### Avogadro’s Law and Avogadro’s Number explanatory notes

The usual statement of Avogadros Law is:

Equal volumes of an ideal gases at the same temperatures and pressures contain equal numbers of molecules.

how do we show that this is the case?. Well...

Think about two ideal gases - we will call them 1 and 2.

Using the equation derived by considering the movement of molecules in an ideal gas,

we can write:  P1V1  =  1/3N1m1c12

and     P2V2  =  1/3N2m2c22

but if pressure and volume are equal then:

P1 = P2

V1 = V2

and if the temperatures are equal then the kinetic energy of the molecules are equal so:

1/2m1c12  = 1/2m2c22

and therefore N1 must equal  N2

f there are equal numbers of molecules then the relative mass these gases must entirely depend on the mass of the molecules themselves. Reversing the argument if we have two quantities of ideal gases the masses of which are in the same ratio as the masses of their molecules, then they must have equal numbers of molecules.

The value of Avogadro's number is given as the number of molecules in a mole.

A mole is the molecular mass expressed in grams.

The value of Avogadro’s number is: 6.0221415 x 1023

that is, there are 6.0221415 x 1023 molecules in a mole of any (ideal) gas.

### What is a mole

So, what is a mole

A mole is the molecular mass expressed in grams.

The atomic mass of hydrogen is 1. There are two atoms of hydrogen in a molecule, so the molecular mass is 2amu. The mass of a mole of hydrogen is then 2 grams.

The atomic mass of oxygen is 16. There are two atoms in a molecule so the molecular mass is 32amu. A mole of oxygen therefore has a mass of 32 grams.

Carbon dioxide has the formula CO2. The mass of each oxygen atom is 16 and the atomic mass of carbon is 12. The total molecular mass is therefore 44 amu.

44 grams of carbon dioxide would be one mole.

Examples

If we have 1 gram of hydrogen then it will contain 6.02 x 1023  x 1/2  molecules

that is 3.01 x 1023  molecules.

1 gram of oxygen will contain  6.02 x 1023  x 1/32  which is 1.88 x  1022  molecules

0.5 grams of carbon dioxide would contain  6.02 x 1023  x 0.5/44

which is 6.84 x1021  molecules.

Useful pages on the kinetic theory of gases and the gas laws are: