# Balancing Chemical Equations with 5 Examples

Today we are talking about one of my favorite topics, which is balancing chemical equations. This is one of my favorite topics because it has elements of chemistry (since we are dealing with chemical equations), math (since we need to balance numbers on both sides of the equation), and puzzle-type fun (since we have to work to put all the pieces of the puzzle together to get a balanced equation). What could be better?

Before we get too excited, though, let’s take a step back and discuss this process systematically.

### Chemical Equations

First, some background. When we talk about chemical equations, we are generally talking about the conversion, or chemical reaction, of starting materials into products. This means that before we do a reaction, we have a certain type of molecule (or types of molecules), and after the reaction, we have different molecules. How does this happen? The chemical transformation that occurs involves breaking certain chemical bonds and forming new bonds, all of which end up creating new molecules from the original starting materials.

When we do these chemical reactions, we are following key laws of matter and energy. In particular, there is a law of conservation of matter, which states that matter cannot be created or destroyed; rather, it can only be converted from one form to another. This means that every atom that is in our starting materials needs to also be found in our products, and every atom found in our products must have come from atoms in the starting materials. Otherwise, we would be violating a fundamental law of matter! Not a good thing to do.

### How do we ensure that we are following the law of conservation of matter?

We look at the chemical equation that represents the particular reaction, and we count the number and types of different atoms to ensure that we have the same number and types of atoms on both sides of the equation. Sometimes, however, when we do this counting, we will see that we do not actually have the same number and types of atoms on both sides of the equation. Rather than concluding that we have violated a fundamental law of matter, however, we can simply balance the chemical equation and correct the discrepancy between the number and types of atoms on both sides of the equation.

What does it mean to balance the chemical equation? Let’s use a real-world reaction to discuss this process in more detail.

Consider the Haber process, which is a reaction between nitrogen gas and hydrogen gas to produce ammonia gas. We can represent each species involved in this chemical reaction by using the chemical formulas for these molecules: nitrogen is N2, hydrogen is H2, and ammonia is NH3. We use a subscript of (g) to indicate that all of the molecules are found in the gas phase, and an arrow to represent the fact that chemical transformation is occurring.

N2(g) + H2(g) → NH3(g)

This equation actually means that we are breaking bonds between the two nitrogen atoms in the nitrogen gas and the bonds between the hydrogen atoms in hydrogen gas, and forming new bonds between the nitrogen and hydrogen in the ammonia gas product. We can represent the bonds that exist in each molecule with straight lines between the atoms, and then re-write the equation as shown below.

In order to check that we have followed the law of conservation of matter, we can count the number and types of atoms on both sides of the chemical equation, which gives us the following information:

Starting materials: 2 nitrogen atoms, 2 hydrogen atoms

Products: 1 nitrogen atom, 3 hydrogen atoms

These numbers are not the same, which means that the chemical equation as written is not balanced. This is problematic, because we cannot write an equation that implies that one nitrogen atom has simply disappeared from the starting materials (going from two nitrogen atoms in the starting materials to one nitrogen atom in the product), nor can the equation imply that we have created a hydrogen atom from thin air in the product (going from two hydrogen atoms in the starting material to three in the product).

We balance this equation by recognizing that often times, more than one molecule of each species can be involved in the chemical reaction. This means that multiple hydrogen or nitrogen molecules can be involved in creating multiple ammonia molecules, and that by balancing the equation, we can figure out how many of each molecules are involved in the overall chemical reaction.

We balance the equation by changing the coefficients of each species (i.e., the number that appears in front of each molecule), because these coefficients represent the number of molecules involved in the overall reaction. Importantly, when there is no number there, it implies a number “1,” meaning that one molecule is involved in the reaction. We cannot change the subscripts, i.e., the small numbers written on the right of the atom symbols, because changing the subscripts would change the actual molecules and thereby change the fundamental nature of the chemical reaction that is occurring.

In this reaction, we see that if we add a 3 in front of H2, and a 2 in front of NH3, that leads to a reaction which has the same number and types of atoms on both sides of the chemical equation:

N2(g) + 3H2(g) → 2NH3(g)

We can also represent this reaction by showing the chemical structures of each species:

Checking this reaction, we see that each molecule on both sides of the reaction has two nitrogen atoms and two hydrogen atoms, which means that the equation is balanced. It also means that the overall chemical reaction involves one molecule of nitrogen gas and three molecules of hydrogen gas reacting to form two molecules of ammonia gas.

So overall, the process for balancing a chemical equation includes:

1. Writing the correct chemical formulas for the reactants and products
2. Manipulating the coefficients to ensure that the numbers and types of atoms on each side of the arrow are equal to each other.
3. After you are done with step 2, checking to make sure that the values match up.

Let’s practice balancing chemical equations in a few other examples:

#### Balancing Chemical Equations Example 1: Photosynthesis

One of the most important chemical processes is photosynthesis, or the process by which plants take in carbon dioxide and water and convert that into glucose and oxygen. I can write the (unbalanced) chemical equation for photosynthesis by using the chemical formulas for each of these species,

CO2 + H2O → C6H12O6 + O2,

where CO2 = carbon dioxide, H2O = water, C6H12O6 = glucose, and O2 = oxygen.

A quick glance at this equation indicates that it is not balanced in its current form, as there is a single carbon atom (C) on the left side of the equation but six carbon atoms on the right side. I can start to balance this by adding a coefficient of 6 in front of CO2:

6CO2 + H2O → C6H12O6 + O2

I also see that the left side has two hydrogen atoms (H) whereas the right side has 12, and so I add a coefficient of 6 in front of H2O to ensure 12 hydrogen atoms on the left side as well (multiplying the coefficient by the subscript = 6 x 2 = 12):

6CO2 + 6H2O → C6H12O6 + O2

Now I see that although my carbons and hydrogen atoms are balanced, I have more oxygen atoms on the left side (18 atoms) than on the right side (8 atoms). I want to address this issue without disturbing the balanced carbon and hydrogen atoms, and so I decide to add a coefficient to the O2 species on the right side (since that will only affect the oxygen atoms and not the carbon or hydrogen atoms). If I add a coefficient of 6 in front of the O2 molecule, I will end up with 18 oxygen atoms on the right side of the equation as well.

6CO2 + 6H2O → C6H12O6 + 6O2

I now do a final check to make sure that there is the same number and types of atoms on both sides of the chemical equation: 6 carbon atoms, 12 hydrogen atoms, and 18 oxygen atoms, which confirms that my equation is balanced correctly!

#### Balancing Chemical Equations Example 2: Reaction of aluminum with hydrochloric acid

This reaction can be used as a really exciting (albeit somewhat dangerous) demonstration of the reaction with a concentrated acid and a soda can. The (unbalanced) chemical reaction can be written as follows:

Al + HCl → AlCl3 + H2

We can see right away that this isn’t balanced, and so we will start by adding a 3 in front of the HCl.

Al + 3HCl → AlCl3 + H2

We then see that the number of hydrogen atoms isn’t balanced, and so we will add a “1.5” temporarily in front of the H2:

Al + 3HCl → AlCl3 + 1.5H2

This equation is technically balanced, but it has a problem: the coefficient of 1.5 in front of H2. Our coefficients always have to be whole numbers (because they represent the number of molecules, and we can’t have half of a molecule). In order to address this issue, we multiply all of the coefficients by 2, which allows us to keep the balance in the equation and arrive at a situation with whole number coefficients:

2Al + 6HCl → 2AlCl3 + 3H2

A quick check shows that we have the same number and types of atoms on both sides of the equation (2 Al atoms, 6 H atoms, and 6 Cl atoms), which means that the equation is balanced!

#### Balancing Chemical Equations Example 3: Burning propane gas in the presence of oxygen to form carbon dioxide and water

This reaction is a key part of how we use hydrocarbon gas as a source of fuel, but it is also part of how human activity is contributing to climate change. The unbalanced chemical reaction can be written as follows:

C3H8 + O2 → CO2 + H2O

Here we have to add a 3 in front of CO2, as well as a 4 in front of H2O:

C3H8 + O2 → 3CO2 + 4H2O

We have balanced the number of carbon and hydrogen atoms, and now need to balance the number of oxygen atoms, which we can do by adding a 5 in front of the O2:

C3H8 + 5O2 → 3CO2 + 4H2O

This balanced equation has 3 carbon atoms, 8 hydrogen atoms, and 10 oxygen atoms on both sides of the equation. Success!

#### Balancing Chemical Equations Example 4: Rusting of iron in the presence of oxygen and water to produce iron oxide

This chemical makes iron-containing objects turn color over time, from shiny metallic to a dull brown-red in color. Moreover, the properties of these materials can change as well, with reduced material strength and performance due to the rusting process.

The unbalanced chemical equation for this rusting process is shown below:

Fe + O2 + H2O → Fe(OH)3

We are going to start by balancing every atom except oxygen, because the fact that oxygen appears in multiple species on the left side of the equation means that it is more difficult to balance.

We have to add a 3 in front of H2O and a 2 in front of Fe(OH)3 in order to balance the hydrogen atoms. This means that we also have to add a 2 in front of Fe, resulting in the following equation:

2Fe + O2 + 3H2O → 2Fe(OH)3

The only atom which is not balanced now is oxygen, because we have five oxygen atoms on the left side of the equation and six oxygen atoms on the right side. If we use the same “trick” of temporarily adding a non-whole number coefficient to the equation, we can write the following balanced equation:

2Fe + 1.5O2 + 3H2O → 2Fe(OH)3

This equation is now balanced, and so I can multiply every coefficient by 2 in order to arrive at a balanced equation with whole number coefficients:

4Fe + 3O2 + 6H2O → 4Fe(OH)3

Checking all atoms shows that we have succeeded in balancing the equation – 4 Fe atoms, 12 O atoms, and 12 H atoms on both sides of the equation. Success!

#### Balancing Chemical Equations Example 5: Acid-base reaction with the production of carbon dioxide

An interesting reaction occurs between sodium carbonate (a base) and hydrochloric acid (an acid), to produce sodium chloride, water, and carbon dioxide, according to the following unbalanced chemical equation:

Na2CO3 + HCl → NaCl + H2O + CO2

I can start the balancing process by adding a 2 in front of NaCl in order to balance the Na atoms, and then adding a 2 in front of HCl to make sure that the Cl atoms are also balanced:

Na2CO3 + 2HCl → 2NaCl + H2O + CO2

This reaction has the same number of hydrogen atoms (2) on both sides of the chemical equation, as well as the same number of carbon atoms (1) and oxygen atoms (3). This means that the equation is now balanced correctly. Success!

Let’s conclude with some general tips about balancing chemical equations:

1. Generally, it makes sense to start the balancing by focusing on atoms that appear in only one species on each side of the equation.
2. Although the final balanced equation needs to have whole numbers as coefficients, you can use non-whole numbers temporarily, particularly if it is easier to balance the chemical equation in that way.
3. Multiplying all coefficients by the same number (or dividing by the same number) will not affect the balance of the chemical equation, and can be used to address non-whole number coefficients (that you may have introduced temporarily).
4. Always double check your equation at the end, to make sure that the number and types of atoms on both sides of the equation are equal to each other. Only then will you be able to conclude that you have successfully balanced the equation.

Author: Mindy Levine, Ph.D.

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