**Explanation:**

**Solubility in water**

The solubility of a substance refers to its ability to dissolve in a solvent, such as water. Some substances are highly soluble and readily dissolve in water, while others are insoluble and do not dissolve or only dissolve to a very small extent.

**Solubility rules**

There are certain solubility rules that can be used to determine whether or not a substance is soluble in water. These rules are based on the general behavior of different types of compounds and their interactions with water.

**Solubility of sulphates**

Sulphates are a type of compound that contain the sulphate ion (SO4^2-). The solubility of sulphates can vary depending on the specific cation (positive ion) that is associated with the sulphate ion.

**Solubility of lead sulphate**

Lead sulphate (PbSO4) is generally considered to be insoluble in water. This is due to the relatively low solubility product constant (Ksp) of lead sulphate. The Ksp is a measure of the extent to which a compound will dissolve in water. A lower Ksp value indicates lower solubility.

**Solubility of zinc sulphate, potassium sulphate, and sodium sulphate**

On the other hand, zinc sulphate (ZnSO4), potassium sulphate (K2SO4), and sodium sulphate (Na2SO4) are all highly soluble in water. These compounds have higher solubility product constants and readily dissociate into their respective cations (Zn^2+, K+, Na+) and sulphate ions.

**Conclusion**

In summary, lead sulphate (PbSO4) is not soluble in water, while zinc sulphate (ZnSO4), potassium sulphate (K2SO4), and sodium sulphate (Na2SO4) are all soluble. This is due to the differences in the solubility product constants and the behavior of these compounds when in contact with water.