0.2 M magnesium chloride corresponds to 0.4 M chlorine ions. Now this concentration of chlorine ions must also be considered for evaluating the solubility product. (The given Ksp of AgCl is not correct as it should be 10 to the power -10 and not -2).

Solubility of AgCl in 0.2M magnesium chloride

To determine the solubility of AgCl in 0.2M magnesium chloride (MgCl2), we need to consider the common ion effect and the solubility product constant (Ksp) of AgCl.

Common Ion Effect:
When a compound is dissolved in a solution containing a common ion, its solubility decreases. In this case, AgCl is being dissolved in a solution of MgCl2, which contains chloride ions (Cl-). Since AgCl is also an ionic compound that contains chloride ions, the presence of additional chloride ions from MgCl2 reduces the solubility of AgCl.

Solubility Product Constant (Ksp):
The solubility of a sparingly soluble salt, like AgCl, is determined by its solubility product constant (Ksp). Ksp represents the equilibrium constant for the dissolution of AgCl in water and can be calculated using the concentrations of the ions produced.

The Ksp expression for AgCl is:
Ksp = [Ag+][Cl-]

Given that the Ksp of AgCl is 1.8×10^-2, we can use this information to determine the solubility of AgCl in 0.2M MgCl2.

Calculating Solubility:
Since MgCl2 is a strong electrolyte, it dissociates completely in water to form Mg2+ and 2Cl- ions. Therefore, the concentration of chloride ions in the solution is 0.2M × 2 = 0.4M.

To determine the solubility of AgCl, we need to consider the equilibrium between the dissolved and undissolved AgCl. Let's assume the solubility of AgCl is "s" moles per liter.

The concentration of Ag+ ions in the solution will also be equal to "s" moles per liter.

Using the Ksp expression, we can write:
Ksp = [Ag+][Cl-]
1.8×10^-2 = s × 0.4

Solving for s, we find:
s = (1.8×10^-2) / 0.4
s ≈ 0.045 M

Therefore, the solubility of AgCl in 0.2M MgCl2 is approximately 0.045 M.

Summary:
The solubility of AgCl in 0.2M MgCl2 is determined by the common ion effect and the solubility product constant (Ksp). The presence of additional chloride ions from MgCl2 decreases the solubility of AgCl. By using the Ksp expression and considering the concentration of chloride ions in the solution, we can calculate the solubility of AgCl to be approximately 0.045 M.