Balancing Equations
Balanced equations obey the law of conservation of mass.  The total mass before a reaction takes place
will equal the total mass after the reaction is complete.  The number of atoms which take part in a
chemical reaction will also remain constant.  Balancing an equation can sometimes involve trial and error.
The following rules and suggestions can go a long way in keeping down the errors.

1. The equation will be understood to proceed from left to right. The reactants are on the left side of
    the arrow and the products are on the right.

2. Equations are balanced by adjusting COEFFICIENTS in front of formulas, never by changing
    subscripts within formulas.  Remember that a 1 is understood when a coefficient is not present.

3. It is best to start with an element that appears in only one compound on each side of the arrow.

4. Next balance any element that appears in more than one compound on either the right or left.

5. Balance free elements last. That is balance any element that appears in elemental form on the
    right or left.

6. When polyatomic species (NH₄⁺, SO₄^-2, OH^-, etc.) appear on both sides of the arrow in
    compounds or as ions, balance them as units rather than individual elements.

7. Leave the coefficients in the lowest whole number ratio.

____Mg + ____O₂ ----> ____MgO
(Sum of coefficients = 5)

Example 2   General Rxn

____C₂H₈N₂ + ____N₂O₄ ----> ____N₂ + ____H₂O + ____CO₂
(Sum of coefficients = 12)
 

Neutralization  In a neutralization reaction, an acid reacts with a base to produce a salt (or salt solution)
and water if the base is a hydroxide base (NaOH, Al(OH)₃).  To derive the formula of the salt, couple the
anion of the acid with the cation of the base.

H₂SO₄(aq) + 2 NaOH(aq) ---->  Na₂SO₄(aq) + 2 H₂O(aq)

Example 3   Neutralization Rxn

____HClO₄(aq)  +  ____Ca(OH)₂(aq) ---->
(Sum of coefficients = 6)

Example 4   Neutralization Rxn

____H₃PO₄(aq)  +   ____Mg(OH)₂(aq)  ---->
(Sum of coefficients = 12)

Precipitation  In a precipitation reaction, two aqueous solutions react to form an insoluble product.
To derive the formulas of the products of a precipitation, couple the cation of the first reactant with the
anion of the second reactant and couple the cation of the second reactant with the anion of the first.
In other words, rearrange the ions of the reactants to give two new neutral compounds.

AgNO₃(aq) + NaCl(aq) ---->  AgCl(s) + NaNO₃(aq)

Example 5    Precipitation

____Na₂CO₃(aq) + ____Ca(NO₃)₂(aq) ----> Sodium nitrate + Calcium carbonate
(Sum of coefficients = 5)
 
 
 

Example 6    Precipitation

____Fe₂(SO₄)₃ + ____BaCl₂ ----> Iron(III) chloride  + Barium sulfate
(Sum of coefficients = 9)
 
 
 

Oxidation   Chemical processes involving the transfer of electrons are called oxidation reactions (redox).
The combustion of a hydrocarbon is a redox reaction.  Hydrocarbons undergo complete combustion to
yield carbon dioxide and water.

CH₄(g) +  2 O₂(g) --->  CO₂(g) + 2 H₂O(g)

Example 7   Combustion

____C₂H₆(g) + ____O₂(g) --->
(Sum of coefficients = 19)
 

Example 8   Combustion

____C₄H₁₀(g) + ____O₂(g) --->
(Sum of coefficients = 33)