At `30^(@) C` the solubility of `Ag_(2)CO_(3) (K_(SP)=8xx10^(-12))` would be gretest in one litre of:

Options

A. `0.05 M Na_2CO_3`
B. `0.05 M AgNO_3`
C. Pure water
D. `0.05 M NH_3`

Answer

To determine the greatest solubility of \( \text{Ag}_2\text{CO}_3 \) at \( 30^\circ C \), we need to analyze how its solubility is affected by the presence of other ions in solution. The solubility product constant (\( K_{sp} \)) for \( \text{Ag}_2\text{CO}_3 \) is given as \( 8 \times 10^{-12} \).

### Step-by-Step Solution:

1. **Understanding the Dissociation of \( \text{Ag}_2\text{CO}_3 \)**:
\[ \text{Ag}_2\text{CO}_3 (s) \rightleftharpoons 2 \text{Ag}^+ (aq) + \text{CO}_3^{2-} (aq) \]
The solubility product expression is:
\[ K_{sp} = [\text{Ag}^+]^2 [\text{CO}_3^{2-}] \]

2. **Analyzing the Effect of Common Ions**:
- **In \( \text{Na}_2\text{CO}_3 \)**: This compound provides \( \text{CO}_3^{2-} \) ions. The presence of \( \text{CO}_3^{2-} \) will shift the equilibrium to the left, decreasing the solubility of \( \text{Ag}_2\text{CO}_3 \) due to the common ion effect.
- **In \( \text{AgNO}_3 \)**: This compound provides \( \text{Ag}^+ \) ions. Similarly, the presence of \( \text{Ag}^+ \) ions will also shift the equilibrium to the left, further decreasing the solubility of \( \text{Ag}_2\text{CO}_3 \).

3. **Evaluating Pure Water**:
- In pure water, there are no common ions present. Therefore, the solubility of \( \text{Ag}_2\text{CO}_3 \) will be at its maximum compared to the previous two cases.

4. **Considering Ammonia**:
- When \( \text{Ag}_2\text{CO}_3 \) is mixed with ammonia (\( \text{NH}_3 \)), it forms a complex ion:
\[ \text{Ag}_2\text{CO}_3 + 2 \text{NH}_3 \rightleftharpoons [\text{Ag(NH}_3)_2]^+ + \text{CO}_3^{2-} \]
The formation of this complex ion increases the solubility of \( \text{Ag}^+ \) ions in the solution, thereby increasing the overall solubility of \( \text{Ag}_2\text{CO}_3 \).

5. **Conclusion**:
- The greatest solubility of \( \text{Ag}_2\text{CO}_3 \) occurs in ammonia due to the formation of the complex ion, which effectively removes \( \text{Ag}^+ \) ions from the solution and shifts the equilibrium to the right.

### Final Answer:
The solubility of \( \text{Ag}_2\text{CO}_3 \) would be greatest in one litre of ammonia solution.