Answer (b) BaSO₄ > Hg₂Cl₂ > CrCl₃ > Cr₂(SO₄)₃

Explanation

Cr₂(SO₄)₃ ⇌ 2Cr³⁺ + 3SO₄^2-

                 2s             3s

K_sp = (2s)²(3s)³ = 4s² x 27s³ = 108s⁵

s = \((\frac{K_{sp}}{108})^{\frac{1}{5}}\)

Hg₂Cl₂ ⇌ 2Hg²⁺ + 2Cl^-

K_sp = (2s)²(2s)² = 16s⁴

s = \((\frac{K_{sp}}{16})^{\frac{1}{4}}\)

BaSO₄ ⇌ Ba²⁺ + SO₄^2-

              s            s

K_sp = s²

s = \(\sqrt{K_{sp}}\)

CrCl₃ ⇌ Cr³⁺ + 3Cl^-

K_sp = s x (3s)³ = 27s⁴

s = \((\frac{K_{sp}}{27})^{\frac{1}{4}}\)

Hence the correct order of solubilities of salts is

\(\sqrt{K_{sp}}\) > \((\frac{K_{sp}}{16})^{\frac{1}{4}}\) > \((\frac{K_{sp}}{27})^{\frac{1}{4}}\) > \((\frac{K_{sp}}{108})^{\frac{1}{5}}\)