# Balancing Equations

Balancing Chemical Equations
Dr. MJ Patterson

Most textbooks recommend a method for balancing chemical equations called "balancing by inspection."  Realistically, the method should be called "Guess and Guess Again."  The basic idea is that you try a coefficient and see how it affects the rest of the equation.  Then you try another coefficient, probably in front of a different compound, and see how it affects the equation.  You keep going this way until you have achieved a balanced equation.

Key Terms

Subscripts are numbers that follow an element in a compound formula to indicate how many atoms of that element are present in one molecule of the compound.  Once the subscripts are set for a compound, do not try to adjust them.

Coefficients are the numbers used to balance equations.  They appear in front of a compound to tell you how many molecules of that compound are needed to balance the equation.  If there is not a coefficient in front of a compound, it is understood to be a 1.

Hints for Balancing Equations

1. Start with an element that appears in only one spot on both sides of the equations.
2.    If a polyatomic ion appears on both sides of the equation, treat the entire ion as a single unit rather than breaking it down into the elements.
3.    A balanced equation has the smallest whole number ratios possible for coefficients.
4.    Save pure elements (as opposed to compounds) for the last.  You can force whatever coefficient is needed for that last element.
5.    Guess, and guess again!

Example 1:
Balance the thermite reaction:

Fe2O3 + Al => Al2O3 + Fe

Solution 1:
Oxygen is already balanced with 3 on each side.  Iron has two on the left but only one on the right.  Aluminum has one on the left and two on the right.  Since aluminum and iron both appear as pure elements, we can force the coefficients that we need and balance the equation easily.  Put a 2 in front of aluminum on the left, and a 2 in front of iron on the right.

Fe2O3 + 2 Al => Al2O3 + 2 Fe

Double check:  there are two irons on both sides, three oxygens and 2 aluminums.

Example 2:
Balance the following equation which shows the combustion (or burning) of propane:

C3H8 + O2 => CO2 + H2O

Solution 2:
There are 3 carbons on the left, but only 1 on the right.  There are 8 hydrogens on the left, but only 2 on the right.  There are 2 oxygens on the left, but 3 on the right.

Of the three atoms, carbon and hydrogen are the best to start with.  We should save oxygen for last for two reasons.  It appears by itself as the element on the left, and it appears in more than one place on the right.

Starting with carbon, we can put a 3 in front of CO2 on the right side to balance out the carbons.  Likewise, we can put a 4 in front of H2O on the right side to balance the hydrogens.

C3H8 + O2 =>  3 CO2 +  4 H2O

This gives us a total of 3 carbons on both sides, 8 hydrogens on both sides, 2 oxygens on the left and 10 oxygens on the right.  To balance the oxygens, we put a 5 in front of O2 on the left side.

C3H8 + 5 O2 => 3 CO2 + 4 H2O

Example 3:
Balance the following equation which represents some of the reactions in a water softening system.

NaCl + CaCO3 => Na2CO3 + CaCl2

Solution 3:
Since the carbonate ion is intact on both sides of the equation, we can treat it as one unit instead of breaking it down into carbon and oxygen.

As written, the calciums and carbonates are balanced with one on each side.  The sodiums and chlorides both have one on the left and two on the right.  We can balance both the sodium and chloride by placing a 2 in front of NaCl on the left.

2NaCl + CaCO3 => Na2CO3 + CaCl2