The osmotic pressure ( ) of a polymer solution having a mass concentration of 20 g L ⁻¹ is measured at various temperatures ( T ). A plot of versus T yields a straight line with a slope of 4.15 10⁻⁵ atm K ⁻¹ . The molar mass of the polymer is ________ g mol ⁻¹ . (Given: R = 0.083 L atm K ⁻¹ mol ⁻¹ )

Step-by-step solution

The osmotic pressure is given by the formula: = C R T M where C is the mass concentration in g L ⁻¹ , R is the gas constant, T is the temperature, and M is the molar mass. For a plot of versus T , the slope is given by: Slope = C R M Given that the slope is 4.15 10⁻⁵ atm K ⁻¹ and C = 20 g L ⁻¹ : 4.15 10⁻⁵ = 20 0.083 M M = 1.66 4.15 10⁻⁵ M = 40000 g mol ⁻¹ Answer: 40000