Calculating How Long Scuba Divers' O2 and He Mixture Will Last

[teleport]

Hi, I have been struggling a little with this question.

Scuba divers breathe a mixture of O2(g) and He(g) to avoid "the bends, a condition caused by nitrogen in the blood. If 65.0g O2(g) and 2.00g He(g) are placed in a 5.0L tank at 25oC, calculate:

If the average human takes 15 breaths per minute, and breathes in 0.50L at 1.00 atm, calculate how long the gas in the tank will last?

This is what I've done:

Pressure in the tank:

n(He) = (2.00 g He)/(4.00 g/mol) = 0.500 mol He

n(O2) = (65.0 g)/(32 .00 g/mol) = 2.03125 mol O2

n(total) = n(He) + n(O2) = 2.53125 mol

P(total) = (n(total)RT)/V = (2.53125)(0.082057)(298)/5.0
P(total) = 12.379 atm

time to empty:

P1V1 = P2V2
(1.00 atm)(0.50 L) = (12 atm)x,

where x is the volume breathed in one breath

x = 0.0416667 L

in one min: Vbreathed = 15x = 0.625 L

(1 min)/(0.625 L) = t/(5.0 L)

Therefore t = 8.0 min.

Is all that right or instead of using the total pressure in the tank I should use the partial pressure of O2? The answer should be 7.8 min which I'm not getting. But I have also tried it with O2 partial volume and I don't get the answer. Am I missing something? Any help is appreciated. Thanks.

 

[chemisttree]

Try calculating the number of moles of ideal gas per breath and applying that answer to the number of moles of He/O2 available.

I get 8.2 minutes... 8 minutes if significant figures are observed.

 

[Blueshift5]

I would say that your calculations and approach seem correct. However, it is important to consider the partial pressure of O2 in the tank, as this is the gas that is being consumed by the divers. The partial pressure of O2 can be calculated by multiplying the total pressure by the mole fraction of O2 in the tank. In this case, the mole fraction of O2 would be (2.03125 mol O2)/(2.53125 mol total) = 0.802, so the partial pressure of O2 would be (0.802)(12.379 atm) = 9.922 atm. Using this partial pressure in your calculations may give you a more accurate result. Additionally, it is always a good idea to double check your calculations and units to ensure accuracy. Overall, your approach seems sound and with some minor adjustments, you should be able to get the correct answer.