A 0.1 M aqueous solution of a cobalt complex CoCl ₃ x NH ₃ is isotonic with a 0.1 M aqueous solution of CaCl ₂ at the same temperature. Assuming complete dissociation of both the compounds and that the coordination number of cobalt is 6 , the value of x is ________.

Step-by-step solution

For the strong electrolyte CaCl ₂ , it dissociates completely into 1 Ca ²⁺ and 2 Cl ^- ions. The van 't Hoff factor for CaCl ₂ is i₁ = 3 . Effective concentration of CaCl ₂ = i₁ C₁ = 3 0.1 = 0.3 M . Let the van 't Hoff factor for the cobalt complex be i₂ . Since the solutions are isotonic, their effective concentrations are equal: i₂ 0.1 = 0.3 i₂ = 3 . This means the complex dissociates into 3 ions in aqueous solution. This is possible if the complex yields 1 complex cation and 2 chloride counter-ions. Thus, 1 chlo