Module 0502

The Avogadro constant: How many particles is that?

A mole of stuff - one packet of particles

Every packet of every stuff, same number of particles

How many particles in the packets?

One mole of any substance contains the same number of particles as 1 mol of any other. That number is staggeringly large. Just how many? You won’t believe it! You won’t even be able to understand it!

Well, even Prof Bob can't, but if you are really interested in learning chemistry for understanding (as distinct from just passing the next exam) ...........

Watch Prof Bob and Aussie arrive at the ridiculous number that is the Avogadro constant

This post is closely related to post 0501 Chemical amount of a species and its unit, mole, as well as post 0503 The Avogadro constant: Why that number?

KEY IDEAS - The Avogadro constant: How many?

Keep an open mind. It's not so long ago that everybody in the world, except indigenous Australians, took it for granted that swans are white.

An apology. My website editor does not allow formatting of superscripts and subscripts. I can do 'pretend' subscripts by dropping the font size, but superscripts (such as charges on ions, and exponents of the power of 10) remain inline and same font size. I hope that you can deal with this and that it is not too disconcerting.

Different stuffs: Same number per packet, different masses

1 mol of any (and every) substance is the amount of it that contains 6.022 × 10^23 specified particles (See Module 0501 Chemical amount and its unit of measurement, mole).

More precisely, the value is 6.02214076 × 10^23, but four significant figures is enough for our present purposes.

This number is called the Avogadro constant (symbol NA ). In some older books, it is referred to as Avogadro’s number.

Although the number of particles in each 'packet' is the same for every substance, the mass of 1 mol of any substance is different from the mass of 1 mol of every other substance - because the atoms of different substances have different masses. The relative masses of 'packets' of substances corresponds with the relative masses of the particles of each substance.

For example:

There are 6.022 × 10^23 iron atoms (Fe) in 55.85 g (1 mol) of iron, Fe(s)
There are 6.022 × 10^23 water molecules (H2O) in 18.02 g (1 mol) of water, H2O(l)
There are 6.022 × 10^23 sodium ions (Na+) in 58.45 g (1 mol) of sodium chloride, NaCl(s)
There are 6.022 × 10^23 nitrogen molecules (N2) in 28.01 g (1 mol) of nitrogen gas, N2(g).

Think about it: Rank, in order, the masses of one atom of iron, one molecule of water, and one molecule of nitrogen.

How big a number is the Avogadro constant?

How many is 602214076000000000000000?

This number is so big that it is impossible to visualise. But there are stories that help us to realise that it is too big to visualise. Such as …

If we have 1 mol of a substance and we could remove one million particles every second, non-stop, day and night, it would take us 1.9 × 10^10 years to count out all of the particles. The duration of time since the “big bang” is estimated to be 1.5 × 10^10 years (15 billion) years. So, by now we would have counted out only 80% of the particles!

The important “takeaway message”: The number of particles in 1 mol of a substance is more than we can comprehend.

To learn chemistry with understanding, we need to have good visualisation - at the level of atoms and molecules - of the substances and reaction mixtures that we are considering.

Try to form a mental picture of this many water molecules (6.022 × 10^23) dashing and crashing within an 18 g (= 18 mL) sample of liquid water, or of N2 molecules darting around in a sample of 28.01 g of nitrogen gas.

And the number of them is not just in the thousands, or even in trillions, ....... so many more! It’s a crowded environment!

This might be a useful image in future.

Another analogy about the number of particles in 1 mol

You can find in chemistry textbooks all sorts of analogies about the number of particles in 1 mol of any substance abound in chemistry textbooks. Naturally enough: after all, it's pretty difficult to get your head around it.

Prof Bob thinks that the counting-out exercise in the video is the most effective eye-opener of all. But here's another thought ....

There are about 8 billion (8 000 000 000) people on Earth. The number of people on another 70 trillion (70 000 000 000 000) equally populated planets is the about the same as the number of water molecules in 18 g (or 18 mL) of water.

Chew on that!

Do we always need to know how many particles?

The ratio of the numbers of particles in samples of two substances is the same as the ratio of the chemical amounts (in moles) - See post 0501 Chemical amount of a species and its unit, mole.

So, we usually don’t need to know the absolute number of particles in a sample of stuff - just whether the numbers are equal, or in the ratio 3:1, or whatever ......

Why, oh why?

I can feel your puzzlement. I hear you saying "OK, that is all very logical, but why is it that number 6.022 x 10^23?"

Well, why don't you jump to to Module 0503 The Avogadro constant: Why is it that number?

Anyway, who, or what, is Avogadro?

Well Lorenzo Romano Amedeo Carlo Avogadro di Quarenga e di Cerreto (known to his mates as Amedeo, and probably to his sister as Ammy) was an Italian nobleman who was also a chemist and physicist.

He lived from 1776 to 1856. He was born two years before English settlement at Sydney, one month before the USA Declaration of Independence, and .... (insert your own relevant context).........

You can learn more about him at Amedeo Avogadro.

He not only has a constant, he also has a law!

Perhaps you might like to find out about Avogadro's law, which relates the volume of a gas to the chemical amount of the gaseous substance - which of course involves the Avogadro constant.

SELF CHECK: Some thinking tasks

Can you believe what Prof Bob just told us!!? That many, in only 18 g of water? And in 56 g of iron? No way! But if Prof Bob says so ......

1.         We usually write numbers out in full in groups of three digits (such as 10 600, or 1 342 000).Which of the following is the Avogadro constant?
            A:        60 230 000 000 000 000 000
            B: 602 300 000 000 000 000 000 000
            C: 0.000 000 000 000 000 000 006 023
            D:        60 231 023

2.         How many years (approximately) would it take to count out, at 1 Fe atom per second, all of the atoms in 55.85 g of iron, Fe(s).
            A:        1.07 × 10^18 years
            B:         3.42 × 10^14 years
            C:         55.85 years
            D:        1.91 × 10^16 years

3.         If we had a sample of iron with mass 55.85 g, and we could count out one atom per second continuously, what percentage of the mass would have been counted out by now if we began at the time of the Big Bang 15 000 000 000 years ago?
            A:        100%
            B: 7.85 × 10^-5 %
            C: 7.85 %
            D:        7.85 × 10^-5 %

4.         What mass of water contains the same number of water molecules as there are sodium ions in 5.845 g of sodium chloride?
            A: 5.845 g
            B:         0.100 g
            C: 1.802 g
            D: 6.023 × 10^22

Answers: 1(B); 2(D); 3(B); 4(C)

Oops!

I was reflecting upon the content of this module when I went to a restaurant to order an avocado toast. The waiter was a chemistry student. I am still trying to work out why I received 602214076000000000000000 pieces of toast! Any ideas?

If I ate one piece of toast every second continuously 24/7, how long would it take me to eat my breakfast?

LEARNING CHEMISTRY FOR UNDERSTANDING

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