How much gas is released given partial pressure

[disneychannel]

Homework Statement

The solubility of N₂ in blood at 37 degree and at a partial pressure of 0.8 atm is 5.6 x 10^-4 mol/L?
a deep sea diver breathes compressed air with the partial pressure of N₂ equal to 4 atm. Assume that the total volume of blood in the body is 5 L. Calculate the amount of N₂ gas released (in liters at 37 degree and 1 atm) when the diver returns to the surface of water, where the partial pressure of N₂ is 0.8 atm2. The attempt at a solution

I got the answer of 0.389, but someone told me it is 0.35. Is my answer correct?

 

[Borek]

I got even different value. Please show how you got your result.

 

[disneychannel]

Thanks, the answer is 0.385

 

[Borek]

No!

At the surface amount of dissolved nitrogen is 5 L * 5.6x10^-4 mol/L = 2.78x10^-3 mol.

Under water pressure of the nitrogen is five times larger, so the amount of dissolved gas is also five times larger - that means 5 * 2.78x10^-3 mol = 0.0139 mol.

0.0139 moles of gas at given conditions (1 atm, 37°C) occupies 0.356 L - but it is not the correct answer! That would be the correct answer if all gas were released, but nitrogen dissolves in blood even on the surface. We have already calculated how much will be left dissolved, we have to take it into account.

Correct answer is below 0.3L.