Solubility product (Ksp) is the product of the concentrations of the ions in a saturated solution of a sparingly soluble salt at a particular temperature. The lower the value of Ksp, the lower is the solubility of the salt.

Explanation:

The solubility product of a sparingly soluble salt (MX) is given by the equation:

Ksp = [M+][X-]

where [M+] and [X-] are the concentrations of the cation and anion in the saturated solution.

The solubility of a salt is inversely proportional to its Ksp value. Therefore, the lower the Ksp, the lower is the solubility of the salt.

Out of the given sulphides, the solubility product of PbS is the lowest. This is because:

- Lead (Pb) is a large ion and has a high charge density, which makes it form strong bonds with sulphur ions (S2-).
- The ionic radius of S2- is larger than that of F-, Cl-, Br-, and I-. Therefore, the lattice energy of PbS is lower than that of other metal sulphides.
- Lead sulphide (PbS) is an ionic compound that is almost insoluble in water. Its solubility product is only 3.2 x 10^-28.
- On the other hand, FeS, MnS, and ZnS have higher solubility products and are more soluble in water.

Therefore, PbS has the lowest solubility product among the given sulphides.

PbS has the lowest solubility product of all the sulphides. Pb2+ cation belongs to group-2 of salt analysis sulfides of group-2 and has lower solubility products.