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Zumdahl Chemistry Chapter3: Balancing chemical equation

The principle that lies at the heart of the balancing process is that atoms are conserved in a chemical reaction. The same number of each type of atom must be found among the reactants and products. When the equation for this reaction is balanced, the identities of the reactants and products must not be changed. The formulas of the compounds must never be changed in balancing a chemical equation. That is, the subscripts in a formula cannot be changed, nor can atoms be added or subtracted from a formula. 

To balance a chemical equation It is always best to start with the most complicated molecules (those containing the greatest number of atoms). For example, consider the reaction of ethanol with oxygen, given by the unbalanced equation.

Balancing carbon atoms: In the left side (reactants) we have only two carbon atoms and the right side (products) we have one carbon atom. To balance the carbon atoms we place the coefficient 2 before CO₂.
Balancing hydrogen atoms: In the left side (reactants) we have six hydrogen atoms and the right side (products) we have two hydrogen atom. To balance the hydrogen atoms we place the coefficient 3 before H₂O.
Balancing oxygen atoms: In the left side (reactants) we have three oxygen atoms and the right side (products) we have seven oxygen atom. To balance the oxygen atoms we place the coefficient 3 before O₂. finally we get a balanced equation.