If `S_(0), S_(1), S_(2)`, and `S_(3)` are the solubility of AgCI in water, `0.01M CaCI_(2), 0.01M NaCI`1, and `0.5M AgNO_(3)` solutions, respectively, then which of the following is true ?

Options

A. `S_(0)gtS_(2)gtS_(1)gtS_(3)`
B. `S_(0)=S_(2)=S_(1)=S_(3)`
C. `S_(3)gtS_(1)gtS_(2)gtS_(0)`
D. `S_(0)gtS_(2)gtS_(3)gtS_(1)`

Explanation

To solve the problem of determining the order of solubility of AgCl in different solutions, we can follow these steps:

### Step 1: Understand the Dissociation of AgCl
AgCl dissociates in water to form Ag⁺ and Cl⁻ ions:
\[ \text{AgCl} \rightleftharpoons \text{Ag}^+ + \text{Cl}^- \]

### Step 2: Identify the Common Ion Effect
The solubility of AgCl will be affected by the presence of common ions (Ag⁺ or Cl⁻) in the solution. The common ion effect states that the solubility of a salt decreases in a solution that already contains one of its ions.

### Step 3: Analyze Each Solution
1. **In Pure Water (S₀)**: There are no common ions, so AgCl will have its maximum solubility.
2. **In 0.01 M CaCl₂ (S₁)**: CaCl₂ dissociates to give 2 Cl⁻ ions per formula unit:
\[ \text{CaCl}_2 \rightarrow \text{Ca}^{2+} + 2\text{Cl}^- \]
Therefore, the concentration of Cl⁻ ions is 0.02 M. This will decrease the solubility of AgCl compared to pure water.
3. **In 0.01 M NaCl (S₂)**: NaCl dissociates to give 1 Cl⁻ ion per formula unit:
\[ \text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^- \]
The concentration of Cl⁻ ions is 0.01 M, which will also decrease the solubility of AgCl, but less than in CaCl₂.
4. **In 0.5 M AgNO₃ (S₃)**: AgNO₃ dissociates to give 1 Ag⁺ ion per formula unit:
\[ \text{AgNO}_3 \rightarrow \text{Ag}^+ + \text{NO}_3^- \]
The concentration of Ag⁺ ions is 0.5 M, which will significantly decrease the solubility of AgCl due to the high concentration of the common ion Ag⁺.

### Step 4: Determine the Order of Solubility
- **Highest Solubility**: S₀ (pure water) - no common ions.
- **Next Highest**: S₂ (0.01 M NaCl) - lower concentration of Cl⁻ compared to CaCl₂.
- **Next**: S₁ (0.01 M CaCl₂) - higher concentration of Cl⁻ (0.02 M).
- **Lowest Solubility**: S₃ (0.5 M AgNO₃) - highest concentration of Ag⁺.

### Final Order of Solubility
The order of solubility from highest to lowest is:
\[ S_0 > S_2 > S_1 > S_3 \]

### Conclusion
Thus, the correct answer is that the solubility of AgCl in different solutions follows the order:
\[ S_0 > S_2 > S_1 > S_3 \]

---