In a saturated solution of AgCl, NaCl is added gradually. The concentration of `Ag^(+)` is plotted against the concentration of `Cl^(-)`. The graph appears as :

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Answer

To solve the problem of how the concentration of \( \text{Ag}^+ \) changes as \( \text{NaCl} \) is added to a saturated solution of \( \text{AgCl} \), we can follow these steps:

### Step 1: Understand the Dissociation of \( \text{AgCl} \)
The dissociation of silver chloride (\( \text{AgCl} \)) in water can be represented as:
\[ \text{AgCl (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^- (aq) \]
In a saturated solution of \( \text{AgCl} \), the concentrations of \( \text{Ag}^+ \) and \( \text{Cl}^- \) are in equilibrium.

### Step 2: Adding \( \text{NaCl} \)
When \( \text{NaCl} \) is added to the solution, it dissociates completely into \( \text{Na}^+ \) and \( \text{Cl}^- \):
\[ \text{NaCl (s)} \rightleftharpoons \text{Na}^+ (aq) + \text{Cl}^- (aq) \]
This increases the concentration of \( \text{Cl}^- \) ions in the solution.

### Step 3: Apply the Common Ion Effect
The increase in \( \text{Cl}^- \) concentration due to the addition of \( \text{NaCl} \) will shift the equilibrium of the \( \text{AgCl} \) dissociation reaction to the left, according to Le Chatelier's principle. This results in a decrease in the concentration of \( \text{Ag}^+ \):
\[ \text{Ag}^+ + \text{Cl}^- \rightleftharpoons \text{AgCl (s)} \]
Thus, as \( [\text{Cl}^-] \) increases, \( [\text{Ag}^+] \) decreases.

### Step 4: Relationship Between Concentrations
The solubility product constant (\( K_{sp} \)) for \( \text{AgCl} \) is given by:
\[ K_{sp} = [\text{Ag}^+][\text{Cl}^-] \]
If we let \( s \) be the solubility of \( \text{AgCl} \), then:
\[ K_{sp} = s^2 \]
As \( [\text{Cl}^-] \) increases (due to the addition of \( \text{NaCl} \)), \( [\text{Ag}^+] \) must decrease to maintain the constant \( K_{sp} \).

### Step 5: Graphical Representation
When plotting \( [\text{Ag}^+] \) against \( [\text{Cl}^-] \):
- Initially, as \( [\text{Cl}^-] \) increases, \( [\text{Ag}^+] \) decreases.
- The graph will show a downward trend, which can be represented as a curve that approaches the x-axis but does not touch it, indicating that \( [\text{Ag}^+] \) approaches zero as \( [\text{Cl}^-] \) increases.

### Conclusion
The graph of \( [\text{Ag}^+] \) versus \( [\text{Cl}^-] \) will appear as a downward curve, indicating the inverse relationship due to the common ion effect.

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