Mathematical relationships that are important in chemical calculations

The mole (a chemist's counting unit)
The concept of amount in moles is central to chemistry because it allows us to keep track of the number of molecules, atoms, or ions present in a given sample of a substance. One mole of a type of particle is equal to 6.022 × 10²³ of that particle just like a dozen is equal to 12 particles.

Relating amount in moles of atoms and formulae for substances
The subscripts in the formula for a pure substance indicate

• the relative numbers of the atoms in one formula unit of the substance, and
• the relative amounts in moles of those atoms in one mole of the substance. 
   

  1 molecule of H2O contains		2 atoms of H		and 1 atom of O
  6.02 × 1023 H2O molecules  contain		2 × 6.02 × 1023 atoms of H		and 1 × 6.02 × 1023 atoms of O
  1 mole of H2O contains		2 moles of H		and 1 mole of O

  
  The mathematical relationship between the amount in moles of a substance and the amount in moles of the atoms that comprise the substance is used in many chemical calculations.
   

 Relating amount in moles and mass of a substance
The molar mass (M) is the mass of one mole of substance. The unit is g mol^–1.
 The molar mass is a very important quantity because it allows the chemist to relate the mass (m) of a substance (which can be measured) to the amount in moles (n) (which cannot be measured).