Fact checking "I fucking love science"

I saw this in my timeline:

As with all such things, I thought: "Is that true?" Being a sceptic doesn't mean reserving your scepticism to alternative medicine, religion and superstition etc. It means, at least as far as I see it, questioning everything - from advertsing claims to random internet forwards.

Granted, I can't help escape certain biases of my brain, but I do my best. Often, I can't find out if something is true or not, as I don't have the time. Fortunately though, it's the summer holidays, so I have the time (though I really should be cleaning the kitchen) to find out. So, with some rough and ready back of the envelope calculations, let's see how valid the above is!

These are useful to see if you're in the right sort of area with right or wrong, but, as I expect we will see, aren't terrifically accurate. I'm blogging as I do the calculations...

First bullet point: For this I also wondered "Support two humans, for how long?"

We'll assume a single tree does absorb 22.7kg/year of carbon dioxide. Why? Well, what's a standard tree? Hard to define. So we'll give them that.

The simple equation for photosynthesis (how a plant turns carbon dioxide into sugar, so it can grow etc) is:

carbon dioxide  +   water  ------- >  glucose  +   oxygen

It takes six molecules of carbon dioxide and six molecules of water to make one molecule of glucose and six molecules of oxygen. (I'd add the chemical symbol formula, but can't see how to do subscripts).

So for every carbon dioxide molecule absorbed, one molecule of oxygen is released.

If it absorbs 22.7kg of carbon dioxide, then it must release 16.51kg of oxygen in that time. This is because the relative atomic mass of carbon dioxide is 44, and for oxygen 32.

32/44*22.7 = 16.51

So, in a year, a tree will release 16.51kg of oxygen.

How much oxygen do we need each year?

At rest, humans need to breathe in about 5 - 8 litres of air a minute. It can increase to 40 - 60 litres of air during exercise. Let's just assume we have a sedentary person who's always at rest.

So, in a day, our hypothetical person needs 7,200 to 11,520 litres of air, if they stay entirely at rest.

One litre of air is about 21% oxygen, and in total weighs about 1.286g (at standard atmospheric pressure). So one litre of air contains 0.286g of oxygen.

So that means, in a day, someone at rest needs 2.05 to 3.29kg of oxygen a day.

So 16.51kg of oxygen in a year provides 8.05 to 5.01 man days of oxygen.

So, in a year, if two people stayed entirely at rest, a mature tree will provide enough oxygen to keep them going for at least two and a bit days.

Second bullet point:

The average car release 149g/km of carbon dioxide.

So it's saying an acre of tree consumes 149*41483 = 6181kg of carbon dioxide.

This means it will release 4495kg of oxygen.

We know (from above) that 16.51 kg of oxygen is, at best enough to keep one person going for eight days. So about 2kg of oxygen is about one man day.

So 4495kg of oxygen is enough for about 2192 man days of oxygen.

If we divide that by 18, that's 121.8 days. So actually, according to their figures, one acre is enough to keep 18 people going for about 3 months at best.

So that second bullet point isn't true, given the figures they've used. Remember, these calculations aren't the most accurate, but we are not even close to having an acre of trees produce enough oxygen for 18 people to live for a year. And that's even if those 18 people sat around doing nothing - not even planting more trees!

Of course, I have made the assumption that one acre of trees does indeed take up the amount of carbon dioxide released by a car that's travelled 26,000 miles.

Third bullet point: We're not told how long the tree takes to produce the oxygen. So, it's got to be true, assuming the tree doesn't die.

So, why have I just gone ahead an gone sceptic on a Facebook post that's not doing any harm, and is promoting a good message (I am a big fan of trees and plants in general!)?

Trees are important - but they're important enough that we don't have to make stuff up.

It's not as if the real figures are hard to find, this report took me 3 minutes to find using google:

Arboriculture & Urban Forestry 2007. 33(3):220–226.
Oxygen Production by Urban Trees in the United States
David J. Nowak, Robert Hoehn, and Daniel E. Crane

"A commonly cited statement is an acre of trees (100% tree canopy) can provide enough
oxygen for 18 people (e.g., American Forests 2006; TreePeople 2006), but based on this study, this estimate appears to be high by at least a factor of two. The number is more on the order of eight people per acre of tree cover (100% tree canopy)."

Trees are important, but let's make sure people know how important they really are.


UPDATE: It's been pointed out this post makes it look like I'm underselling plants. Which is a bad thing to do, let's not forget they (in no particular order, and by no means complete):

Act as carbon sinks; provide habitats for wildlife; hold soil together and help prevent erosion; provide sustainable building materials; can help clear areas of pollutants and contaminants; reduce stress.

My take home message, which I didn't make clear is that: when you have something awesome, you don't need to oversell it or make stuff up to extol its virtues.

UPDATE 2: Another thing I should have mentioned: When we breath in, we don't actually use all of the oxygen inhaled. As has been pointed out below, exhaled air is 16% oxygen, whereas inhaled air is 21% oxygen. So we're only using about 23.8% of the oxygen we breath in. So, this obviously affects the calculations. One should expect the answer to the first bullet point to be four times higher. But it is not.

"If oxygen levels are below 16% at atmospheric pressure most people faint due to hypoxia. If oxygen levels fall below 11% individuals may die by suffocation. The amount of oxygen in the air depends on its partial pressure - inhaling pressurized gas while scuba diving which is below 16% oxygen does not cause hypoxia (because the air is pressurized)."

So actually, we can only use about half of the oxygen we breath in. So this would double the man days of oxygen. Of course, this then also assumes that the trees and our people are in a sealed environment - otherwise we could talk about all the oxygen being used, and another source of oxygen to supply that which is used in the body, but which is needed so the lungs can function. But then it all starts to get more complicated, and, as I said at the start,  these were just back of the envelope calculations, I didn't want to get bogged down - it was just to see if we were in the right ball park figure. And we weren't.

Given I was being quite liberal with the assumption that the people are entirely at rest, I was happy to just leave out this line of thinking as it seemed to complicated things, but I guess I was wrong.