Workers in underwater diving suits necessarily breathe air at greater than norma

Question

Workers in underwater diving suits necessarily breathe air at greater than normal pressure. If they are returned to the surface too rapidly, N_2, dissolved in their blood at the previously higher pressure, comes out of solution and may cause emboli (gas bubbles in the bloodstream), bends, and decompression sickness. Blood at 37degree C and 1 bar pressure dissolves 1.3 mL of N_2 gas (measured for pure N_2 at 37degree C and 1 bar) in 100 mL of blood. Calculate the volume of N2 likely to be liberated from the blood of a diver returned to 1 bar pressure after prolonged exposure to air pressure at 300 m of water (below the surface). The total blood volume of the average adult is 4.7 L; air contains 78 vol% N2.

Explanation / Answer

Solubility of N2 = 1.3mL/100 of blood = 1.3mL/22400mL per 100mL=5.8 *10^-5 moles/100mL = 5.8 *10^-4 moles/L

Inside sea water, pressure increases 1atm per 10 meter of the depth. So, pressure at 300m is 30 atm.

30 atm = 30.39 bar.

So the solubility of nitrogen in blood at 4atm partial pressure is =30.39 bar/1bar * 5.8 *10^-4 moles/L = 176.26*10^-4 moles/L

So the amount of excess nitrogen is = (176.26*10^-4- 5.8 *10^-4) = 170.46 *10^-4 moles/L

total amount of excess N2 in 4.7 L blood = 170.46 *10^-4 moles/L *4.7L =0.0801moles

considering air contains 78 % of N2 = 0.0801 mL *78/100 = 0.0625 moles

Use ideal gas equation to convert it to 1 bar and 370C.

PV = nRT

V = nRT/P = 0.0625 moles * 0.082 latm/K/mol * 310 K/1 atm = 1.58 L

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