Two solutions of a polymer (molar mass = 83000 g mol ⁻¹ ) are prepared at 300 K . Solution A has a mass concentration of 20 g L ⁻¹ and a volume of 100 mL . Solution B has a mass concentration of 60 g L ⁻¹ and a volume of 300 mL . When these two solutions are mixed, the osmotic pressure of the resulting solution is x 10⁻³ atm . The value of x is ________. (Given: R = 0.083 L atm K ⁻¹ mol ⁻¹ )

Step-by-step solution

First, calculate the final mass concentration ( C_f ) of the mixture: C_f = C₁ V₁ + C₂ V₂ V₁ + V₂ C_f = 20 100 + 60 300 100 + 300 C_f = 2000 + 18000 400 = 20000 400 = 50 g L ⁻¹ Now, calculate the osmotic pressure of the final solution using the formula = C_f R T M : = 50 0.083 300 83000 = 50 24.9 83000 = 1245 83000 = 0.015 atm Expressing this in the required format: = 15 10⁻³ atm Thus, the value of x is 15 . Answer: 15