The solubilities of AgCl in water, 0.01M `CaCl_2,` 0.01 M NaCl and 0.05 M `AgNO_3` are denoted by `S_(1), S_(2), S_(3) and S_(4)` respectively. Which of the following relationships is correct?

Options

A. `S_(1) gt S_(2) gt S_(3) gt S_(4)`
B. `S_(1) gt S_(3) gt S_(2) gt S_(4)`
C. `S_(1) gt S_(2)=S_(3) gt S_(4)`
D. `S_(1) gt S_(3) gt S_(4) gt S_(2)`

Explanation

To solve the problem of determining the relationships between the solubilities \( S_1, S_2, S_3, \) and \( S_4 \) of AgCl in different solutions, we will analyze the effect of the common ions present in each solution on the solubility of AgCl.

### Step-by-Step Solution:

1. **Understanding the Dissociation of AgCl:**
AgCl dissociates in water as follows:
\[
\text{AgCl} \rightleftharpoons \text{Ag}^+ + \text{Cl}^-
...