In the following reaction.
`AgCl +KI hArr KCl +AgI`
as KI is added, the equilibrium is shifted towards right giving more AgI precipitate , because

Options

A. both AgCl and AgI are sparingly soluble
B. the `K_(sp)` of AgI is lower than `K_(sp)` of AgCl
C. the `K_(sp)` of AgI is higher than `K_(sp)` of AgCl
D. both AgCl and AgI have same solubility product

Explanation

To understand why the equilibrium shifts to the right in the reaction \( \text{AgCl} + \text{KI} \rightleftharpoons \text{KCl} + \text{AgI} \) when KI is added, we can break it down into a step-by-step explanation.

### Step 1: Identify the Reaction
The reaction involves silver chloride (AgCl) and potassium iodide (KI) reacting to form potassium chloride (KCl) and silver iodide (AgI).

### Step 2: Understand the Concept of Equilibrium
In a chemical reaction at equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. Any change in concentration, temperature, or pressure can disturb this equilibrium.

### Step 3: Apply Le Chatelier's Principle
Le Chatelier's Principle states that if a system at equilibrium is subjected to a change, the system will adjust itself to counteract that change and restore a new equilibrium.

### Step 4: Analyze the Effect of Adding KI
When KI is added to the system, the concentration of potassium ions (K\(^+\)) and iodide ions (I\(^-\)) increases. This increase in concentration disturbs the equilibrium.

### Step 5: Determine the Direction of Shift
According to Le Chatelier's Principle, the system will respond by shifting the equilibrium to the right to reduce the concentration of the added reactant (I\(^-\)). This shift produces more products, specifically KCl and AgI.

### Step 6: Formation of Precipitate
As the equilibrium shifts to the right, more AgI is formed. AgI is less soluble in water compared to AgCl, leading to the precipitation of AgI.

### Step 7: Consider Solubility Product (Ksp)
The solubility product (Ksp) of a compound is a constant that indicates its solubility in water. Since AgI is less soluble than AgCl, the Ksp of AgI is lower than that of AgCl. The formation of AgI precipitate indicates that the system is favoring the formation of a less soluble product.

### Conclusion
Thus, when KI is added, the equilibrium shifts to the right, resulting in the formation of more AgI precipitate due to the disturbance in equilibrium and the lower solubility of AgI compared to AgCl.

---