Question

The freezing point of blood serum is about - 0.56 deg C. What is its osmotic pressure at 37 deg C?

Answer 1

Freezingpoint depression is given by:
ΔT = K_f·i·m
where
K_f cryoscopic constant of solvent K_f = 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 ·ρ_w
(at 37°C ρ_w = 994kg/m^³)

Solve freezing point equation for molality
m = ΔT/(K_f·i)

=>
c = [ΔT/( K_f·i)] · ρ_w

=>
π = i · [ΔT/( K_f·i) ] ·ρw · R · T = [ΔT/K_f] ·ρ_w · R · T = [0.56K / 1.86Kkg/mol ] · 994kg/m³ · 8.314472J/mol K · 310K = 771361.3 Pa = 7.613atm