Question

When scuba diving, it is important to come back to the surface of the water from deep dives slowly. If this does not happen, then the diver can get the “bends”. Using the information provided below, determine the moles of N₂ and O₂ dissolved in 7.5 L of blood at 298 K at a depth of 100.0 feet below the surface of the water and at the surface of the ocean. If the diver were to suddenly return to the surface, how many moles of N₂ and O₂ would “undissolve” from the blood (assume no loss of gas molecules from the system)? What volume would this amount of N₂ and O₂ occupy at the surface of the ocean? What would happen to a human if that volume of N₂ and O₂ were not expelled through the lungs? Based on your answers, explain why returning to the surface of the ocean after a deep dive is so important, and what the “bends” is. (Henry’s Law constants at 25°C K(O₂) = 4.40×10⁹ Pa, K(N₂) = 8.68×10⁹ Pa.)

Answer 1

a) Partial pressure of gas = mole fraction X total pressure

pN2= 0.79 x 1bar = 0.79 bar

Now henry's law constant for nitrogen in water = 9.04 x10⁴ bar

Mole fraction of nitrogen in blood = Partial pressure / Henry's constant = 0.79 / 9.04 X 10^4 = 8.73 X 10^-6

Moles of nitrogen in blood = Mole fraction of nitrogen in blood X total moles of water and nitrogen

Moles of water = Volume x density / molecular weight = 7.5 X 1 X 1000 / 18 = 420

Moles of nitrogen in blood = 8.73 X 10^-6 X 420 = 3.67 X 10^-3

b) pO2 = 0.21 X 1 bar = 0.21 bar

Now henry's law constant for oxygen in water = 4.3×10⁴ bar

Mole fraction of O2 in blood = Partial pressure / Henry's constant = 0.21/ 4.3 X 10^4 = 4.88 X 10^-6

Moles of O2 in blood = Mole fraction of O2 in blood X total moles of water and O2

Moles of water = Volume x density / molecular weight = 7.5 X 1 X 1000 / 18 = 420

Moles of O2 in blood = 4.88 X 10^-6 X 420 = 2.049 X 10^-3