### 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: P_{1}V_{1} = 1/3N_{1}m_{1}c_{1}^{2}

and P_{2}V_{2} = 1/3N_{2}m_{2}c_{2}^{2}

but if pressure and volume are equal then:

P_{1 = }P_{2}

V_{1 = }V_{2}

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

1/2m_{1}c_{1}^{2} = 1/2m_{2}c_{2}^{2}

**and therefore N _{1} must equal N_{2}**

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 10^{23}

**that is, there are 6.0221415 x 10 ^{23} 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 10^{23 }x 1/2 molecules

that is 3.01 x 10^{23} molecules.

1 gram of oxygen will contain 6.02 x 10^{23} x 1/32 which is 1.88 x 10^{22} molecules

0.5 grams of carbon dioxide would contain 6.02 x 10^{23} x 0.5/44

which is 6.84 x10^{21} molecules.

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