Mole is a measure of number. "Mole"-concept helps us to weigh or count definite-numbers of atoms (excluding the minute errors) just using a macroscopic pan-balance. If I know it is glucose, and take 180 gram of it ( since C6 H12 O6 has molecular weight 180); the sample contain 1 moles or avogadro numbers (N.A) or 6.023 * 10 ^ 23 molecules of glucose. Similarly, 18 gram H2O must contain 1 mole or 6.023 * (10 ^ 23) water molecules.
Let start with some macroscopic objects.
If we take 1 truck full of bricks and another truck full of brick-chips; the second truck would contain many times more brick chips than bricks in first one. Simple.
But if we took 1 truck brick (total mass of brick very heavy); and 1 bucket brick-chips (total mass of brick-chips much lighter than truckful bricks)... then? Perhaps the both will contain same (at least almost) number of particles.
I.e. if we take heavy objects in massive-amount, and lightweight objects in lighter amount; the number of objects of both cases, would tend to same.
In Quantitative terms:
Say each brick-chip= 1 gram. 1 brick= 1000 gram.
Now, if we take 1234 * 1 gram brick-chips and 1234 * 1000 gram bricks; we'll get the same number of unit-particles in both case.
Or if we take X * 1 gram brick-chips at a place,
and X * 1000 gram bricks at another place;
in both case we would get the same number.
1 atom of hydrogen (H) weigh 1 a.m.u. 1 molecule of Glucose ( C6 H12 O6 ) weighs 180 a.m.u. 1 molecule of H20 weighs 180 a.m.u.
Now, 1 gram = 6.023 * (10 ^ 23) Dalton or N.A a.m.u. ( * )
So just like our above mentioned brick example;
1 gram of hydrogen (H) atom (or N.A amu H) , or 180 gram glucose (i.e. N.A * 180 amu glucose ), or 18 gram water ( N.A * 18 amu water) would contain the same number of particle (Which is here 6.023 * (10 ^ 23) pieces or N.A. pieces due to relationship between gram and amu). This way 1 mole of any substance would contain NA number of molecules
Avogadro number (N.A.) in this example working the same way as X in previous brick example.
Here is a simplified diagram comparing real-life example and chemistry-example.
1 C6 H12 O6 + 6 O2 = 6 CO2 + 6 H2O
The numbers at left side of compound's formula, or the stoichiometric coefficient; is smallest possible number of molecules to complete a reaction.
we're given certain amount of glucose, and asked for amount of CO2 evolved after complete combustion in O2 ?
We can calculate that freshly from a.m.u. Larger calculation.
But mole concept help a lot since we can determine quantities of reactants and products directly in gram, from molecular formula and stoichiometric coefficients, without using any unit conversion between gram and a.m.u.
If we could multiply the whole reaction
(180 amu + 6 * 32 amu = 6 * 44 amu + 6 * 18 amu for respective compound)
with NA (could run NA numbers of such reactions at a time)
180 amu * NA + 6 * 32 amu * NA = 6 * 44 amu * NA + 6 * 18 amu * NA (respective compound)
1 mole glucose + 6 mole O2 = 6 mole CO2 + 6 mole H2O.
180 gram + 6 * 32 gram = 6 * 44 gram + 6 * 18 gram (respective compound).
once we knew the fact instead molecule we could use mole; and we could easily write reaction for a mole parallel reactions. Then we convert between moles to gram using the chemical formula, we can easily determine the required or obtained amount of certain reactant or product. For a certain given value of 1 reactant or product
for say 2 H2 + O2 = 2 H2O. From this reaction we easily conclude 2 mole of H and 1 mole of O2 forms 2 moles of H2O; or 2 * 2 g H2 and 32 g O2 makes 2 * 18 g H20. Now using unitary method we could find an asked amount of reactant or product from some given amount of reactant or product.
( * ) : http://chemistry.bd.psu.edu/jircitano/mole.html
Google Unit-conversion Result
Avogadro constant in wikipedia
Atomic Mass unit in Wikipedia
Mole (unit) in Wikipedia
Atomic mass in wikipedia
Molecular mass in wikipedia
Molar mass in Wikipedia
What we've been taught in basic chemistry classes