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

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In summary, the conversation discusses the use of a mixture of O2 and He for scuba diving in order to prevent the condition known as "the bends". It also involves calculating the time it would take for the gas in a 5.0L tank to run out, based on the average human breathing rate and volume of each breath. The calculated time is 8.2 minutes, or 8 minutes when rounded to significant figures.
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teleport
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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.
 
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  • #2
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.
 
  • #3


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.
 

1. How do you calculate the duration of a scuba diver's O2 and He mixture?

The duration of a scuba diver's O2 and He mixture can be calculated by multiplying the tank capacity (in cubic feet) by the pressure (in atmospheres) and dividing that by the breathing rate (in cubic feet per minute). This will give you the total time in minutes that the mixture will last.

2. What is the typical tank capacity for a scuba diver's O2 and He mixture?

The typical tank capacity for a scuba diver's O2 and He mixture is around 80 cubic feet. However, this can vary depending on the size and type of tank being used.

3. What is considered a safe pressure for a scuba diver's O2 and He mixture?

A safe pressure for a scuba diver's O2 and He mixture is typically around 2000-3000 psi (pounds per square inch). This ensures that there is enough air for the duration of the dive and allows for a safe ascent to the surface.

4. How does the breathing rate affect the duration of a scuba diver's O2 and He mixture?

The breathing rate directly affects the duration of a scuba diver's O2 and He mixture. The higher the breathing rate, the faster the mixture will be depleted. It is important for divers to maintain a steady and controlled breathing rate to conserve their air supply.

5. Are there any other factors that can affect the duration of a scuba diver's O2 and He mixture?

Aside from tank capacity, pressure, and breathing rate, other factors that can affect the duration of a scuba diver's O2 and He mixture include depth, water temperature, and physical exertion. Deeper dives and colder water temperatures can cause the mixture to be used up faster, while physical exertion can increase the breathing rate and deplete the mixture quicker.

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