The freezing point of blood serum is about - 0.56 deg C. What is its osmotic pressure at 37 deg C?
Freezingpoint depression is given by: ΔT = Kf·i·m where Kf cryoscopic constant of solvent Kf = 1.86Kkg/mol i van't Hoff factor of solute. m Molality = mole solute / kg solvent
Osmotic pressurie point depression is given by: π = i·c·R·T where i van't Hoff factor of solute. c Molarity = mole solute / m³ solution R universal gas constant T absolute temperature in K
Assume that 1. van't Hoff factors does not change between -0.56°C and 37°C 2. volumes of solution is equal to the volumes of solvent contained of solution.
Then you can calculate the molarity from multiplying by pure water density. c = m ·ρw (at 37°C ρw = 994kg/m³)
Solve freezing point equation for molality m = ΔT/(Kf·i)
=> c = [ΔT/( Kf·i)] · ρw
=> π = i · [ΔT/( Kf·i) ] ·ρw · R · T = [ΔT/Kf] ·ρw · R · T = [0.56K / 1.86Kkg/mol ] · 994kg/m³ · 8.314472J/mol K · 310K = 771361.3 Pa = 7.613atm