)).
- The overall reaction can be summarized as:
\[ CaCO_3 \rightarrow CaO + CO_2 \quad (Limestone decomposition) \]
\[ CO_2 + NH_3 + H_2O \rightarrow NH_4HCO_3 \quad (Formation of ammonium bicarbonate) \]

2. **Reaction with Salts**:
- The ammonium bicarbonate then reacts with sodium chloride (\( NaCl \)) to produce sodium bicarbonate (\( NaHCO_3 \)) and ammonium chloride (\( NH_4Cl \)):
\[ NH_4HCO_3 + NaCl \rightarrow NaHCO_3 + NH_4Cl \]

3. **Precipitation of Sodium Bicarbonate**:
- Sodium bicarbonate (\( NaHCO_3 \)) is less soluble in water and precipitates out of the solution:
\[ NaHCO_3 \downarrow \]

4. **Formation of Sodium Carbonate**:
- The precipitated sodium bicarbonate can then be heated to form sodium carbonate (\( Na_2CO_3 \)):
\[ 2 NaHCO_3 \rightarrow Na_2CO_3 + H_2O + CO_2 \]

5. **Why Not Potassium Carbonate?**:
- If we replace sodium chloride (\( NaCl \)) with potassium chloride (\( KCl \)), the reaction would produce potassium bicarbonate (\( KHCO_3 \)):
\[ NH_4HCO_3 + KCl \rightarrow KHCO_3 + NH_4Cl \]
- Unlike sodium bicarbonate, potassium bicarbonate (\( KHCO_3 \)) is highly soluble in water and does not precipitate out. Therefore, it cannot be separated from the solution.

6. **Conclusion**:
- Since \( KHCO_3 \) remains dissolved in the solution, \( K_2CO_3 \) cannot be obtained through the Solvay process, as there is no precipitation step to isolate it.

### Final Answer:
\( K_2CO_3 \) cannot be prepared by the Solvay process because potassium bicarbonate (\( KHCO_3 \)) is more soluble in water and does not precipitate out, preventing the formation of \( K_2CO_3 \).