Do we share molecules with Magellan?

There is a question that gives rise to a lot of debate which is “what are the odds that we breath, eat, drink molecules of matter that have gone through someone else before?”  Here is a correct approach to the question, but a little confusing the way it is presented.

The reasoning is quite simple: for example, water is an important part of anyone’s life.  So in the case of Magellan (pictured above) what are the chances for his water molecules (that he used in his life-time) to be found in a glass of water we drink, or a drop of rain from the sky?

We need to solve 2 questions,

(Q1) How many molecules circulate in anyone’s body in their entire life-time?

– We know that our body regenerates entirely in 7 years.

– 60% of our body is made of water.

– We assume that our avg body weight is 50 kg in a life-time (linear increase from 0 to 20, steady weight of 80kg till 70)

– average life-time of 70 years.

H2O  (kg/life-time) = (60% x 50kg) x(70 yrs / 7yr to regenerate completely)

300 kg of water in 1 life-time.  18gm of water represents 1 mol of water molecules (6 x 1023)

300 kg = 1028 molecules of water will circulate in the body in the entire life-time of an average person.

(Q2) How many water drops are there on earth?

– A recent survey by the US Ocean Survey concluded that there is about 1.3 x1021 litres of water on Earth (oceans, lakes,rivers).

– 1 drop of water is about 10mm3, or 10-5 litre (assuming the average density of water of 1gm/cm3).

So we can calculate 1.3×1026 drops of water on Earth.

Then IF we assume that all 1028 molecules of Magellan’s life-time are spread evenly in the entire water reserve of Earth, we can calculate how many of these molecules are present in each drop of water on earth:

1028  / 1.3 x1026 = about 80 molecules in each drop of water.

Note: This is a quick, back-of-the-envelope calculation and therefore full of assumptions.  There are 2 main ones which would affect considerably the above number.  The first is that we assume that the 1028 in a life-time are unique molecules, however this is simply wrong, because the chances are that someone will ingest their own water molecules (localised ocean, rain, river cycle), so this number would in reality be lower.

The 2nd main assumption is that these molecules are evenly spread throughout the world, and again this is not quite right.  Possibly in time our climate and ocean currents would carry water molecules across the world, but there would always be pockets of higher concentration.  However, this is somewhat offset by the fact that in this specific example, Magellan went round the world and spent a major part of his life in India and other Portuguese colonies around the world, so his molecules of water where naturally disseminated in various places around the world.