Avogadro's Number (Mole) - Numberphile

Uploaded by numberphile on 23.10.2012

MARTYN POLIAKOFF: I'm a chemist.
And therefore, I suppose the most obvious number for me to
talk about is Avogadro's number.
And Avogadro's number is very big.
Surprisingly, although I'm a chemist, I can never remember
the exact value.
So let me just look it up.
It is 6.02214--
and there's some argument for further decimal places--
times 10 to the 23.
So this is a very, very big number.
And it is related to atoms and molecules.
So Avogadro was an Italian chemist who worked at the
beginning of the 19th century.
And shortly after John Dalton had proposed the idea of
atoms, Avogadro was thinking of the number of atoms and
molecules inside a flask a bit like this one.
So you imagine the gas inside here.
From those ideas, he developed the hypothesis about the
number of molecules of any gas inside a flask.
But it's easier for me to explain it to you with some
atoms here.
So imagine that we have here hydrogen; carbon, which is
black; oxygen; and uranium, which is big.
After the time of Avogadro, people started measuring the
relative mass of these atoms.
So hydrogen has a mass 1, carbon 12, oxygen 16, and
uranium 238.
These are for particular isotopes.
These weights are defined by the number of protons, the
positively charged particles, and neutrons, the neutral
ones, in the nucleus.
So for example, in carbon, you have six
protons and six neutrons.
Whereas in uranium, you have 92 protons.
And I can't work out the number of neutrons, but they
add up to 238.
I'll leave that for you to calculate.
Later chemists took Avogadro's idea and developed it into the
statement that if you take 1 gram of hydrogen, 12 grams of
carbon, 16 grams of oxygen, or 238 grams of uranium, the
number of atoms in that sample will be exactly the same.
And that number was given the name Avogadro's number in
honor of Avogadro, who started thinking about these things in
the first place.
BRADY HARAN: Professor, is that fact a lovely
Or is that inevitable that that would have happened
because of the way the weights of atoms work?
MARTYN POLIAKOFF: This is inevitable.
It's not a coincidence.
It's not just like the number of my birthday, December the
16th, is the same as the mass of oxygen.
It's something that's inevitably true because of the
way that these mass scale has been done.
It is the relative masses of the different atoms.
The big question is, how can you actually work out what the
number of these atoms are?
Because there's so many of them.
You can easily say that even a simple experiment that you
could do at school or college will tell you it's 6
times 10 to the 23.
But it is the decimal points and the numbers after the
decimal point that are really the key.
And the more numbers you can measure, the more precisely
you know the number.
Now, you can ask, what's the point of measuring these
things so precisely?
Why do we want to know this number so precisely?
And the reason is that it has become very important in
recent years for the definition of the unit of
mass, the kilogram.
As you know, we have a whole series of fundamental units--
the second, the meter, and so on, the ampere.
So you can define most of these units, such as the
meter, in terms of the speed of light.
But what do you use for the kilogram?
Now, there's still some argument.
But one approach is to say if we could define Avogadro's
number, then we could relate that to the mass of carbon-12
or whatever.
And then this would become a fundamental constant.
And we would no longer have to rely on a lump of platinum or
iridium stored in a vault to define what
we mean by a kilogram.
The way that people are approaching this is to measure
the mass of a lump of silicon.
The reason they've chosen silicon is
because it is an easy--
or relatively easy-- material to handle and purify.
So, they have made this spherical lump.
Imagine now this is a real ball, about the size of the
one I'm holding, but made out of silicon.
And very special silicon, the isotope silicon-28.
So that's just one isotope of silicon.
And they have grown a single crystal of silicon-28 and then
machined it into a spherical ball.
And using this ball because you can measure its diameter.
And you can measure, using X-rays, the distance between
the layers of atoms.
You can calculate the number of atoms in the ball.
You can't get the nearest atom.
But all being well, they may be able to get to 1 part in 10
to the minus 8.
That means, effectively, they can measure the number or
calculate the number to nine significant figures.
That's 6 point and then eight numbers.
And each of those digits, they can be certain, is right.
BRADY HARAN: Still a long way off the whole number.
MARTYN POLIAKOFF: It's a long way off, but it's near enough
to define the kilogram as accurately as people want.
It might be worth giving you an idea how big 6 times 10 to
the 23 really is.
And one of my friends, Colin Johnson, has calculated--
and I haven't checked his calculation--
that if you went round the entire coast of the UK and on
every sandy beach used an excavator to remove all the
sand to a depth of 1 meter.
And then you piled all that sand up somewhere and then
counted the number of grains of sand, it would be about 6
times 10 to the 23.
So if you took a lump of gold just slightly
less than 197 grams--
which, because gold's dense, is not very big, probably much
smaller than any of these balls--
in that lump there would be the same number of atoms as in
this huge pile of sand that you've got from excavating all
the beaches to a depth of 1 meter.
So you get the idea.
It's a big number.
The other thing is that most chemists don't use Avogadro's
number very often.
But what they do use is the unit that is called a mole.
And a mole is Avogadro's number of molecules.
And they talk about reactions very often in terms of moles.
Now, some of you may know that in English, and American
English, mole is the name of a small, furry creature that
burrows under the ground.
And in America, every year they celebrate chemistry on
so-called Mole Day.
And they have all sorts of cartoon moles that tries to
make people enthusiastic about chemistry.
I appear on YouTube quite frequently,
but not on this channel.
But on Brady's other channel, the chemistry channel, called
Periodic Table of Videos.
And we have a lot of fans.
And last year, on Mole Day, a fan in a school in Seattle
produced a mole.
She's called Melinda, and she's in honors chemistry 3A.
BRADY HARAN: That's the girl, not the mole.
And she called this mole that she made Moltyn Moliakoff.
And I think it's rather sweet.
And some of you who have a good imagination may think
that there's a vague resemblance between
the mole and me.
I think it's great that young people, like Melinda, get so
enthusiastic about chemistry and our channel that they make
models like this.
And I would encourage you, even if you're a maths buff,
have a look at our chemistry channel.
Because chemistry is more fun than you think.
And it has bigger explosions than on maths.
-Look at--
-I'm just going to check that there's none left.