How much Oxygen is there for a person to survive in an air-tight enclosure?

Introduction:
Have you ever wondered how long a person could survive in a closed, air-tight space with the Oxygen that is available?
I have.
This relates to the other web page on Oxygen: "Is There Enough Oxygen in the Atmosphere?"
Some of the numbers I will use here are from that page.
If you don't want to go through the details of calculation, you will see the results in larger red print as you go down the page.

(1) How much Oxygen does an average person need in a day to live?
3 sources:
   
(a) According to NASA the average person needs 0.84 kg of O2 per day (day and night activity).

    (b) According to MadSci:  The amount of air breathed by an average adult varies from 6 Litre/minute (when at rest) to 50 Litre/minute after hard exercise.  So, at rest the amount of Oxygen absorbed by the blood in the lungs is 300 milliLitre/minute to 3,500 mL/minute.
            My Calculations for
a person at rest:  In 1 day the volume of O2 absorbed by a person at rest is 300mL/minute x 60 minute/hour x 24 h/day = 432,000 mL/day or 432 L/day.  Since the mass of 1 mole of O2 is 32 gram and 1 mole of any gas has a volume of 22.4 L, the number of mole/day is 432 L/day / 22.4 L/mole = 19.28 mole.  
The mass of O2 needed per day is then 19.28 mole x 32 gram/mole =
617 gram or 0.617 kg of Oxygen per day, which is less than the NASA figure.

            My Calculations for a person doing hard exercise all day In 1 day the volume of O2 absorbed by a person at rest is 3,500 mL/minute x 60 minute/hour x 24 h/day =5,040,000 mL/day or 5,040 L/day.  Since the mass of 1 mole of O2 is 32 gram and 1 mole of any gas has a volume of 22.4 L, the number of mole/day is 5,040 L/day / 22.4 L/mole = 225 mole.  
The mass of O2 needed per day is then 225 mole x 32 gram/mole =
7,200 gram or 7.2 kg of Oxygen per day, which is much more than the NASA figure.  This is an unrealistic figure because a person doesn't do hard exercise day and night, but it does give an upper limit to Oxygen consumption for the average person.

An aside:  About 5L of blood passes through your lungs every minute. Adult does from 12 to 18 breaths/minute.
According to Dr. Garfield Kirchner, neighbour, 'one does not breathe the entire lungs volume with every average breath, but only a small bit, I think around 500 ml -- called the tidal volume.  A yawn or a sigh will force one to breath more as will deep sleep'.  Lungs can hold up to 4 to 6 L -- called the Vital Capacity.
'Inspiratory reserve: the room for extra air beyond a normal tidal breath is about 3 L.
Expiratory reserve: the amount that can be forcefully expired beyond a normal tidal breath (exhalation) is 1.1 L.
Residual Volume: that which is left in the lungs after the most forceful exhalation is 1.2 L.'

Very roughly 5% of Volume of air is consumed in each breath (about 21% O2 in and about 16% O2 out).
CO2 output is another issue not covered here.

        (c) Body tissues need 14.7 L of Oxygen/hour.  So, in 1 day they need 14.7 L/h x 24h/day = 352.8 L/day.
This is 352.8 L/day/22.4L/mole  = 15.75 mole/day.
Which is 15.75 mole/day x 32 gram/mole = 504 gram/day or 0.504 kg/day of Oxygen.  This is the absolute minimum required.  This confirms we are in the right ball park.

We will use the 3 following figures:
0.617 kg for an average person at rest
0.84 kg for an average person going about his regular duties, including sleeping
 7.2 kg for an average person that does continuous heavy exercise day and night (just to make a comparison).

(2) How long would it take to use up all the O2 in 1 cubic metre (1 m3 of space at sea level)  -- this is not realistic, but what the heck -- see a more realistic situation in part (3) below

The volume in Litre (L) in cubic metre (m3)is:  1000L/m3.  
21 % of the atmosphere consists of O2 by volume.  So, 1000 L of air consists of 0.21 x 1000 L = 210 L of O2.
1 mole of any gas at STP has a volume of 22.4 L.  Therefore 210 L of O2 is 210L/22.4L/mole = 9.38 mole.
The mass of 9.38 mole of Oxygen is: 9.38 mole x 32 gram/mole = 300 gram or 0.3 kg.
How long would the 3 persons under different exercise modes last  in an air-tight enclosure of 1 m3 that has 0.3 kg of Oxygen?

   For a person at rest  For a person doing NASA 
 type activity
 For a person exercising hard all day
Oxygen needed
by 1 person/day
 0.617 kg/day  0.84 kg/day  7.2 kg/day
 Length of time 
needed to use all
the Oxygen in 1 m3
0.3 kg / 0.617 kg/day
= 0.48 day 
 0.3 kg / 0.84 kg/day
= 0.36 day
 0.3 kg / 7.2 kg/day
= 0.042 day

(3) According to psu.edu the lowest % Volume of O2 a person can survive at standard pressure is 
about 17.5%.  How long would it take to use up just the O2 in 1 m3 for life? [realistic]

The volume in Litre (L) in cubic metre (m3)is:  1000L/m3.  
21 % of the atmosphere consists of O2 by volume.  So, 1000 L of air consists of 0.21 x 1000 L = 210 L of O2.
If 17.5% of the atmosphere consists of O2 by volume, then 1000L of air would consist of 0.175 x 1000 L = 175 L of O2.
Useable Oxygen is therefore 210 L - 175 L = 35 L for a person.
1 mole of any gas at STP has a volume of 22.4 L.  Therefore 35 L of O2 is 35L/22.4L/mole = 1.6 mole.
The mass of 1.6 mole of Oxygen is: 1.6 mole x 32 gram/mole = 51 gram or 0.051 kg.
How long would the 3 persons under different exercise modes last  in an air-tight enclosure of 1 m3 that has 0.3 kg of Oxygen, but only .051 kg is useable?

   For a person at rest  For a person doing NASA 
 type activity
 For a person exercising hard all day
Oxygen needed
by 1 person/day
 0.617 kg/day  0.84 kg/day  7.2 kg/day
 Length of time 
needed to use all
the useable Oxygen
in 1 m3.
0.051 kg / 0.617 kg/day
= 0.083 day  or
 2 hours
 0.051 kg / 0.84 kg/day
= 0.061 day or
 1.5 hours
 0.051 kg / 7.2 kg/day
= 0.0071 day or
 10 minutes

(4) What about other spaces such as rooms, houses, etc.?  How long would one person last?
We're assuming a completely enclosed place - no more Oxygen in or out.
We're also assuming 1 person.
We will use a conversion factor of 0.3 m/foot and a conversion factor of 0.09 m2/ft2

  Length of time before 
the Oxygen level drops 
to 17.5% of the air
   
   For a person at rest  For a person doing NASA 
 type activity
For a person exercising hard all day
  Room 
12 ft wide x 12 ft long x 8 ft ceiling
 3.6 m x 3.6 m x 2.4 m = 31.1m3
 31.1 m3 x 0.083 day/m3
 = 2.6 days
 31.1 m3 x 0.061 day/m3
 = 1.9 days
 31.1 m3 x 0.0071 day/m3
 = 0.22 days or 5.3 h
 House 
 1500 square feet x 8 ft ceiling
 135 m2 x 2.4 m = 324 m3
 324 m3 x 0.083 day/m3
 = 27 days
 324 m3 x 0.061 day/m3
 = 19.8 days
324 m3 x 0.0071 day/m3
 = 2.3 days

CO2 build-up would also happen.

O. Hooge, B.C. Canada
tfrisen@shaw.ca
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