How long could Earth's oxygen supply last if no new oxygen were produced?

Question

I read in an article or heard in some documentary that there's so much oxygen in the atmosphere that even if all photosynthesis stopped, there's already enough to last us a long time.

Is this correct? Why or why not? If so, how long is this 'long time', roughly? I've seen estimates between 15,000 to 150,000 years.

Answer 1

Disclaimer:

This is going to be a very mathematical answer. Before answering it, I assume that you are only asking about humans, assuming that all other organisms don't require $O_2$ to survive (as it will complicate the answer many many times).

List of variables:

V     = total volume of air on earth (in l)
V'    = total volume of oxygen on earth (in l)
V(1)  = volume of oxygen used by 1 person in whole lifetime (in l)
V(a)  = volume of oxygen used by whole mankind (one generation) in whole lifetime (in l)
V(p)  = percentage of total oxygen used by whole mankind (one generation) in whole lifetime

Method used:

$ \%\hspace{1mm}Volume\hspace{1mm}of\hspace{1mm}O_2\hspace{1mm}used\hspace{1mm}per\hspace{1mm}generation = \underline{\hspace{3mm}Volume\hspace{5mm}of\hspace{5mm}O_2\hspace{5mm}in\hspace{5mm}air\hspace{3mm}}\times\hspace{1mm}100$ $\hspace{83mm}Volume\hspace{1mm}of\hspace{1mm}O_2\hspace{1mm}used\hspace{1mm}by\hspace{1mm}humans$

$Number\hspace{1mm}of\hspace{1mm}years = \underline{\hspace{2mm}Number\hspace{1mm}of\hspace{1mm}years\hspace{1mm}in\hspace{1mm}1\hspace{1mm}generation\hspace{2mm}}$ $\hspace{42mm}\%\hspace{1mm}Volume\hspace{1mm}of\hspace{1mm}O_2\hspace{1mm}used\hspace{1mm}per\hspace{1mm}generation$

Procedure:

Lets first find out the total amount of air on earth.

From this:

The air sphere measures 1999 kilometres across and weighs 5140 trillion tonnes.

From here:

At sea level and at 15 °C air has a density of approximately 1.225 kg/m3

Total volume of air:

$volume = mass \hspace{1mm} / \hspace{1mm} density$

$V = 5140 \times 10^{12} \hspace{1mm} tonnes \hspace{1mm} / \hspace{1mm} 1.225 \hspace{1mm} kg.m^{-3}$

$V = 4195.9 \times 10^3 \times 10^{12} \hspace{1mm} m^3$

$V = 4195.9 \times 10^3 \times 10^{12} \times 10^3 \hspace{1mm} l$

$V = 4195.9 \times 10^{18} \hspace{1mm} l$

Now, from this, 20.95% of this is $O_2$ i.e.

$V' = 4195.9 \times 10^{18} \times 20.95 / 100$

$V' = 87904.489 \times 10^{16}$

$V' = 879.04 \times 10^{18} \hspace{1mm} l$

Moving on to next part, from this:

a human being uses about 550 liters of pure oxygen per day.

From this:

71 years was the average life expectancy at birth of the global population in 2013.

$V_1 = 550 \hspace{1mm} l.day^{-1}.person^{-1} \times 25915 \hspace{1mm} days$

$V_1= 142.53 \times 10^5 \hspace{1mm} l.person^{-1}$

From this:

The world population (the total number of living humans on Earth) was 7.349 billion as of July 1, 2015.

So

$V_{a} = 142.53 \times 10^5 \hspace{1mm} l.person^{-1} \times 7.349 \times 10^9 people$

$V_{a} = 1047.452 \times 10^{14} \hspace{1mm} l$

Finally

$V_p = V_a / V' \times 100$

$V_p = (1047.452 \times 10^{14}) / (879.04 \times 10^{18}) \times 100$

$V_p = 1.191 \times 10^{-2}$

$V_p = 0.0191 \hspace{1mm} \% $

This gives the percentage of total $O_2$ in air used by one human generation. From this, we can find the number of years for which $O_2$ will last, as I have done below:

$25,915 \hspace{1mm} days = 71 \hspace{1mm} years$

$71 \hspace{1mm} years = 0.0191 \hspace{1mm} \%$

$1 \hspace{1mm} \% = 71 / 0.0191 \hspace{1mm} years$

$100 \hspace{1mm} \% = 3717.277 \times 100 \hspace{1mm} years$

$\hspace{13mm} = 371,727.748 \hspace{1mm} years$

Conclusion:

So, yes at least humans can live for a very long time without plants doing any photosynthesis (ideally). 371,727 years seems too large a period of time, but it is just based on ideal assumptions, this number would come down (maybe into your specified range) when more variables are added.

For example:

To show extent of deviation by addition of factors, I add a very general, but complex factor in the expression: air pollution.

How much $CO_2$ is released per year can be estimated from this:

In 2011, utility coal plants in the United States emitted a total of 1.7 billion tons of CO2

And with the contribution of countries like China, India, Europe, etc. that number should rise up to at least 2.5 million tonnes (its just that I couldn't find the worldwide data on it).

Now:

$1 \hspace{1mm} C + 1 \hspace{1mm} O_2 \rightarrow 1 \hspace{1mm} CO_2$

$2.5 \times 10^9 \hspace{1mm} kg \hspace{1mm} CO_2 \Rightarrow 2.5 \times 10^9 \hspace{1mm} kg \hspace{1mm} O_2$

So, 2.5 million tonnes more $O_2$ is being used each year from the environment. But, there is another twist in this. From this:

WHO reports that in 2012 around 7 million people died - one in eight of total global deaths – as a result of air pollution exposure.

It means that 7 million people less will consume $O_2$ each year i.e.

$Net \hspace{1mm} population = 7349 \times 10^6 - 7 \times 10^6$

$\hspace{32mm} = 7.342 \times 10^9$

$V_{a} = 142.53 \times 10^5 \times 7.342 \times 10^9$

$V_{a} = 1046.455 \times 10^{14} \hspace{1mm} l$

$V_p = V_a / V' \times 100$

$V_p = (1046.455 \times 10^{14}) / (879.04 \times 10^{18}) \times 100$

$V_p = 1.1904 \times 10^{-2}$

$V_p = 0.01904 \hspace{1mm} \% $

$25,915 \hspace{1mm} days = 71 \hspace{1mm} years$

$71 \hspace{1mm} years = 0.01904 \hspace{1mm} \%$

$1 \hspace{1mm} \% = 71 / 0.01904 \hspace{1mm} years$

$100 \hspace{1mm} \% = 3728.991 \times 100 \hspace{1mm} years$

$\hspace{13mm} = 372,899.159 \hspace{1mm} years$

So, overall number increases instead of decreasing. This example was just to show how adding more factors to the equation would deviate the overall answer, and how large that deviation can be.

Answer 2

The answer above gives a nice calculation how much oxygen there is, and how much we use. There are some BIG other factors that warrant a second answer IMO.

Starting at 371 thousand years (above).

• Animals: according to http://xkcd.com/1338/ (probably sourced somewhere reliable) humans make up only ~20% of the walking biomass, so we would burn through the oxygen supply 5 times faster.
• Fuels: my guess for an average fuel consumption would be around 5 metric tons per annum (http://data.worldbank.org/indicator/EN.ATM.CO2E.PC/countries, 17 metric tons of CO2 per annum for the USA, 1,7 for India). To get 5 tons of CO2 we need 3,6 tons of O2. From the above calculation I calculate that we use 245 kg per year of O2, so for our fuel we need 15 times more oxygen than for breathing.

That leaves us with around 5000 years to live. However, from http://www.engineeringtoolbox.com/co2-comfort-level-d_1024.html I guesstimate that above something like 1-5% CO2 is not survivable on the long term, leaving us with only 250-1250 years to leave before we slowly suffocate.

Of course we would die long before that from starvation.