Balancing Chemical Equations

Chemical Reactions

The following diagrams graphically illustrate two simple chemical reactions. Notice the difference between the subscripts (ex. H₂) and the coefficients (shown in red) in these reactions. When balancing reactions, the coefficients can (and usually need to be) changed, but the subscripts present in the molecular formula can not be altered.

H₂ + Cl₂ --> 2 HCl

Reaction of H2 + Cl2

2 H₂ + O₂ --> 2 H₂O

Reaction of H2 + O2

Definitions

In a chemical reaction, atoms are NOT created or destroyed. What changes in a chemical reaction is the connections (bonds) between atoms. In the first reaction shown above, two hydrogen atoms (H) start out bonded to each other. During the course of the chemical reaction, this H-H bond breaks and a new H-Cl bond is formed.

A balanced chemical equation is a 'description' that accounts for all of the atoms in a chemical reaction. Every atom that appears in the reactant side (left side = starting material) MUST be accounted for in the products (right side). If five carbon atoms are present on the left side of a chemical equation, there must be exactly five carbon atoms on the right side. This is accomplished by changing the coefficients (the numbers in front of the formula). You are NOT allowed to change to formula to balance a chemical equation.

Balancing Chemical Equations

While there is not set procedure for balancing equations that works every time, the following steps will generally produce a balanced equation without requiring excess steps.

Be sure that the formulas for each compound are written correctly. (Usually this will be taken care of).
Select the 'simplest' element to begin balancing the equation. The 'simplest' element is an element that only occurs in one compound in the reactants and in one compound in the products.
Change the coefficients of the compounds containing the selected element so that the same number of atoms of this element occur on both the reactant and product sides of the equation.
Go back to Step #2, selecting the 'next simplest' element. Repeat steps 2-4 as until every element is 'balanced'.
After you are finished, check the final balanced equation to make sure every element is still balanced.

In general, you only want to change any coefficient one time. If you change a coefficient a second time, you will probably cause one of the 'earlier' elements to become 'unbalanced'.

Example: Combustion of ethanol

Question: Balance the following equation for the combustion of ethanol.

CH₃CH₂OH + O₂ ----> CO₂ + H₂O

In this reaction, all of the compounds have the correct formulas. The next step is to select the 'simplest' element. Either carbon (C) or hydrogen (H) could be used. For this example, we will select carbon. Following step #3, we change the coefficients in front of ethanol (CH₃CH₂OH) and carbon dioxide (CO₂). Since there are two carbon atoms in ethanol and only one carbon atom in CO₂, we add a two in front of CO₂.

1 CH₃CH₂OH + ____ O₂ ----> 2 CO₂ + ____ H₂O

This equation now has two carbon atoms on the reactant side and two carbon atoms on the product side, so the carbon atoms are balanced. The 'next simplest element' is hydrogen (H). Like before, we change the coefficients in front of ethanol and water (H₂O) to balance this element. One ethanol molecule contains six (6) hydrogen atoms, and one water molecule contains two (2) hydrogen atoms. To balance this, we need three water molecules (3x2=6).

1 CH₃CH₂OH + ____ O₂ ----> 2 CO₂ + 3 H₂O

Finally, we need to balance the oxygen atoms. On the reactants (left) side of this equation we have three (3) oxygen atoms, while on the product (right) side we have seven (7) oxygen atoms. (Two O atoms/CO₂ times 2 = 4 oxygen atoms PLUS one O atom/H₂O times 3 = 3 oxygen atoms. 4+3=7).

Since the reactant side has fewer oxygen atoms, we need to change one or both coefficients to increase the number of oxygen atoms. However, we do NOT want to change the coefficient in front of ethanol because we have already used this to balance carbon. (This is why I put a one in front of this molecule). Changing the coefficient in front of oxygen (O₂) will give the correct answer.

1 CH₃CH₂OH + 3 O₂ ----> 2 CO₂ + 3 H₂O

Finally, it is a good idea to check to be sure the equation really is still balanced.

	1 CH₃CH₂OH	+	3 O₂	---->	2 CO₂	+	3 H₂O
Carbon (C):	2	+	0	=	2	+	0
Hydrogen (H):	6	+	0	=	0	+	6
Oxygen (O):	1	+	6	=	4	+	3