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Avogadro's number is simply used as a way of telling us how much of a substance we have.
The number is 6.022 x 1023, and if we have that number of particles, we can make it easier by saying we have one mole of particles. The particles could be atoms of an element, molecules of a compound, or even sweets in a jar (but in Chemistry you'll only really be dealing with compounds and elements!)
For example, instead of saying we have 1.044 x 1024 atoms, its easier to say that we have 2 moles of atoms ([1.044 x 1024 ] / [6.022 x 1023] = 2), because the number is smaller and more manageable.
The reason Avogadro's number is so important is because it is the number of atoms in one mole of atoms- and the definition of a mole is the number of Carbon-12 atoms present in 12 grams of Carbon-12.
This means if we have one mole of carbon-12 atoms (which have a relative atomic mass of 12), we have 12 grams of it. So Avogadro's number is used primarlily to convert between mass of a substance in grams, and the mass of a substance in terms of relative atomic mass (Ar), or relative molecular mass (Mr) if it's a compund.
The relationship is: number of moles = mass (g) / Ar
If we plug in the values from the definition, we see that the definition is consistent with the equation:
number of moles = 12 / 12
= 1 mole
We can use this equation for any solid substance with a known atomic (or molecular) mass. For example:
Calculating the number of moles in 85g of Magnesium solid-
number of moles (n)= mass / Ar of magnesium
n = 85 / 24
= 3.5 mol (to 1 decimal place)
We can also use the equation for compounds, but we need to add up the Ars of each component to find the overall Mr.
E.g. 20g of NaOH(s). [NB: Mr of NaOH = 23 + 16 + 1 = 40]
n = 20 / 40
= 0.5 molsee more