*This lesson is by Lynda Jones. It was originally on a website, balancingequations.info, but that website no longer exists.*

### Our first idea: the law of conservation of mass: Every atom which goes* into* a chemical reaction must come out of it as well..

*into*

### Example: 3 **red**, 2 **yellow** and 5** blue** atoms go *into* the reaction.

*into*

### And they all come out the other side.

### That is the first condition you must meet to have a balanced equation.

**“Conservation”** means that nothing gets lost, nothing gets created out of thin air.

### “Mass” refers to the amount of matter.

### There is no such thing as “losing atoms” in a chemical reaction. Nor can atoms suddenly appear when they weren’t there in the first place.

**Coefficients and Subscripts:**

### Know how to interpret the **two kinds of numbers** found in chemical equations.

**two kinds of numbers**

**Large numbers** in **red** are called **“coefficients,”** because they “appear with” the formulas and act as multipliers. (“Co” means “with” and “efficient” comes from a Latin word meaning “to accomplish.”

### **small numbers** in **blue** are called **“subscripts,”** because they are written below the line. (“Script” for “writing” and “sub” for “below.”)

**Color Coding to make it simple**

### For now we’ll use colored circles as our “atoms” and the first letters of their color names as our “chemical symbols.” For example:

**Subscripts Tell How Many Atoms of Each Kind**

**The subscript** tells us how many atoms of each kind exist in any formula.

The **subscript** is ALWAYS written **AFTER **the symbol of the atom to which it refers.

### When an atom appears only ONCE in a formula, we don’t write the subscript, because it’s not needed.

**Combining Two Different “Color” Atoms**

### What happens when we combine two or more different atoms together? How do we write the formulas then? We’ll write the formula for a molecule made of one atom of blue and one atom of white.

### Since we are only working with colors and not actual element symbols, it does not matter whether we write “B” first or “W” first.

### Notice also that the formula stays the same, regardless of the molecule’s orientation.

### Now we will write the formula for 1 atom of blue and 2 atoms of white.

### In most cases when 1 atom of one kind and 2 of another are put together, the *single* atom will be the central atom of the molecule, as shown in the first four examples in the box above.

### The last two examples, in which blue is NOT the central atom, were added to show that the formula describing how many atoms there are of each kind is the same, regardless of how the atoms are connected or how they are oriented in space.

### Now we will combine 1 atom of blue and 3 atoms of white.

### In this case, the atoms will almost always connect with each other as shown in the first example, although the second example is still possible.

### Main point: the subscript written after a symbol tells how many atoms of that kind there are in the formula. It does not give any information about HOW the atoms are connected to each other.

**Just a side note: **There ARE rules for writing chemical formulas, such as which atom symbol is written first, and the formulas CAN show something about connectivity, especially in the case of organic molecules (molecules which exist in living creatures)

### Our goal here is to understand enough about formulas to balance a chemical equation, so we will ignore the rules of writing sophisticated chemical formulas for now.

### Here is one more set of examples showing how the subscript gives us information about the number of each kind of atom in a formula.

**Coefficients are Multipliers**

### Let’s see how coefficients are used in chemical equations.

### A **coefficient** is a **multiplier**. Here are some examples.

### The **coefficient** multiplies, and applies to, the ENTIRE FORMULA written after it, not just the first letter.

### When you have the balanced equation, you can multiply the **coefficient** by the **subscript** for each atom in the formula to find out how many total atoms you have of each kind.

### (Remember, when there is only one atom of a kind in the formula there is no subscript written, so we use **“1”** as the subscript multiplier.)

## Don’t make this mistake:

### The number of atoms of each kind is the same in both cases, but these two molecules are VERY different from each other.

### Don’t write “3 BW2” as “B3W6” or anything like that.

## Balancing Equations

### Now let’s start actually balancing equations. Just remember that once formulas in the initial equation are correct, the **ONLY **thing you can do is to add **groups** by changing the **coefficients**.

### Once the formulas are correct, you must **NOT** change the **subscripts**.

**Example 1: **

### Look at this simple equation. Underneath it are drawings of the molecules these formulas represent. Find the lowest number of groups of each formula – such that all the atoms are accounted for, and balanced on both sides of the equation.

### The **“reactants side”** of the equation is anything written **BEFORE** the arrow. The **“products side”** of the equation is anything written **AFTER** the arrow.

….

### It can be seen by inspection that there are 2 **red** atoms on the left and only 1 **red** atom on the right. Thus, this equation is NOT balanced.

### In order to balance the equation, we need at least 1 more **red** atom on the right side, but we cannot add JUST 1 **red** atom. Rather, we must add an entire **GROUP** of atoms which contains our **red** atom of interest.

### It’s like buying a box of crayons. In order to get one crayon of a certain color, you must buy the entire box, because they just don’t come one crayon at a time.

### We have to add at least one **red** atom to the right side, but in order to do that, we have to add one entire group, so let’s do that and see what we get.

### Adding the group balances our **red** atoms, giving us 2 **red** atoms on each side. However, now the **whites** are unbalanced. We have 2 **white** atoms on the left side of the arrow but 4 on the right side. What should we do? Of course, **“add a group.”**

### Now if we look at the equation, we see that there are the **same number** of **each kind** of **atom** on **both** sides of the equation.

### So this equation is now balanced. All that is left for us to do is write down the **coefficients.**

### Remember, you cannot represent “2 W2” as “W4.”

## Nor can you represent “2 RW2” as “R2W4.”

So the balanced equation is:

## Example 2

nnn

### First let’s balance the **blue** atoms. How many **blue** atoms are there on the left, or **“reactants side”** of the equation? How many on the right, or **“products side”**?

### In order to get one more atom of **blue** on the right side, what do we need to add? Yes, we need to add an entire **group.** So let’s do that.

### See that we have also added the red **coefficient**, **2**, in front of the formula, BW3 , to reflect the addition. This now balances our **blue** atoms, but the **whites** are still unbalanced. How many **white** atoms do we have on the right side of the equation? *[Answer: 6]*

### And how do we get 6 atoms of **white** on the left hand side? Yes, by adding groups. What is the total number of groups we need on the left to balance the **6 whites** on the right?

So now we have another correctly balanced equation.

## Example 3

### With this equation, first let’s look at the yellow atoms. There is 1 yellow on the left, but 2 yellows on the right. What do we do?

### OK. This balances our yellows, but our reds are still unbalanced. What do we do next?

### The **ONLY** thing we can EVER do in balancing equations, once the formulas are correct, is to **ADD groups.**

### So what groups should we add? If we add one group of R2, as shown below, this still doesn’t balance the **reds.**

### Can you guess the secret? The secret is to find the **least common multiple,** (yes, an application of math!) between the original 2 **reds** on the left side and the 3 **reds** on the right.

### What is the **least common multiple **of 2 and 3? [Answer: 6] How do we get 6 **reds** on both sides?

### Yes, “3 groups of 2” and “2 groups of 3.”

### But now the **yellows** are unbalanced again. What do we do next? Remember, 4 Y does NOT equal Y4.

### We change the** coefficient** in front of “Y” to 4.

### So the final balanced equation is:

### One last word: When balancing equations, you ALWAYS want the lowest possible numbers. For example, the above equation may also be written as

### All of these equations are also technically “balanced,” but on a test ONLY the lowest numbered choice, i.e., “4Y + 3R2 => 2Y2R3” would be correct. We **ALWAYS** want the equations with the **lowest numbers.**

**Review:**

### You should now understand the basics for balancing chemical equations.

### 1. **ALL** balanced equations must obey the **Law of Conservation of Mass**, which means that they must have the **same number** of atoms of **each kind** on **both sides** of the equation.

### 2. The **subscript **tells how many atoms of each kind there are in a formula.

### 3. The **coefficient** is a multiplier, multiplies every atom in the formula along with its **subscript,** and is the **ONLY** number which may be changed in balancing equations.(Once formulas are correct, the ONLY way to add atoms is by adding **groups.**)

### 4. P.S. You **ALWAYS** want the lowest possible numbers.

## Additional materials

Go to this game: Balance all 10 equations. Write the balanced equation.

Go to this game: Balance all 11 equations. Write the balanced equations

Chembalancer from FunBasedLearning

Balancing Chemical Equations

Chemistryland teaches all about balancing equations

Online alternate texbook Chap 4: Chemical Rxns and Balancing equations

## Learning Standards

Massachusetts Science Tech Curriculum Frameworks

HS-PS1-7. Use mathematical representations and provide experimental evidence to support the claim that atoms, and therefore mass, are conserved during a chemical reaction. Use the mole concept and proportional relationships to evaluate the quantities (masses or moles) of specific reactants needed in order to obtain a specific amount of product.

College Board Standards For Success in Science

C-PE.1.4.5 Given a simple chemical reaction (e.g., synthesis of water, decomposition of hydrogen peroxide, combustion of methane)

C-PE.1.4.5a Write a balanced chemical reaction.

C-PE.2.3.1 Construct a balanced symbolic representation, based on given reactants and products, of a chemical reaction. Construct a molecular-level representation of the chemical reaction, and explain, using the concept of atoms, why matter is conserved during any change.