Which of the following sulphates is not soluble in water?

The solubility of sulphates in water varies depending on the metal cation present. Most alkali metal sulphates, such as sodium sulphate (Na₂SO₄) and potassium sulphate (K₂SO₄), are highly soluble in water. Zinc sulphate (ZnSO₄) is also soluble due to the moderate size and charge of Zn²⁺ ions, which allow hydration to overcome lattice energy.

Barium sulphate (BaSO₄), however, is practically insoluble in water. The Ba²⁺ ion has a large ionic size and forms a very strong ionic lattice with SO₄²⁻ ions. The lattice energy of BaSO₄ is very high, and the energy released during hydration is not sufficient to dissolve the compound. As a result, it remains solid in water.

The insolubility of BaSO₄ is exploited in various applications: it is used as a radiocontrast agent in medical imaging because it passes through the digestive system without dissolving, and in analytical chemistry to test for the presence of sulphate ions. Its stability and non-reactivity in water also make it useful in industrial processes where insoluble compounds are needed.

In contrast, soluble sulphates like Na₂SO₄ and K₂SO₄ dissociate easily in water into their respective ions (Na⁺, K⁺, and SO₄²⁻), allowing them to participate in chemical reactions and provide essential nutrients in agriculture.

Understanding the solubility trend of sulphates is a fundamental topic in inorganic chemistry, highlighting the effects of ionic size, charge, and lattice energy on the solubility of ionic compounds.

Hence, among the given options, barium sulphate (BaSO₄) is the water-insoluble sulphate.