Two solutions are prepared at the same temperature. The first solution contains 5.0 g of an unknown non-electrolyte polymer dissolved in 250 mL of solution. The second solution contains 0.0585 g of NaCl dissolved in 100 mL of solution. If the two solutions are isotonic and NaCl is completely dissociated, the molar mass of the unknown polymer is ________ g mol ⁻¹ . (Given: Molar mass of NaCl = 58.5 g mol ⁻¹ )

Step-by-step solution

Moles of NaCl = 0.0585 58.5 = 0.001 mol Molarity of NaCl solution = 0.001 100 10⁻³ = 0.01 M Since NaCl is completely dissociated, its van't Hoff factor i = 2 . Effective concentration of NaCl = i C = 2 0.01 = 0.02 M For isotonic solutions, the effective concentrations of the solutes must be equal. Molarity of polymer solution = 0.02 M Moles of polymer = Molarity Volume in L = 0.02 0.25 = 0.005 mol Molar mass of polymer = Mass Moles = 5.0 0.005 = 1000 g mol ⁻¹ Answer: 1000