# Number of moles and Avagadro’s number

We all like food. Talking about food, I got a dozen bananas yesterday from the grocery store. Now it is understood that I brought 12 bananas when I mentioned a ‘dozen’ because ‘a dozen = 12’.

It is easy to deal everyday items in such quantities like pair or a couple. But when it comes to molecules, these ways of counting are not convenient. Because we cannot do appreciable work with just 12 atoms. Hence scientists use something called as a mole.

Back to the bananas, if I ask my mother to get me a dozen of bananas, she would. Accurately. But if I ask her to get me one mole of water, she will put me up for adoption. Because nobody told my mom what 1 mole means, nor she reads my blog.

Back in his days, Avogadro had a lot of free time, so he sat at his desk and calculated a unique number which he named after himself, the Avogadro’s number which is 6.022 x 1023.

This number is significant for a reason, it is what 1 mole means. So, when I asked my mother to get me 1 mole of water, I expected to get a glass with 6.022 x 1023 molecules of water. But my mother does not know how to count these many molecules. She should definitely start reading my blog.

The trick to count these many molecules is to not count-count them, but to weigh them. So only if she could weigh 6.022 x 1023 molecules of water. This is what Avogadro figured out. He calculated that  6.022 x 1023 molecules of any compund equals to its molecular weight but in grams (hence molecular weight is also called as molar mass).

If you look at the periodic table, under every element, its atomic weight is mentioned. Let’s look up for Hydrogen (H) and Oxygen (O) as water is made up of them. Hydrogen weighs about 1 units while oxygen weighs about 16 units (we will come to the units in a minute). Since the formula of water is H2O, one molecule of water contains 2 atoms of hydrogen while 1 atom of oxygen, so it makes sense that the weight of one molecule of water would be weight of 2 H atoms and 1 O atom combined. That is: (1)(2) + (16)(1) = 18units.

So, the trick is: if my mother weighed 18 grams of water, she would actually be weighing 1 mole of water i.e. 6.022 x 1023 molecules . To put it simply, 1 mole of anything equals the atomic/molecular weight of that substance but taken in grams. Hence the unit of atomic or molecular weight is grams/mole, meaning one mole of that compound would contain that many grams.

Let’s take another example. My friend owns a cow and she won’t quit farting. Cows fart methane gas whose composition is CH4. We know the weight of a hydrogen atom from the previous example to be 1gram/mole. Weight of one carbon atom, C, equals to 12grams/mole. So, the weight of one molecule of methane would be = (12)(1) + (1)(4) = 16grams/mole. And you guessed it right, one mole of methane would contain 16 grams of methane.

I read somewhere that one dairy cow in the UK can produce about 110kg of methane. Can you guess how many moles of methane does that cow produce? Well, we know one mole of methane will weigh 16 grams, so if we knew how many grams does 110kg mean, we can figure it out.

1kg = 1000g, so 110kg = 110,000g
If 16g CH4 = 1mole CH4, then, 110,000g CH4 would mean = 110,000/16 = 6875 moles!

That’s a lot of moles. Well can you guess how many molecules does that many moles contain?
Avogadro said one mole would contain 6.022 x 1023 molecules, so:
6875 moles would contain = 6875 x 6.022 x 1023 = 41,401.25 x 1023 molecules of methane! Insane.

To conclude this page, I would like to say that chemistry involves a lot of thinking and drawing conclusions but that does not mean we always run the same train of thought while solving every problem. We should formulate conclusions and use them to save time. So, the conclusion for today is:
number of moles = mass of compound/molecular weight of the compound or
n=m/M.