The solubility of AgCl will be maximum in which of the following?

AgCl is a sparingly soluble salt that dissociates as:

$$\text{AgCl} \rightleftharpoons \text{Ag}^+ + \text{Cl}^-$$

$$K_{sp} = [\text{Ag}^+][\text{Cl}^-]$$

Analysis of each option:

Option A: 0.01 M HCl

HCl provides Cl$$^-$$ ions (common ion effect). This will suppress the dissolution of AgCl, reducing its solubility.

Option B: 0.01 M KCl

KCl also provides Cl$$^-$$ ions (common ion effect). This will similarly reduce the solubility of AgCl.

Option C: Deionised water

There are no common ions present. The solubility of AgCl will be determined solely by its $$K_{sp}$$ without any suppression.

Option D: 0.01 M AgNO$$_3$$

AgNO$$_3$$ provides Ag$$^+$$ ions (common ion effect). This will also suppress the dissolution of AgCl.

Conclusion:

Since options A, B, and D all introduce a common ion (either Cl$$^-$$ or Ag$$^+$$), the solubility of AgCl is reduced in all of them. Only in deionised water is there no common ion effect, so AgCl has maximum solubility there.

Hence, the correct answer is Option C (Deionised water).