**Is there enough Oxygen in the atmosphere?**

**Introduction:**

Have you ever wondered if there is enough
Oxygen in our relatively tiny atmosphere to run all our cars, planes, and so on?

Oxygen is burned (and therefore taken out of our atmosphere) in these cars,
planes, trains, fires in prodigious amounts. Will there be a concentrated
enough amount of Oxygen for us, other animals and plants to breath comfortably
for long?

I've wondered about this.

What about all the Carbon Dioxide that results from this burning? Only
about 0.03% of the atmosphere consists of Carbon Dioxide -- a Greenhouse
gas. How much is being added to the atmosphere each year?

What about burning Natural Gas for heating, generating electricity?

So the following are some calculations to check on this.

**Calculations:
**The following calculations are only
for the world's Gasoline (Petrol in England) consumption.

We are

(1) What is the total mass of the atmosphere?

(a) Calculate the surface area of the
Earth:

Area of a sphere = 4 x Pi x Radius^{2},
Radius^{2} means Radius Squared.

The Radius of the Earth is 6.37 x 10^{6} m

Area of the Earth = 4 x Pi x ( 6.37 x 10^{6}m)^{2}

= 5.099 x 10^{14 }m^{2 }(5.1 x 10^{14 }m^{2})^{
}(This agrees with E. Kossina's calculations.)

Area of the Oceans is 3.61 x 10^{14} m^{2
}Area of the Continents is 1.49 x 10^{14 }m^{2
}Mean Height of the Continents is 875 m

Fraction of Earth's Surface that consists of Continents is 1.49/3.61 = 0.292

Mean Height above Sea Level of both Continents and Oceans is 0.292 x 875m = 256 m

Atmospheric Pressure at Sea Level is 101.325 KPa (kiloPascal) or 101,325 N/m^{2}
(Newton/metre^{2)}

At 256 m elevation the atmospheric pressure is less, 0.97039 times the pressure
at sea level.

0.97039 x 101,325N/m^{2 }

= 98,325 N/m^{2}

Total Force of the atmosphere on Earth's surface is 98,325N/m^{2}
x 5.10 x10^{14}m^{2}

= 5.02 x 10^{19 }N

Equivalent mass of atmosphere: F=mg ---> m=F/g ---> m =
5.02 x 10^{19}N / 9.8N/kg

**
m = 5.12 x 10 ^{18 }kg**

(This agrees closely with 5.14 x 10

(2) How much Volume and Mass of Oxygen is in the Atmosphere?

Gas | % of Atmospheric Molecules | Molecular Mass (amu) | % times Molecular Mass |

Nitrogen (N_{2}) |
78.09 | 28 | 2186.52 |

Oxygen (O_{2}) |
20.95 | 32 | 670.4 |

Argon (Ar) | 0.93 | 40 | 37.2 |

Carbon Dioxide (CO_{2}) |
0.03 | 44 | 1.32 |

Total | 2895.44 |

Fraction of atmosphere consisting of Oxygen by mass: 670.4 / 2895.44

= 0.23153 or 0.23

The volume of 1 mole of any gas is 22.4 L at STP.

**Mass of Oxygen (O _{2}) in the atmosphere is**:
0.23 x (5.12 x 10

This is in the right "ball park". The estimate in the Handbook is 1.5 x 10

1 mole of O

Number of moles of O

**(3) How many Litre of O _{2} are used when 1
Litre of gasoline is burned (assuming 100% efficiency)?**

Gasoline consists of C_{8}H_{18}, that is each molecule
of Gasoline consists of 8 Carbon and 18 Hydrogen atoms.

Every 2 molecules of gasoline needs 25 molecules of Oxygen and gives off 16
molecules of Carbon Dioxide and 18 molecules of water:

2C_{8}H_{18} + 25O_{2} --> 16CO_{2}
+ 18H_{2}O

or

C_{8}H_{18} + 12.5O_{2} --> 8CO_{2}
+ 9H_{2}O

So, 1 mole of gasoline needs 12.5 mole of Oxygen.

1 mole of gasoline (C_{8}H_{18}) has a mass of 8 x 12 + 18 x
1 = 114 gram

An aside: 12.5 mole of O_{2} has a mass of 12.5 x 32 = 400 gram

Density of gasoline is 0.75 g/mL (gram/milliLitre)

Using Density = Mass/Volume, therefore Volume = Mass/ Density, the Volume of 1
mole of gasoline is: 114g / 0.75g/mL = 152 mL

So, the number of mole in **1 Litre of liquid gasoline is**:
1L/0.152L/mole = **6.6 mole**

1 mole (152 mL) of liquid gasoline uses 12.5mole of O_{2} gas.
Therefore 1L of gasoline uses 12.5L/mole of O_{2} x 6.6mole = 82.5
mole of O_{2}.

**The Volume of 82.5mole of O _{2} is**:
82.5mole x 22.4L/mole =

**An Alternate method for the above calculation:
**The Volume of 12.5 mole of Oxygen is 12.5mole x 22.4 L/mole is: 280 L
of Oxygen.

**1L** of liquid gasoline uses 6.6 times as
much Oxygen as **1 mole** of gasoline would use.

Therefore, 6.6 x 280 L of Oxygen is: 1848 L of Oxygen.

Each Litre of gasoline uses 1848 L of Oxygen.

**(4) How much gasoline is used by the World
in one year?**

Stats from earthtrends.wri.org: For 1997 the
population of the Earth was: 5,821,127,100. For 2004 it is: 6,364,315,000,
an increase of 9.3%.

The amount of gasoline used in the world per capita in 1997 was: 161.4 L/y.

In comparison North America 1997 per capita consumption of gasoline was: 1519.8
L/y.

Therefore the total gasoline consumption in
the world for 1997 was: 161.4L/person/year x 5,821,127,100person = 9.395 x 10^{11
}L/y

Total amount of O_{2} used in burning this amount of gasoline is: 1848L of O_{2}/L
of gasoline x 9.395 x 10^{11}L of gasoline/y

= **1.7
x 10 ^{15 }L of O_{2} per year for the whole world.**

**(5) How many years at this rate of burning
will all the O _{2} in the atmosphere be used?**

To use all the O_{2} would require:
8.4 x 10^{20}L/1.7 x 10^{15}L/y = 494,118 years or rounded off to **about
500,000 years.**

There would be no Oxygen left, none even to breath. BUT, this is a long,
long time!

How long would it take to decrease the Oxygen
from 20.95% of the atmosphere to 19.95% of the atmosphere?

1% x
494,118y/20.95% = 23,585 y or **about
24,000 years.**

**In terms of a human's lifetime this seems like a long, long
time.
Remember we are NOT considering the burning of any other fossil fuel or wood or
anything that needs Oxygen.**

**(6) What about Carbon Dioxide, a greenhouse
gas?
How much does it increase with the burning of gasoline alone?**

1 mole of gasoline produces 8 mole of Carbon
Dioxide (CO_{2}).

There are 6.6 mole of gasoline in 1 L.

So, for every Litre of gasoline burned produces 6.6 mole of gasoline x 8mole of
CO_{2}/mole of gasoline = 52.8 mole of CO_{2}.

Volume of CO_{2} gas given off when burning 1 L of gasoline is: 52.8mole
x 22.4L/mole = 1164.8 L

The fraction of the atmosphere by mass that is
CO_{2} is: 1.32/2895.44 = 0.00046 or 4.6 x 10^{-4}

Mass of CO_{2} in the atmosphere: 4.6 x 10^{-4} x 5.12 x 10^{18}kg
= 2.355 x 10^{15 }kg (or 2.4 x 10^{15}kg)

1 mole of CO_{2} has a mass of 0.044 kg.

Number of moles of CO_{2} in the atmosphere is: 2.4 x 10^{15}kg/0.044kg/mole
= 5.5 x 10^{16} mole

Number of Litre of CO_{2} in atmosphere is: 5.5 x 10^{16}mole x
22.4L/mole = 1.23 x 10^{18} L.

From earlier, the volume of gasoline used
worldwide (1997) in one year was 9.395 x 10^{11} L/y.

Total Amount of of CO_{2} produced is: 9.395 x 10^{11}L of
gasoline/y x 1164.8 L of CO_{2}/L of gasoline = 1.1 x 10^{15} L
of CO_{2}/y.

% increase in CO_{2} per year = 1.1 x
10^{15}/1.23 x 10^{18} x 100% = 0.089% or 8.9 x 10^{-4}

Total % increase in CO_{2} in one year is: 8.9 x 10^{-4} x 0.03 = 2.7
x 10^{-5}

So, in one year the Carbon Dioxide content of the atmosphere would change from 0.03% to 0.030027%.

To increase CO_{2} by a third: 1.23 x 10^{18}/3
= 4.1 x 10^{17}.

would take: 4.1 x 10^{17}/1.1 x 10^{15} = 372 years.

**Remember this is only due to burning
gasoline, NOT Natural gas, coal, diesel etc.**

**(7) What about Natural Gas?**

Natural Gas is 93% methane (CH_{4}).

When it burns, 1 Litre of methane uses 2 Litre of Oxygen and produces 1 Litre of
Carbon Dioxide. and 2 Litre of water:

CH_{4} + 2O_{2} --> CO_{2} + 2H_{2}O

You calculate!

**An e-mail from Brother John:**

I
looked at the above and after I did I felt relieved, I now don't really need
to get rid of my van and buy a horse for about another 500,000 years.

A reply:

More realistic is the 24,000 for a loss of Oxygen to about
20%. And 24,000years/% x 3% = 72,000 years, since you cannot
live below, say about 18% Oxygen. Over time humans and other animals
could evolve to survive at lower Oxygen concentrations.

But you have to divide this by about 5 to include all the
other fuels, so, back to about 15,000 years.

This is a long time for us, but geologically it is a very
short time (compared to modern humans, having existed about 60,000 years and
our immediate hominoid ancestor having lived about 4 million years, etc.).

Likely we will run out of any kind of fuel long before that
time, so there likely is no danger of running out of Oxygen for humans.

Not to worry, right? You and I won't be alive that
much longer:-)

Keep breathing,

Ord

O. Hooge, B.C. Canada

tfrisen@shaw.ca

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