Answer:
The amount of N₂ gas released is 0.4546 l.
Explanation:
The solubility of gas is proportional to the partial pressure of the gas. Thus:
[tex]\frac{c_1}{P_1}= \frac{c_2}{P_2}\\c_2=\frac{c_1 \times P_2}{P_1}\\c_2=\frac{5.6 \times10^{-4} \frac{mol}{l} \times 4.1 atm}{0.8 atm}\\c_2= 2.87\times 10^{-3} \frac{mol}{l}[/tex]
The nitrogen concentration in the surfacing divers blood decreases by:
[tex]\Delta c=c_2 - c_1= 2.87\times 10^{-3} \frac{mol}{l} - 5.6 \times10^{-4} \frac{mol}{l}= 2.31\times10^{-3} \frac{mol}{l}[/tex]
The amount of nitrogen released is given by the multiplication of Δc and volume of blood in human body:
[tex]n= \Delta c \times V_{blood}=2.31\times10^{-3} \frac{mol}{l} \times 6.2l=0.0143 mol[/tex]
Using ideal gas law we can calculate the volume at 0.8 atm and 37°C (310.15K):
[tex]PV=nRT\\0.8 atm \times V=0.0143 mol \times 0.082\frac{l . atm}{mol.K} \times 310.15 K\\V=\frac{0.0143 mol \times 0.082\frac{l . atm}{mol.K} \times 310.15 K}{0.8 atm}\\V=0.4546 l[/tex]
