COMEDK2024Morning ShiftChemistryIonic EquilibriumActual
A ₃ ~B ₄ is a sparingly soluble salt with a solubility of s g / L . If the Molar mass of A ₃ ~B ₄ is Mg / mol , what is the expression for its K _ sp ?
Options
- A8413( ~s M )^8
- B5185( ~s M )^6
- C6912( ~s / M )^7
- D5184( ~s / M )^7
Correct answer
C. 6912( ~s / M )^7
Step-by-step solution
The salt A ₃ B ₄ dissociates in water as follows: A ₃ B ₄ (s) 3 A ⁴⁺ (aq) + 4 B ³⁻ (aq) The solubility of the salt is given as s g/L. The molar mass of the salt is M g/mol. Therefore, the molar solubility S in mol/L is given by: S = s M mol/L From the stoichiometry of the dissociation, the concentration of A ⁴⁺ is 3S and the concentration of B ³⁻ is 4S . The solubility product constant K_ sp is defined as: K_ sp = [ A ⁴⁺]^3 [ B ³⁻]^4 Substituting the concentrations in terms of S : K_ sp = (3S)^3 (4S)^4 K_ sp = (27