Question

A scuba diver is at a depth of 385 m, where the pressure is 39.5 atm. What should be the mole fraction of O2 in the gas mixture the diver breathes in order to have the same partial pressure of oxygen in his lungs as he would at sea level? Note that the mole fraction of oxygen at sea level is 0.209.

Answer 1

Partial pressure of gas that part of gaseous mixture depend on the mle fraction of the said gas and on the total pressure of the mixture ( Dalton law of Partial Pressures )

we know that at a depth of 385m the total pressure is 39.5 atm

According to dalton law od partial pressures we can write [ Pi = X i. Ptotal ]

P(O2 355m) = X ( O2 355m ) * 39.5

at sea level total pressure of atmosphere is eqal to 1atm and mole fraction of O2 is 0.209

this means at sea level we have

P(O2 sea level) = 0.209 * 1atm

since the partial pressure of oxygen gas at sea level must equal to partial pressure at a depth of 355m

0.209* 1.00atm = X ( O2 355m ) * 39.5

X ( O2 355m ) = 0.209/39.5

X ( O2 355m ) = 0.00529.