Two solutions are prepared and found to be isotonic at the same temperature. Solution A contains 3.42 g of sucrose (molar mass = 342 g mol ⁻¹ ) dissolved in 100 mL of water. Solution B contains 1.90 g of MgCl ₂ (molar mass = 95 g mol ⁻¹ ) dissolved in 500 mL of water. The percentage dissociation of MgCl ₂ in Solution B is _____.

Step-by-step solution

For Solution A (sucrose, a non-electrolyte): Moles of sucrose = 3.42 342 = 0.01 mol Volume = 100 mL = 0.1 L Molarity of A, C_A = 0.01 0.1 = 0.1 M For Solution B ( MgCl ₂ , an electrolyte): Moles of MgCl ₂ = 1.90 95 = 0.02 mol Volume = 500 mL = 0.5 L Molarity of B, C_B = 0.02 0.5 = 0.04 M Since the solutions are isotonic, their osmotic pressures are equal: _A = _B C_A RT = i C_B RT 0.1 = i 0.04 i = 0.1 0.04 = 2.5 For the dissociation of MgCl ₂ : MgCl ₂ Mg ²⁺ + 2 Cl ^- Number of ions, n = 3 The van't Hoff factor i is