what is the total volume of nitrogen gas dissolved in their blood when they are at 50.0 m depth?

Question

A SCUBA diver spends an hour working at a depth of 50.0 m where the pressure is 5.00 atm. Their blood gas concentration of nitrogen has time to fully equilibrate so that the concentration of nitrogen is given by Henry's Law. The Henry's Law constant for nitrogen in blood is 6.90 x 10^-4 M atm^-1.

 

Assuming they have a blood volume of 5.00 L, what is the total volume of nitrogen gas dissolved in their blood when they are at 50.0 m depth? The volume of nitrogen should be calculated at a pressure of 1.00 atm and a temperature of 20.0 C.

 

You can assume the temperature of the diver's blood is 37.0 C and that they are breathing compressed air with a composition of 78% N2, 21% O2, and 1% Ar (by volume) at a total pressure of 5.00 atm.

Answer 1

6.90x10^-4 M / atm x 5.00 atm = 3.45x10^-3 M = 3.45x10^-3 mols N₂ / L blood

total moles N₂ = 3.45x10^-3 mols N₂ / L blood x 5.00 L blood = 0.01725 mols N₂

Volume of N₂ @ 1.00 atm and 20ºC = nRT/P (from the ideal gas law)

Volume = (0.01725 mols)(0.0821 Latm/Kmol)(293K) / 1.00 atm

Volume N₂ = 0.415 L