How Is Oxygen Partial Pressure Maintained in Deep Sea Diving?

[clipperdude21]

1. A deep sea diver has descended a distance of 50m below the ocean surface. Asummer that he is supplied with air from the survace.
a) what is oxygen partial pressure in the lungs of the diver at this depth.
b) suppose we want the oxygen partial pressure in the lungs of the diver at this depth to be the same as that at the surface. This can be done by providing the diver with a mixutre of helium and air. Use Dalton;s Law to compute the proper mixing ratio in moles between helium and air and explain the mechanism.

Homework Equations

3. (a) I got this right I am pretty sure. I just did P=patm + pgh and got 605,700. Then multiplied it by 0.21 since oxygen is 21% of air and got 127,197 Pa.
(b) I couldn't do this one!

 

[Astronuc]

It would be helpful if one showed the steps and units.

for part b. at the surface the pressure of air is 1 atm, 14.7 psia, or 101325 Pa, of which ~0.21 is oxygen.

What is the mixture of He/O2 such that the oxygen partial pressure is the same as the surface pressure when the diver is 50 m below the surface?

 

[ogb p]

Great job on part (a)! Your calculation for the oxygen partial pressure in the lungs of the diver at 50m depth is correct. As for part (b), we can use Dalton's Law to calculate the proper mixing ratio of helium and air to achieve the same oxygen partial pressure at this depth as at the surface.

Dalton's Law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas in the mixture. This means that the total pressure in the lungs of the diver must be the same as at the surface, but with a different composition of gases.

To calculate the mixing ratio, we can use the equation Ptotal = P1 + P2, where Ptotal is the total pressure, P1 is the partial pressure of helium, and P2 is the partial pressure of air. We know that the total pressure at the surface is 101,325 Pa and the partial pressure of oxygen in air is 21% of that, or 21,325 Pa. We also know that the total pressure at 50m depth is 605,700 Pa, and we calculated the partial pressure of oxygen to be 127,197 Pa in part (a). Therefore, we can set up the following equation:

101,325 = P1 + 0.21P2
605,700 = P1 + P2

Solving for P1 and P2, we get P1 = 44,594 Pa and P2 = 560,106 Pa. This means that the proper mixing ratio of helium to air is 44,594:560,106, or approximately 1:12.5 in moles. This means that for every 1 mole of helium, there should be 12.5 moles of air in the mixture.

The reason for using helium is that it is less dense than air, which means it takes up less space in the lungs and allows for easier breathing at depth. This is because at depth, the pressure increases and gases become more compressed. By using a mixture of helium and air, we can achieve the same oxygen partial pressure in the lungs of the diver as at the surface, while also reducing the risk of nitrogen narcosis and decompression sickness.