Jul 21 2009

## A mole of me!

I’ve just made an awesome discovery! I was having a surf and came across this page detailing the chemical composition of the human body broken down by element. This is an awesome, awesome thing because armed with that page, knowledge of my own body mass, and a periodic table, I can calculate my own atomic mass, and therefore how much one Mole of me would weigh!

So – here goes. At the gym this morning, the scales told me I was 67.4 kilograms. Ok, so that’s not hugely accurate, given I’m going to be working with atomic weights, but it’ll do. The table on the web site, sadly, doesn’t show each element as a percentage, but rather as an amount of kilograms based on a 70kg man. As I’m slightly less than this, I need to adjust each of the figures down by 3.714% (so *nearly* pi!). I’m obviously far too lazy to do it by hand, so I’ve put together a little spreadsheet (linked at the bottom of this page) which will allow you to put in a number and it’ll work out the weights for you.

So, now equipped with the knowledge of how much of my body mass is composed of each element, I need to work out what percentage of my body mass each element comprises – another column added to the spreadsheet. Summing this column gives me a total of 104% which is a little high an error margin. Given that the original page provides a total of 70.1kg for a 70kg man, I’m inclined to believe the error comes from a combination of rounding errors in the orginal source as well as precision errors in my calculations. Given I’m calculating to a precision of 14 decimal places, 4% does seem a little high, but hey – it’s lunchtime.

Anyway, now I know what percentage of my body is composed of which element, it’s time to put in a column for the number of molecules in each percentage. For example, 63.7982195845697000% of my body is Oxygen, with an atomic weight of 15.9990. One Mole is the atomic weight expressed in grams – in this case, 15.9990 grams. Conveniently, one Mole contains Avogadro’s number of atoms (we’re dealing in elements here, not compounds) and works out to a neat 6.022 x 10^23. So, by working out how many Moles of each element are in the percentage of my body mass comprised of that element, I can tell how many atoms of that element there are. More or less 🙂 So my next column is simply the amount of mass comprised of that element divided by the atomic weight expressed in kilograms.

Almost there! I now know how many moles of each element there are. Now I’m ready to work out how many atoms of each molecule there are, and out of the bottom will drop the number of atoms that make me! So – my number of moles column x Avogadro’s number will do the trick.

And is it happens, I have 6.14 x 10 ^ 27 atoms! WOOHOO! That’s LOADS!

But hang on – I still haven’t worked out how much a mole of me as a compound weighs. This isn’t so easy, because I’m not a compound but a collection of loads of compounds. So to actually calculate a single atomic weight for the whole of complex little me would effectively involve taking the atomic weight of each element, multiplying it by the number of atoms of that element and then adding them all together. Which would be a pretty vast number, really, and not a proper atomic weight. But just for completeness sake, it’s (drumroll please)

4.06 x 10 ^ 28

Ummmm. Suppose I should really get back to work now. If you want the spreadsheet, you can download it from: