One mole is the number of molecules in eighty grams of water which is very little water, about three teaspoonfuls. Such a little volume of water contains 6.02·1023 molecules (the Avogadro’s number) which is a huge number of molecules. To picture how big this number is I wonder how long it would take to count all molecules in one mole one by one? One year? One century?… Let’s do some maths. To make the task a little bit easier I will suppose we are able to count ten units per second which is a very fast counting rate. Counting that fast, we would count…
10 molecules in 1 second
600 molecules in 1 minute
36,000 molecules in 1 hour
864,000 molecules in 1 day
315,360,000 molecules in 1 year.
As we have to count from 1 to the Avogadro’s number, we just have to divide it by the number of molecules counted in a year (6.02·1023/ 315,360,000), which leads us to an enormous number of years: 1.9·1015. This number is much more impressive if we don’t use scientific notation: 1,900,000,000,000,000 years, in other words, almost two quadrillion years (in Spanish: mil novecientos billones). Is it that long? Let’s compare it with other long times:
First human-ish beings appeared 4.5 million years ago
Earth exists since 4.5 billion (4.5·109) years ago
The Universe 14 billion (1.4·109) years ago.
The time we would need to count from one to the Avogadro’s number is about 1,364,000 times longer than the age of the Universe. Mind-blowing, isn’t it? To make the task shorter, let’s imagine that all people (7 billion = 7·109) helped us to count, in that case, the counting would be 7 billion times shorter, which is roughly 270,000 years. All the human beings in our planet working together would need two hundred and seventy thousand years to count the number of molecules in a mole.
As you can see the Avogadro’s number is really huge but it is just the number of water molecules in a sip of water.