- 1. Understanding the Numbers in Chemical Equations
- 2. Step-by-Step Method for Balancing Equations
- 3. Worked Examples
- 4. Common Mistakes to Avoid
- 5. Remember: Law of Conservation of Mass
Chemical equations show what happens during a chemical reaction. For an equation to be balanced – the same number of each type of atom must appear on both sides of the equation. This is because atoms are never created or destroyed in a chemical reaction – they just rearrange to form new substances.
1. Understanding the Numbers in Chemical Equations #
When looking at a chemical equation, you’ll notice two types of numbers:
Large Numbers (Coefficients) #
- Written in front of formulas (e.g., 2 H₂O)
- Tell you how many molecules or formula units are involved
- Multiply everything in the formula
- Example: 2 H₂O means two water molecules (4 H atoms and 2 O atoms total)
Small Numbers (Subscripts) #
- Written at the bottom right of an element symbol (e.g., H₂O)
- Tell you how many atoms of that element are in each molecule
- Part of the chemical formula itself
- Example: H₂O means each water molecule has 2 H atoms and 1 O atom
Counting Total Atoms #
To find the total number of each element in a chemical equation:
- Identify the coefficient (large number) in front of the formula
- Identify the subscript (small number) for the element
- Multiply the coefficient by the subscript
Example: 2 Fe₂O₃
- Iron (Fe) atoms: 2 (coefficient) × 2 (subscript) = 4 atoms
- Oxygen (O) atoms: 2 (coefficient) × 3 (subscript) = 6 atoms
2. Step-by-Step Method for Balancing Equations #
When you have the right side of an equation and need to balance the left side, follow these steps:
- Count the atoms on the right side of the equation
- Write down the formulas of the reactants on the left side (these are usually given)
- Add coefficients to balance each element
- Check that the same number of each atom appears on both sides
3. Worked Examples #
Example 1: ___ Fe + ___ O₂ → 2 Fe₂O₃ #
Step 1: Count atoms on the right side #
Fe atoms – Total of 4
- We have 2 × 2 = 4 atoms FROM 2 Fe₂O₃
O atoms – Total of 6
- We have 2 × 3 = 6 atoms FROM 2 Fe₂O₃
Step 2: Balance the left side #
We need 4 Fe atoms and 6 O atoms on the left side.
For Fe:
- We need 4 atoms
- So we write “4 Fe”
For O₂:
- Each O₂ molecule has 2 oxygen atoms
- To get 6 oxygen atoms, we need 3 O₂ molecules
- 3 × 2 = 6 atoms
- So we write “3 O₂”
Step 3: Write the balanced equation #
4 Fe + 3 O₂ → 2 Fe₂O₃
Step 4: Check #
Left side:
- Fe atoms: 4
- O atoms: 3 × 2 = 6
Right side:
- Fe atoms: 2 × 2 = 4
- O atoms: 2 × 3 = 6
The equation is balanced!
Example 2: ___ Al + ___ HCl → 2 AlCl₃ + 3 H₂ #
Step 1: Count atoms on the right side #
Al atoms – Total of 2
- We have 2 × 1 = 2 atoms FROM 2 AlCl₃
Cl atoms – Total of 6
- We have 2 × 3 = 6 atoms FROM 2 AlCl₃
H atoms – Total of 6
- We have 3 × 2 = 6 atoms FROM 3 H₂
Step 2: Balance the left side #
For Al:
- We need 2 atoms
- So we write “2 Al”
For HCl:
- Each HCl molecule has 1 H atom and 1 Cl atom
- We need 6 Cl atoms, so we need 6 HCl molecules
- This gives us 6 H atoms as well
- So we write “6 HCl”
Step 3: Write the balanced equation #
2 Al + 6 HCl → 2 AlCl₃ + 3 H₂
Step 4: Check #
Left side:
- Al atoms: 2
- H atoms: 6
- Cl atoms: 6
Right side:
- Al atoms: 2
- Cl atoms: 2 × 3 = 6
- H atoms: 3 × 2 = 6
The equation is balanced!
Example 3: ___ Mg + ___ HNO₃ → Mg(NO₃)₂ + H₂ #
Step 1: Count atoms on the right side #
Mg atoms – Total of 1
- We have 1 atom FROM Mg(NO₃)₂
N atoms – Total of 2
- We have 2 atoms FROM Mg(NO₃)₂
O atoms – Total of 6
- We have 6 atoms FROM Mg(NO₃)₂
H atoms – Total of 2
- We have 2 atoms FROM H₂
Step 2: Balance the left side #
For Mg:
- We need 1 atom
- So we write “Mg”
For HNO₃:
- Each HNO₃ molecule has 1 H, 1 N, and 3 O atoms
- We need 2 N atoms, so we need 2 HNO₃ molecules
- 2 HNO₃ gives us 2 H atoms, 2 N atoms, and 6 O atoms
- So we write “2 HNO₃”
Step 3: Write the balanced equation #
Mg + 2 HNO₃ → Mg(NO₃)₂ + H₂
Step 4: Check #
Left side:
- Mg atoms: 1
- H atoms: 2
- N atoms: 2
- O atoms: 2 × 3 = 6
Right side:
- Mg atoms: 1
- H atoms: 2
- N atoms: 2
- O atoms: 6
The equation is balanced!
4. Common Mistakes to Avoid #
- Changing subscripts – Never change the small numbers in a chemical formula as this changes the substance itself
- Forgetting to multiply – Remember to multiply the coefficient (large number) by the subscript (small number) to find the total number of atoms
- Not checking both sides – Always count atoms on both sides to make sure they match
5. Remember: Law of Conservation of Mass #
Balancing equations is based on the Law of Conservation of Mass: matter cannot be created or destroyed in a chemical reaction. The total mass of the reactants equals the total mass of the products.
This is why we need the same number of each type of atom on both sides of a chemical equation!
