7) A human with a body weight of 70 kg has a blood volume of 5.00 liter. The Hen

Question

7) A human with a body weight of 70 kg has a blood volume of 5.00 liter. The Henry's Law constant for the solubility of N2 in blood is 9.04 x 104 Pa at 298 K. The density of blood is about the same as that of water

a) How many moles of nitrogen are absorbed in the blood of this human in air if the composition of the air is 80% N2 at sea level where the pressure is one bar.

b) Assume that the human is a diver who dove to a depth below sea level where the pressure was 50 bar and stayed there for a period, breathing air at that pressure. Now he suddenly rises to the surface. What of volume of N2 in gas form is released in the blood of the diver in the form of gas bubbles?

(The symptoms of arterial blocks induced by the bubbles are known among divers as the bends. They are severe and can cause death or disability.)

Explanation / Answer

A/C Henery law[this is for solute]

Pi= K xi where

Pi=vapour pressure of component i in solution

K= Henery's constant

xi= mole fraction of component i

K=9.04x10^4 pa=0.904 bar

partial pressure of N2 = PN2= Ptotal x fraction of N2 in air= 1x0.8= 0.8bar

PN2 =K X xN2

xN2= mole fraction of N2 in blood =PN2 / K =0.8 / 0.904=0.885

mole fraction of N2= mole of N2 / mole of H2O + mole of N2

nN2= xN2 ( nH2O + nN2) = xN2 X nH2O

nN2= 0.885 x( 5 L x 1 KgL^-1/18x10^-3 Kg mol^-1) = 2.5x10^2 mole

b-when P=50 partial pressure of N2= 50x.8=40bar

mole fraction of N2= 40/0.904=44.25

mole of N2 in blood=44.25 x0.28x10^3=12.39x10^3 mole

V= nRT/P=12.39x10^3x298 x8.314x10^-5/1=306.97 m^3

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