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Lesson 3.1: Chemical Equations

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Chemistry is the science that explains changes in nature that we call transformations. Transformations, unlike the less radical changes that we call physical, are when one kind of thing becomes a different kind of thing. How is it possible for one kind of thing to become a different kind of thing? By a rearrangement of atoms.

Here is an example. Hydrogen gas is one kind of thing. It is made up of hydrogen molecules, H2. Oxygen gas is another kind of thing. It is made up of oxygen molecules, O2. If we combine the atoms of each in a new arrangement, we can make water, H2O, a different kind of thing – a thing with its own unique properties. When combined in the right ratio, nothing but water is made – there is no sign of residual oxygen or hydrogen.

How can we represent this transformation?

That is the topic of this lesson. Transformative changes, called chemical reactions, can be represented by chemical equations. We write the formula for each starting substance, called reactants, separated by a plus sign, followed by an arrow to indicate the transformation, and then the formula for each made substance – each unique substance again separated by a plus sign. The made substance are called products. The order in which the substances are shown, on the reactant or product side does not matter. In the example above, hydrogen and oxygen are the reactants, and there is only one product, water. We can write the hydrogen first or the oxygen – they represent the same thing.

How can we write a chemical equation representing this chemical reaction? Here is a start.

reactant + reactant → product

H2 + O2 → H2O

As written there is a problem with this representation. Not all of the atoms shown on the reactant side are accounted for in the products. In particular, there is one oxygen atom unaccounted for. We say that it is unbalanced.

How can we write the equation so that all of the material is accounted for? Perhaps we can write

H2 + O2 → H2O + O

That does not work either. The equation is now balanced, but if this were correct we would expect two products, water and very reactive oxygen. In fact, we find only the properties of water as product.

Is this any better?

H2 + O2 → H2O2

It is better in being both balanced and showing only one product as found by experiment, but the formula shown is not that of water (but of hydrogen peroxide).

So how do we represent the transformation correctly?

First, we can place coefficients in front of each formula to represent the numbers of molecules involved. This can show more molecules without introducing new substances. We go back and forth adding enough molecules in our equation until all atoms are accounted for without introducing new substances like O or H2O2 in the above example.

We can show this with pictures and then in a shorthand form just using the equation.

Before the reaction took place.


After the first water molecule is made.


Showing another hydrogen molecule allows us to use up the leftover oxygen atom.


Now all molecules are used up and we made only one substance, water. We write the equation as

2H2 + O2 → 2H2O

Example 1: Write the balanced chemical equation for the production of water from its elements.

Start with the unbalanced equation. Make sure the formulas are correct. These cannot change while balancing – all we change are the coefficients.

H2 + O2 → H2O

Step 1: Two water molecules are needed to use up the two oxygen atoms in the oxygen molecule, so place a 2 in front of the H2O to show the two molecules that need to be made.

H2 + O22H2O

Step 2: We cannot make two H2O molecules with just a single H2 molecule, so add a 2 in front of the H2 to show the hydrogen molecules needed.

2H2 + O2 → 2H2O

The equation is now balanced!

How can we use pictures to show the balanced chemical equation for the reaction between methane and oxygen to produce carbon dioxide and water?

Before the reaction took place.


After the first carbon dioxide molecule is made.


Showing another oxygen allows us to use up the leftover hydrogen atoms.


Now all molecules are used up and we made only carbon dioxide and water. We write the equation as

CH4 + 2O2 → CO2 + 2H2O

Example 2: Write the balanced chemical equation for the combustion of methane.

Start with the unbalanced equation. Make sure the formulas are correct. These cannot change while balancing – all we change are the coefficients.

CH4 + O2 → CO2 + H2O

Step 1: Two water molecules are needed to use up the 4 hydrogen atoms in the methane molecule, so place a 2 in front of the H2O to show the two molecules that need to be made.

CH4 + O2 → CO2 + 2H2O

Step 2: We cannot make two H2O molecules and one CO2 molecule with just a single O2 molecule. We need four atoms of oxygen to makes these three molecules, so add a 2 in front of the O2 to show the oxygen molecules needed.

CH4 + 2O2 → CO2 + 2H2O

The equation is now balanced!

Example 3: Write the balanced chemical equation for the combustion of butane.

Start with the unbalanced equation. Make sure the formulas are correct. These cannot change while balancing – all we change are the coefficients.

C4H10 + O2 → CO2 + H2O

Step 1: Four CO2 molecules are needed to use up the four carbon atoms in butane. We add a 4 in front of CO2.

C4H10 + O24CO2 + H2O

Step 2: Five H2O molecules are needed to use up the ten hydrogen atoms in C4H10. We add a 5 in front of H2O.

C4H10 + O2 → 4CO2 + 5H2O

Step 3: To make four CO2 molecules requires 8 oxygen atoms. To make five H2O molecules requires another 5 oxygen atoms. So we need a total of 13 oxygen atoms. Since they come in pairs we need 6.5 molecules of O2.

C4H10 + 6.5O2 → 4CO2 + 5H2O

Step 4: We cannot have half of a molecule (which would introduce an oxygen atom and thus a new substance), so we multiply our coefficients by two. This keeps the ratio of molecules the same but yields whole numbers.

2C4H10 + 13O2 → 8CO2 + 10H2O