An aqueous solution containing 10 g L ⁻¹ of a non-electrolyte macromolecule has an osmotic pressure of 0.083 bar at 300 K . The molar mass of the macromolecule is x 10^3 g mol ⁻¹ . Find the value of x . (Given R = 0.083 L bar K ⁻¹ mol ⁻¹ )

Step-by-step solution

Given: Osmotic pressure, = 0.083 bar Concentration, C = 10 M mol L ⁻¹ Temperature, T = 300 K Gas constant, R = 0.083 L bar K ⁻¹ mol ⁻¹ Using the formula for osmotic pressure: = CRT Substituting the given values: 0.083 = ( 10 M ) 0.083 300 Dividing both sides by 0.083 : 1 = 3000 M M = 3000 g mol ⁻¹ Comparing this with x 10^3 g mol ⁻¹ , we get: x = 3 Answer: 3