# Understanding Avogadro's Number

6,000

10

3

## Introduction: Understanding Avogadro's Number

Avogadro's number is named after the 19th century Italian scientist Amedeo Avogadro and is defined by the number of atoms in 12 grams of the element carbon 12 (with six protons and six neutrons). As one might imagine it takes a lot of atoms to make 12 grams of carbon. It does ... a lot! In fact about 602200000000000000000000 of them.

So Avogadro's number is an amount - like atoms in 12 g of carbon - and can mean different things. For example it is also pretty close to the number of atoms in 1 g of hydrogen. This amount is also called a *mole*. So one mole of carbon weighs 12 g and one mole of hydrogen weighs 1 g.

But 602200000000000000000000 (6.022 x 10 ^ 23) is such a big number that it does not really give any meaning. I have made some calculations, which might give an idea - at least - of how really, really small the atom is. I hope you find it interesting and maybe inspire you to make silly calculations too. And Please do tell me if you find any errors in the calculations or in the text - I am no genious and English is not my mother tongue.

## Step 1: How Much Is a Mole of Sand Really?

Let's imagine we have some grains of sand, which take up the space of one cubic milimeter each on average. We could lay them out in a square 10 x 10 and get one square centimeter with 100 grains of sand. Make a cubic cm and we have 1000. A cubic cm is not very big - especially if we try to find out what a mole or 6.022 x 10 ^ 23 looks like. So let's move on to cubic meters. That would be 1000 x 1000 x 1000 mm or grains of sand. So now we have one billion, 1000000000 or 1 x 10 ^ 9.

Now we have some rather big cubes containing one billion grains of sand each. Laying them out in a bigish square with sides of one kilometer each would give us a billion those cubes. So now we have a patch of land one square kilometer big with a layer of sand one meter thick - in all 1 x 10 ^ 18 grains.

We are getting there, but there is still a bit of way to a mole. If we devide one mole with 1 x 10 ^ 18, we get that we need 602200 patches of one square kilometer each to have a mole of sand. We could stack the patches on top of each other and reach 602.2 kilometers out in space or spread them out in a one meter thick layer. That would take more than the combined area of Spain and Portugal. A mole of sand is a lot, and remember that a mole of atoms will fit in only 12 grams of carbon!

## Step 2: How Long Can We Live on a Mole of Rice Grains?

Moving on from grains of sand to grains of rice. One of the most common foods in the World is rice. There are many types of rice - I opened the cubboard and looked at a pretty normal bag of long grained rice. On the back I could read that 100 grams of uncooked rice holds 1550 kJ of energy. I made this bag of rice my starting point.

I decided that one could live relatively well if one got 10000 kJ worth of food per day. Knowing how much energy there is in 100 g rice, we get that a person must cook 645 grams of raw rice to cover the need. Yes! I know that this is a rather uniform diet, but bare with me - this is an example!

But how many grains of rice is 645 grams? Well, I counted 60 grains in one gram of rice, weighed on my super acurate scales! This means that an avarage person gets 38700 grains of rice per day ... start counting!

Reading the above sandy example, you might conclude that a mole of rice grains is going to feed more than one person for more than one day. In fact we might skip right up to the entire population on Earth, which - in round numbers - is seven billion people or 7 x 10 ^ 9. Each eating 38700 grains of rice per day gives us 2.71 x 10 ^ 14 rice grains if every human on Earth lived on rice for a day. Doing that for a year we need 9.89 x 10 ^ 16 little, individual grains of rice.

Knowing that a mole is 6.022 x 10 ^ 23, we can devide with 9.89 x 10 ^ 16, and - this might make you shiver with excitement - we get that a mole of rice grains will feed the current population of our planet for ... 6088978 years!!

## Step 3: How Many H2O Molecules Evaporate in a Second?

If a mole of grains of rice can feed the World for six million years, then the fact that a mole og hydrogen atoms weighs only one gram means that atoms are really, really, really small! A water molecule is, of cause, much bigger and a mole of H2O molecules weighs a whopping 18 grams!

However, individual H2O molecules are still pretty small relative to, say, a grain of rice or sand. This must mean that when water evaporates from something, quite a lot of H2O molecules must float away in a short time. But how many?

I soaked a piece of tissue and weighed it on my super accurate scales and got a mass of 4.70 grams. I left the wet tissue for 20 minutes, and it so happened that it lost exactly a tenth of a gram. Some molecules had flown away!

20 minutes is 1200 seconds, which means that 0.1 gram / 1200 seconds = 0.00008 grams evaporate every second. Not a lot, you might think, but what if we look at moles per second? 0.00008 grams per second / 18 grams per mol = 0.00000444 moles per second. A mole being 6.022 x 10 ^ 23 we get that 2.67 billion billion or 2.67 x 10 ^ 18 water molecules leaves a wet piece of tissue every second. We fed the World with rice - if they need water, with this method we can give every person on Earth almost 400 million water molecules per second each.

Cheers!

## 3 Discussions

Thanks! I enjoyed making it :-)

I really enjoyed reading this - great write-up (also, your English is just fine :)

Oh so many years of chemestry with this fun number!