4.3 Representations of Reactions

Just as net ionic equations provide information about interactions with ions in aqueous solutions, chemical reaction equations are a great way to visually track physical changes and chemical reactions. However, before we can examine these equations to observe these changes, we need to learn how to properly set up the equation for a chemical reaction. In other words, we need to learn how to balance equations. If an equation isn’t balanced, our answers will be incorrect. But why is it bad if it’s unbalanced, and how can we learn to balance equations easily?🤔

Image Courtesy of Quizizz

Why Do We Balance Reactions?

The law of conservation of mass is a fundamental principle in chemistry that states that the amount of matter stays constant in a closed system. In short, matter cannot be neither created nor destroyed in thin air. 

A chemical reaction is a closed system, so the number of atoms that are produced must be equal to the number of atoms put in. The atoms can still rearrange, though, which is all a chemical reaction really does! In conclusion, we need to make sure that the number of elements in the reactants is the same as those in the products, even if the products are different than what we started with. Whew🤯. That was a lot. Let’s look at an example to make sense of this.

Example #1

Here’s the chemical equation that represents the synthesis of carbon dioxide: CO (g) + O₂ (g) → CO₂ (g)

Step 1 

Get a general feel of the equation, and make sure it’s not already balanced. Take a look at the products and the reactants. Note the number of each element on both sides. If the number of one element is equal on both sides, it’s balanced. 

In this case, there is 1 carbon atom on both sides, so carbon is balanced. However, there are 3 oxygen molecules on the reactant side and 2 on the product side, so oxygen is not.

Step 2

Look at the elements that are only in one compound on both sides of the equation and are already balanced. In this case, it’s carbon. From this, we know that both of those compounds with carbon will have to have the same coefficient. Thus, we can leave the coefficients of CO and CO₂ as 1 for now.

** Remember that we can only change the coefficients of the molecules. If we change the subscript, we would change the molecule completely. For example, 2NO2 represents two molecules of nitrogen dioxide, but N2O4 represents one molecule of dinitrogen tetroxide. Coefficients should always be a whole number.**

Step 3

Find elements that are only in one compound on both sides but have different numbers of atoms on each side. Balance those elements. In our example, we don’t have any in this category (don’t worry😌, the next example will have one!).

Step 4

Look for elements that appear in multiple compounds on one side. Balance those elements. In our equation, that’s oxygen. Since there is less oxygen on the product side, let’s increase the coefficient of CO₂ to 2:

CO (g) + O₂ (g) → 2CO₂ (g)

As stated in step two, since both sides have an equal number of carbon, both CO and CO2 must have the same coefficient so that carbon remains balanced. Thus, we have to increase the coefficient of CO to 2 as well.

2CO (g) + O₂ (g) → 2CO₂ (g)

Now let’s make sure it really is balanced:

Sweet! Both the reactants and products have the same number of each atom. We followed the Law of Conservation of Mass!🥳 

Example #2

Here’s the equation: Li (s) + N₂ (g) → Li₃N (s)

Step 1

Like before, let’s make sure the equation’s not already balanced. Take a look at the products and the reactants and note the number of atoms of each element on both sides. 

There is 1 lithium molecule on the reactant side and 3 on the product side. There are 2 nitrogen molecules on the reactant side and 1 on the product side. Neither lithium nor nitrogen is balanced, so we must find a way to balance both.

Step 2

Look at the elements that are only in one compound on both sides of the equation and have the same number of atoms on both sides. Balance those elements. In our example, no such element exists, meaning no matter what we change, we will not have to make sure that we are unbalancing an element (like we would have carbon in the last example).

Step 3

Find elements that are only in one compound on both sides but have different numbers of atoms on each side. Balance those elements. In our example, both lithium and nitrogen fall into this category. In this situation, it’s more like a guess-and-check, but we can go about it strategically.

Since there are 3 lithium molecules on the right, let’s increase the coefficient of Li to 3.

3Li (s) + N₂ (g) → Li₃N (s)

Lithium is all balanced! Now, looking at nitrogen, we notice that there are 2 on the left and only 1 on the right. Let’s increase the coefficient of Li₃N to 2.

3Li (s) + N₂ (g) → 2Li₃N (s)

Nitrogen looks good! But wait…lithium is no longer balanced! Fear not, we have the power to change coefficients ✊ until the chemical equation is completely balanced. Since there are 6 molecules of lithium on the right, let’s increase the coefficient of Li to 6 on the reactant side.

6Li (s) + N₂ (g) → 2Li₃N (s)

Step 4

Look at the elements that are in more than one compound. In this example, there is no element.

Time to double-check our work. Try to always do this, as you may have "unbalanced" one element when trying to balance another.

Steps to Balancing Equations

Woohoo! We balanced another equation! It’s probably evident that the more practice you do, the better you’ll be at balancing equations. Be sure to keep the steps we used in mind:

1. Make sure the equation isn’t already balanced
2. Find the elements that are only in one compound on both sides and have the same number of atoms on both sides. These must have equal coefficients.
3. Look at the elements that are only in one compound on both sides and have different numbers of atoms on both sides. Balance them.
4. Look at the elements that are in more than one compound. Balance them.
5. Finally, double-check your answer and make sure that the number of element X on the reactants side is the same as on the products side. The key to this is satisfying the law of conservation of mass.

Review Activity

Balance the following equations and include the states of matter of both reactants and products:

1. Na₃PO₄ + AgNO₃ → Ag₃PO₄ + NaNO₃
2. A reaction between iron (III) oxide and carbon monoxide
3. The combustion of ethane (C₂H₆)
4. The synthesis of sulfur trioxide
5. The decomposition of potassium chlorate

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Answers to Balancing Practice Problems

Question 1) Na₃PO₄ (aq) + 3AgNO₃ (aq) → Ag₃PO₄ (s) + 3NaNO₃ (aq)

Question 2) Fe₂O₃ (s) + 3CO (g) → 2Fe (s) + 3CO₂ (g)

Question 3) 2C₂H₆ (g) + 7O₂ (g) → 4CO₂ (g) + 6H₂O (l)

Question 4) 2SO₂ (g) + O₂ (g) → 2SO₃ (g)

Question 5) 2KClO₃ (s) → 2KCl (aq) + 3O₂ (g)