Estimation of the Freezing-Point Depression of Blood

Use the information in Illustration 11.5-4 on the osmotic pressure of an aqueous sodium chloride solution and blood to estimate the freezing point of blood.

Question

Estimation of the Freezing-Point Depression of Blood

Use the information in Illustration 11.5-4 on the osmotic pressure of an aqueous sodium chloride solution and blood to estimate the freezing point of blood.

Accepted Answer

To estimate the freezing point of blood, we will use the estimate of the osmotic pressure of blood at 25°C, 7.498 bar, computed in Illustration 11.5-4. While the freezing point of blood or the aqueous sodium chloride solution is not known, let us assume it is about the same as the freezing point of water, 273.15 K. The osmotic pressure of the sodium chloride solution at this temperature can be simply calculated from the value at 298.15 K by assuming the activity coefficient is independent of temperature, so that

[latex]\Pi(T=273.15 K )=\Pi(T=298.15 K ) imes \frac{273.15 K }{298.15 K }=6.869 bar[/latex]

Then

[latex]6.869 bar imes 10^{5} \frac{ Pa }{ bar } imes \frac{ kg }{ m s { }^{2} Pa }=\frac{6025 \frac{ J }{ mol } imes 1 \frac{ kg }{ s ^{2} m }}{18 imes 10^{-6} \frac{ m ^{3}}{ mol }} \frac{ T _{ f }}{(273.15 K )^{2}}\left(273.15- T _{ f } ight)[/latex]

which has the solution

[latex]T_{f}=272.481 K =-0.67^{\circ} C[/latex]

which is in good agreement with the experimental value of −0.52°C. Note also that the small amount of solute (0.9 wt % NaCl) results in a very large osmotic pressure, but a relatively small freezing-point depression.

Question 12.3.3: Estimation of the Freezing-Point Depression of Blood Use the...

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