Introduction:
The solubility product constant, also known as Ksp, is a measure of the solubility of a compound in a solution. It represents the equilibrium constant for the dissociation of an ionic compound into its constituent ions in a saturated solution at a particular temperature. In this case, we are considering the solubility product of AgCl (silver chloride) in a solution of KCl (potassium chloride) with a concentration of x M.

Solubility Product of AgCl:
The solubility product constant (Ksp) for AgCl can be expressed as follows:
AgCl(s) ⇌ Ag+(aq) + Cl-(aq)
Ksp = [Ag+][Cl-]
The value of Ksp for AgCl at a specific temperature is constant and is determined by the equilibrium concentrations of Ag+ and Cl- ions in a saturated solution of AgCl.

Solubility of AgCl in x M KCl:
When AgCl is added to a solution of KCl, it will undergo a common ion effect. The common ion effect occurs when the solubility of a compound is reduced by the presence of a common ion already present in the solution. In this case, both AgCl and KCl produce Cl- ions when they dissociate in water. Therefore, the solubility of AgCl will be affected by the concentration of Cl- ions from KCl.

The solubility of AgCl in x M KCl can be determined using the following steps:

1. Write the dissociation equation for AgCl in water:
AgCl(s) ⇌ Ag+(aq) + Cl-(aq)

2. Write the dissociation equation for KCl in water:
KCl(s) ⇌ K+(aq) + Cl-(aq)

3. Determine the initial concentration of Cl- ions in the solution:
The initial concentration of Cl- ions is x M, since the concentration of KCl is x M.

4. Use the solubility product constant equation to determine the solubility of AgCl:
Ksp = [Ag+][Cl-]
Since the concentration of Ag+ ions will be equal to the solubility of AgCl, let's assume it is represented by 's':
Ksp = (s)(x)

5. Solve the equation for the solubility of AgCl (s):
s = Ksp / x

Conclusion:
The solubility of AgCl in a solution of x M KCl can be determined using the solubility product constant equation. By considering the common ion effect and the initial concentration of Cl- ions from KCl, the solubility of AgCl can be calculated as s = Ksp / x.