The Ksp of AgCl

The solubility product constant, Ksp, is a measure of the extent to which a sparingly soluble salt dissolves in water. It is the equilibrium constant for the dissociation of the salt into its constituent ions in a saturated solution. In the case of AgCl, the Ksp can be determined using the conductivity measurements of a saturated solution and its molar conductivity at infinite dilution.

Conductivity of a Saturated Solution of AgCl
The conductivity of a solution is a measure of its ability to conduct an electric current. In the case of a saturated solution of AgCl, the conductivity is determined by the presence of Ag+ and Cl- ions. These ions are formed when AgCl dissociates in water according to the following equation:

AgCl (s) ⇌ Ag+ (aq) + Cl- (aq)

The conductivity of the saturated solution is given as 9 x 10^-6 Sm^-1.

Molar Conductivity at Infinite Dilution
The molar conductivity at infinite dilution, Λ°, is a measure of the conductivity of a salt when it is completely dissociated into its constituent ions at infinite dilution. It is determined experimentally by measuring the conductivity of a very dilute solution of the salt.

For AgCl, the molar conductivity at infinite dilution is given as 3 x 10^-4 Sm^2 mol^-1.

Using the Conductivity Data to Determine Ksp
The Ksp of AgCl can be determined using the following equation:

Ksp = (Λ°)^2 / (conductivity of saturated solution)

Substituting the given values:

Ksp = (3 x 10^-4 Sm^2 mol^-1)^2 / (9 x 10^-6 Sm^-1)
= (9 x 10^-8 S^2 m^4 mol^-2) / (9 x 10^-6 Sm^-1)
= 10^-2 mol^2 L^-2

Interpretation of Ksp
The Ksp value of AgCl is 10^-2 mol^2 L^-2. This means that at equilibrium, the product of the concentrations of Ag+ and Cl- ions in a saturated solution of AgCl is equal to 10^-2 mol^2 L^-2. The higher the Ksp value, the more soluble the salt is.

The Ksp value can also be used to determine the solubility of AgCl in water. Since AgCl dissociates into Ag+ and Cl- ions, the solubility of AgCl can be calculated by taking the square root of the Ksp value:

Solubility of AgCl = √(Ksp)
= √(10^-2 mol^2 L^-2)
= 10^-1 mol L^-1

Therefore, the solubility of AgCl in water is 10^-1 mol L^-1.

Conclusion
The Ksp of AgCl is 10^-2 mol^2 L^-2. This value can be determined using the conductivity measurements of a saturated solution and its molar conductivity at infinite dilution. The Ksp value indicates the extent to which AgCl dissociates into its constituent ions in water. The higher the Ksp value, the more