What is the difference in blood oxygen concentration between a person at sea level where the air pressure is 1.0 atm and the top of K2, where the total air pressure is 34.7 kPa?

Question

(You can assume the mole fraction of oxygen in air remains constant at 0.21 (or 21% of the total air pressure is oxygen), the temperature is 37 C, and that the solubility of oxygen in blood at 37 C is approximately 1.0 x 10^-3 mol/L-atm.)

Answer 1

Note: solubility of a gas is dependent on both the temperature and the pressure. The problem states the solubility of O₂ in blood at 37ºC is 1.0x10^-3 mol / Latm. This can be taken as Henry's constant for solubility of O₂ in blood.

Pressure of O₂ @ 1 atm = 1.0 atm x 0.21 = 0.21 atm

Pressure of O₂ @ 34.7 kPa = 43.7 kPa x 1 atm / 101.325 kPa x 0.21 = 0.0906 atm

Use Henry's Law:

C = kP

at 1 atm air pressure...

C = concentration of O₂ = ?

k = Henry's constant = 1.0x10^-3 mol / Latm

P = partial pressure of O₂ = 0.21 atm

C = (1.0x10^-3 mol / Latm)(0.21 atm)

C = 2.10x10^-4 mol / L

at 34.7 kPa air pressure...

C = (1.0x10^-3 mol / Latm)(0.0906 atm)

C = 9.06x10^-5 mol L