20 g hemoglobin in a 1 L aqueous solution (A) at 300 K is separated from pure water by semi permeable membrane. At equilibrium the height of solution in a tube dipped in a solution (A) is found to be 80.0 mm higher than the tube dipped in water. The molar mass of hemoglobin is _______ kg mol ^ -1 . (Nearest integer) (Given : g = 10 m s ^ -2 , R = 8.3 kPa dm ^3 K ^ -1 mol ^ -1 , density of solution = 1000 kg m ^ -3 )
A. A
The osmotic pressure of the solution is balanced by the hydrostatic pressure of the liquid column. = g h Given: Density of solution, = 1000 kg m ^ -3 Acceleration due to gravity, g = 10 m s ^ -2 Height difference, h = 80.0 mm = 0.08 m = 1000 10 0.08 = 800 Pa = 0.8 kPa From the van 't Hoff equation for osmotic pressure: = C R T = n V R T Given: Volume of solution, V = 1 L = 1 dm ^3 Gas constant, R = 8.3 kPa dm ^3 K ^ -1 mol ^ -1 Temperature, T = 300 K Substituting the values: 0.8 = n 1 8.3 300 n = 0.8 2490 mol The mass of hemoglobin is w = 20 g = 0.02 kg . The molar mass M in kg mol ^ -1 is: M = w n = 0.02 0.8 2490 M = 0.02 2490 0.8 = 49.8 0.8 = 62.25 kg mol ^ -1 Rounding to the nearest integer, we get 62. Answer: 62
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