Balancing Equations

Purpose

• Chemical equations must be balanced to obey the law of conservation of mass. The law of conservation of mass states that for every atom you start a reaction with, you must end a reaction with. If we start a reaction with 1 mole of hydrogen atoms, we must end up with one mole of hydrogen atoms; though, they may be in a new compound.

Method of Balancing

• We balance an equation by adding coefficients in front of the chemical substances.– Example: The combustion of hydrogen gas with oxygen gas gives water.

H2 + O2 H2O

Notice that we begin with two hydrogen atoms and two oxygen atoms and end with two hydrogen atoms and one oxygen atom. Since we have less oxygen on the products side of the reaction than on the reactants side, we must add coefficients to balance it out.

• Add a 2 coefficient for H2O to get the oxygens the same

H2 + O2 2 H2O

We now have 2 H and 2 O in the reactants and 4 H and 2 O in the product. Notice how we multiplied the coefficient by everything in the formula. We are still unbalanced.• Add a 2 coefficient in front of H2 to get the hydrogens to both be 4.

2 H2 + O2 2 H2O

We now have 4 H and 2 O in the reactants and 4 H and 2 O in the products. We are now balanced.

Misconception alert

• Many students like to change the formulas to get a reaction to balance. From the previous example, some students may want to change the formula of the water as in the following:

H2 + O2 H2O2

• Do not do this! The combustion of hydrogen produces water, H2O. H2O2 is a different substance that is produced through a different reaction.

• Do not change formulas to balance, only add coefficients!

Another example• Balance the following equation:

C4H9OH + O2 CO2 + H2O

• First let’s balance the carbon by placing a 4 in front of the CO2

C4H9OH + O2 4 CO2 + H2O

Reactants Products

C 4 C 1

H 10 H 2

O 3 O 3

Reactants Products

C 4 C 4

H 10 H 2

O 3 O 9

Continued

Another example continued• Now balance the hydrogen by adding a 5 in front of H2O:

C4H9OH + O2 4 CO2 + 5 H2O

• Finally, balance the oxygen by placing a 6 in front of the O2

C4H9OH + 6 O2 4 CO2 + 5 H2O

Reactants Products

C 4 C 4

H 10 H 10

O 3 O 13

Reactants Products

C 4 C 4

H 10 H 10

O 13 O 13

A few hints to balancing

• If an atom exists on either side of the reaction all by itself, do not balance it until the end, because you can stick any coefficient in front of it and not change any other atom.

• If an atom shows up in many of the substances, leave it alone and it may work out in the end.

• Sometimes, trial and error is necessary. If a 1 coefficient does not work for the first substance, try a 2, then a 3 and so on until you get something that works.

Pause and Practice

• Balance the following reactions:

– Mg + AgNO3 Mg(NO3)2 + Ag

– C6H12 + O2 CO2 + H2O

– Fe2O3 + CO Fe + CO2

Pause and Practice Answers

• Balance the following reactions:

– Mg + 2 AgNO3 Mg(NO3)2 + 2 Ag

– C6H12 + 9 O2 6 CO2 + 6 H2O

– Fe2O3 + 3 CO 2 Fe + 3 CO2

Now try the exercise