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Liquids are incompressible; gases are not incompressible.

When you decrease the volume of a gas by 50%, that's no problem.

It's impossible to do that for a liquid.

In liquids, the atoms and the molecules effectively touch each other, whereas in gases, they are very far apart, so that's why you can compress the gases.

If you take air at one atmospheres, the density is a thousand times less than the density of water.

What it tells you is that the molecules are much further apart.

It is an experimental fact that there is a simple relation between the pressure that you see there, the volume of a gas, the temperature of a gas in degrees Kelvin, and the number of molecules that you have.

Now, when you see the word "molecules," I may often mean "atoms." I realize that helium and neon and krypton and argon are atomic gases, and that O2 and H2 and CO2 are molecular gases.

So I will use that word "molecules" even when I mean "atoms," and maybe vice versa, just for simplicity.

The relation that exists between these quantities, PV equals nRT: pressure, volume, n is the number of moles —

I'll get back to that —

R is the universal gas constant, which is 8.3 joules per degree Kelvin, and T must be in degrees Kelvin.

So, what is a mole? A mole has always about 6.02 times ten to the 23 molecules, or atoms, in the case that you have helium, but I will call that molecules.

And this number is called Avogadro's number.

So that's the definition of a mole.

If you take a mole of helium, or a mole of oxygen, or CO2, or N2, it doesn't matter, it always has this number of molecules, approximately.

Now, each of these substances have very different masses.

If I take, for instance, carbon, then one mole of carbon would weigh very close to 12 grams.

If I take helium, one mole of helium would weigh very close to four grams.

And if I took oxygen two, O2, then one mole would be very close to 32 grams.

So the masses are very different in a mole but not the number of molecules or the number of atoms.

When I take a neutral atom, then we have a nucleus, and the nucleus contains protons and neutrons.

It has Z protons and it has N neutrons.

The protons are positively charged, and it has Z electrons if it is a neutral atom.

There is almost no weight in the electrons; you can almost ignore that.

Everything is in the protons and in the neutrons.

N plus Z is called A, and that's called the atomic mass number.

Let's look at carbon in a little bit more detail.

If we have carbon —

and I call it carbon 12 for now, you'll see shortly why —

then carbon has always six protons in the nucleus; otherwise it isn't carbon.

And when it has six neutrons, then A is 12.

That's why we call it carbon 12.

So the atomic mass number of carbon is 12, but if you had, for instance, carbon 14 —

which happens to be radioactive —

again, six protons, otherwise it wouldn't be carbon, you would have eight neutrons now, and now you would have...

atomic mass number would be 14.

A mole is this number in grams, and so you see carbon...

is the atomic mass number in grams —

you see 12 there.

If you go to helium, it has two protons and two neutrons, so A is four —

that's why you see your four grams.

If you take oxygen, it has eight protons and eight neutrons, so A is 16, but you have O2 in gas form, so now your atomic mass number has to be doubled to 32.

And so a mole of O2 is therefore 32 grams.

When you decrease the volume of a gas by 50%, that's no problem.

It's impossible to do that for a liquid.

In liquids, the atoms and the molecules effectively touch each other, whereas in gases, they are very far apart, so that's why you can compress the gases.

If you take air at one atmospheres, the density is a thousand times less than the density of water.

What it tells you is that the molecules are much further apart.

It is an experimental fact that there is a simple relation between the pressure that you see there, the volume of a gas, the temperature of a gas in degrees Kelvin, and the number of molecules that you have.

Now, when you see the word "molecules," I may often mean "atoms." I realize that helium and neon and krypton and argon are atomic gases, and that O2 and H2 and CO2 are molecular gases.

So I will use that word "molecules" even when I mean "atoms," and maybe vice versa, just for simplicity.

The relation that exists between these quantities, PV equals nRT: pressure, volume, n is the number of moles —

I'll get back to that —

R is the universal gas constant, which is 8.3 joules per degree Kelvin, and T must be in degrees Kelvin.

So, what is a mole? A mole has always about 6.02 times ten to the 23 molecules, or atoms, in the case that you have helium, but I will call that molecules.

And this number is called Avogadro's number.

So that's the definition of a mole.

If you take a mole of helium, or a mole of oxygen, or CO2, or N2, it doesn't matter, it always has this number of molecules, approximately.

Now, each of these substances have very different masses.

If I take, for instance, carbon, then one mole of carbon would weigh very close to 12 grams.

If I take helium, one mole of helium would weigh very close to four grams.

And if I took oxygen two, O2, then one mole would be very close to 32 grams.

So the masses are very different in a mole but not the number of molecules or the number of atoms.

When I take a neutral atom, then we have a nucleus, and the nucleus contains protons and neutrons.

It has Z protons and it has N neutrons.

The protons are positively charged, and it has Z electrons if it is a neutral atom.

There is almost no weight in the electrons; you can almost ignore that.

Everything is in the protons and in the neutrons.

N plus Z is called A, and that's called the atomic mass number.

Let's look at carbon in a little bit more detail.

If we have carbon —

and I call it carbon 12 for now, you'll see shortly why —

then carbon has always six protons in the nucleus; otherwise it isn't carbon.

And when it has six neutrons, then A is 12.

That's why we call it carbon 12.

So the atomic mass number of carbon is 12, but if you had, for instance, carbon 14 —

which happens to be radioactive —

again, six protons, otherwise it wouldn't be carbon, you would have eight neutrons now, and now you would have...

atomic mass number would be 14.

A mole is this number in grams, and so you see carbon...

is the atomic mass number in grams —

you see 12 there.

If you go to helium, it has two protons and two neutrons, so A is four —

that's why you see your four grams.

If you take oxygen, it has eight protons and eight neutrons, so A is 16, but you have O2 in gas form, so now your atomic mass number has to be doubled to 32.

And so a mole of O2 is therefore 32 grams.

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