Balancing Chemical Equations

Overview

Chemical equations must be balanced to obey the Law of Conservation of Mass: atoms cannot be created or destroyed in a chemical reaction. The number of atoms of each element must be equal on both sides.

Basic Rules

1. Never change subscripts (changes the compound)
2. Only change coefficients (the numbers before formulas)
3. Balance one element at a time
4. Save H and O for last (often in multiple compounds)
5. Coefficients should be the smallest whole numbers

Step-by-Step Method

Step 1: Write the unbalanced equation

Step 2: Count atoms on each side

Step 3: Add coefficients to balance

Step 4: Verify all atoms are balanced

Examples

Example 1: Simple Combustion

Unbalanced:

$$\text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$$

Count atoms:

Element	Reactants	Products
C	1	1
H	4	2
O	2	3

Balance H first:

$$\text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}$$

Now count O: Products have $2 + 2 = 4$ oxygen atoms

Balanced:

$$\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \checkmark$$

Example 2: Synthesis

$$4\text{Al} + 3\text{O}_2 \rightarrow 2\text{Al}_2\text{O}_3 \checkmark$$

Example 3: Decomposition

$$2\text{KClO}_3 \rightarrow 2\text{KCl} + 3\text{O}_2 \checkmark$$

Example 4: Single Replacement

$$\text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2 \checkmark$$

Example 5: Double Replacement

$$2\text{AgNO}_3 + \text{CaCl}_2 \rightarrow 2\text{AgCl} + \text{Ca(NO}_3\text{)}_2 \checkmark$$

Types of Chemical Reactions

1. Synthesis (Combination)

$$\text{A} + \text{B} \rightarrow \text{AB}$$ $$2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$$

2. Decomposition

$$\text{AB} \rightarrow \text{A} + \text{B}$$ $$2\text{H}_2\text{O} \rightarrow 2\text{H}_2 + \text{O}_2$$

3. Single Replacement

$$\text{A} + \text{BC} \rightarrow \text{AC} + \text{B}$$ $$\text{Zn} + \text{CuSO}_4 \rightarrow \text{ZnSO}_4 + \text{Cu}$$

4. Double Replacement (Metathesis)

$$\text{AB} + \text{CD} \rightarrow \text{AD} + \text{CB}$$ $$\text{NaCl} + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{NaNO}_3$$

5. Combustion

$$\text{C}_x\text{H}_y + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$$ $$\text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O}$$

Combustion Reactions

For hydrocarbons ($\text{C}_x\text{H}_y$):

$$\text{C}_x\text{H}_y + \left(x + \frac{y}{4}\right)\text{O}_2 \rightarrow x\text{CO}_2 + \frac{y}{2}\text{H}_2\text{O}$$

Example: Octane (C₈H₁₈)

$$2\text{C}_8\text{H}_{18} + 25\text{O}_2 \rightarrow 16\text{CO}_2 + 18\text{H}_2\text{O}$$

Polyatomic Ions

When polyatomic ions appear unchanged on both sides, balance them as a unit.

$$3\text{Ca(OH)}_2 + 2\text{H}_3\text{PO}_4 \rightarrow \text{Ca}_3(\text{PO}_4)_2 + 6\text{H}_2\text{O} \checkmark$$

Tips for Difficult Equations

1. Balance metals first
2. Balance polyatomic ions as units
3. Balance H and O last
4. If you get fractions, multiply everything by the denominator
5. Double-check by counting all atoms

Fraction Example

$$\text{C}_2\text{H}_6 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$$

Step by step:

$$\text{C}_2\text{H}_6 + \frac{7}{2}\text{O}_2 \rightarrow 2\text{CO}_2 + 3\text{H}_2\text{O}$$

Multiply by 2:

$$2\text{C}_2\text{H}_6 + 7\text{O}_2 \rightarrow 4\text{CO}_2 + 6\text{H}_2\text{O} \checkmark$$

State Symbols

Symbol	State
(s)	Solid
(l)	Liquid
(g)	Gas
(aq)	Aqueous (dissolved in water)

Example with States

$$2\text{Na}(s) + 2\text{H}_2\text{O}(l) \rightarrow 2\text{NaOH}(aq) + \text{H}_2(g)$$