Why Do Chemical Equations Need to Be Balanced?

A chemical reaction changes substances into new substances.

For example, hydrogen can react with oxygen to produce water:

hydrogen + oxygen → water

Using chemical formulas:

H₂ + O₂ → H₂O

However, this equation is not balanced.

Count the atoms:

Reactants:

• H = 2
• O = 2

Products:

• H = 2
• O = 1

One oxygen atom appears to have disappeared.

That cannot happen in an ordinary chemical reaction.

The equation must therefore be balanced.

---

The Law of Conservation of Mass

The law of conservation of mass states:

Mass is neither created nor destroyed during an ordinary chemical reaction.

Atoms are rearranged during chemical reactions, but they are not created or destroyed.

Therefore:

total mass of reactants = total mass of products

This is the fundamental reason chemical equations must be balanced.

---

Conservation of Mass at the Particle Level

Imagine a reaction involving several atoms.

Before the reaction, the atoms may be connected in one arrangement.

After the reaction, those same atoms may be connected differently.

The important idea is:

The atoms are rearranged, not replaced.

For example:

Before:

A–A + B–B

After:

A–B + A–B

There are still:

• 2 A atoms
• 2 B atoms

Only their arrangement has changed.

---

Closed and Open Systems

Conservation of mass is easiest to observe in a closed system, where matter cannot enter or leave.

In a closed container:

mass before reaction = mass after reaction

Sometimes a reaction in an open container appears to lose mass because a gas escapes into the surroundings. The matter has not been destroyed; it has simply left the container.

---

Reactants and Products

Every chemical equation has two main sides.

Reactants → Products

The reactants are the substances present at the beginning of the reaction.

The products are the new substances formed.

For example:

2Mg + O₂ → 2MgO

Reactants:

• magnesium, Mg
• oxygen, O₂

Product:

• magnesium oxide, MgO

The arrow means:

reacts to form or produces

---

Reading Chemical Equations

Consider:

2H₂ + O₂ → 2H₂O

This can be read as:

Two molecules of hydrogen react with one molecule of oxygen to produce two molecules of water.

The equation communicates:

• which substances react
• which substances form
• the relative numbers of particles involved

---

Chemical Formulas and Subscripts

A subscript tells us how many atoms of an element are present in one particle or formula unit.

For example:

H₂O

contains:

• 2 H atoms
• 1 O atom

CO₂

contains:

• 1 C atom
• 2 O atoms

CaCl₂

contains:

• 1 Ca atom
• 2 Cl atoms

Subscripts are part of the chemical formula.

---

Coefficients

A coefficient is a number placed in front of a chemical formula.

For example:

3H₂O

The coefficient 3 means:

3 water molecules

Each water molecule contains:

• 2 H atoms
• 1 O atom

Therefore:

3H₂O

contains:

• 6 H atoms
• 3 O atoms

---

Coefficients Multiply the Entire Formula

Consider:

4CO₂

One CO₂ molecule contains:

• 1 C
• 2 O

Four CO₂ molecules contain:

• 4 C
• 8 O

Therefore:

coefficient × subscript = total number of that atom

---

Coefficients and Subscripts Are Different

This distinction is extremely important.

Consider:

2H₂O

The coefficient 2 tells us there are two water molecules.

The subscript 2 tells us each water molecule contains two hydrogen atoms.

Therefore:

2H₂O

contains:

4 H atoms and 2 O atoms

---

Never Change Subscripts to Balance an Equation

Suppose we have:

H₂ + O₂ → H₂O

We need two oxygen atoms on the product side.

It may be tempting to change:

H₂O

to:

H₂O₂

But this changes the substance.

H₂O = water

H₂O₂ = hydrogen peroxide

They are different compounds.

When balancing equations:

Change coefficients, never chemical subscripts.

---

Balancing the Formation of Water

Start:

H₂ + O₂ → H₂O

Count atoms.

Reactants:

• H = 2
• O = 2

Products:

• H = 2
• O = 1

Balance oxygen by placing 2 before H₂O:

H₂ + O₂ → 2H₂O

Now count again.

Products:

• H = 4
• O = 2

Oxygen is balanced, but hydrogen is not.

Place 2 before H₂:

2H₂ + O₂ → 2H₂O

Now:

Reactants:

• H = 4
• O = 2

Products:

• H = 4
• O = 2

Balanced.

---

What Does the Balanced Equation Mean?

The balanced equation:

2H₂ + O₂ → 2H₂O

shows a particle ratio of:

2 : 1 : 2

This means:

2 hydrogen molecules react with 1 oxygen molecule to form 2 water molecules.

It could also represent:

4 hydrogen molecules + 2 oxygen molecules → 4 water molecules

because the same ratio is maintained.

---

A Strategy for Balancing Equations

A reliable method is:

Step 1: Write the correct chemical formulas.

Step 2: Count each type of atom on both sides.

Step 3: Choose an element that is not balanced.

Step 4: Add a coefficient.

Step 5: Count the atoms again.

Step 6: Continue until every element is balanced.

Step 7: Reduce the coefficients to the smallest whole-number ratio if necessary.

Step 8: Perform a final atom count.

---

Example 1: Magnesium and Oxygen

Start:

Mg + O₂ → MgO

Count:

Reactants:

• Mg = 1
• O = 2

Products:

• Mg = 1
• O = 1

Balance oxygen:

Mg + O₂ → 2MgO

Now products contain:

• Mg = 2
• O = 2

Balance magnesium:

2Mg + O₂ → 2MgO

Final count:

Reactants:

• Mg = 2
• O = 2

Products:

• Mg = 2
• O = 2

Balanced.

---

Example 2: Sodium and Chlorine

Start:

Na + Cl₂ → NaCl

Count:

Reactants:

• Na = 1
• Cl = 2

Products:

• Na = 1
• Cl = 1

Balance chlorine:

Na + Cl₂ → 2NaCl

Now products contain:

• Na = 2
• Cl = 2

Balance sodium:

2Na + Cl₂ → 2NaCl

Balanced equation:

2Na + Cl₂ → 2NaCl

---

Example 3: Formation of Ammonia

Start:

N₂ + H₂ → NH₃

Count nitrogen first.

Reactants:

N = 2

Products:

N = 1

Place 2 before NH₃:

N₂ + H₂ → 2NH₃

Now products contain:

H = 6

Place 3 before H₂:

N₂ + 3H₂ → 2NH₃

Final count:

Reactants:

• N = 2
• H = 6

Products:

• N = 2
• H = 6

Balanced.

---

Example 4: Hydrogen Chloride

Start:

H₂ + Cl₂ → HCl

Reactants:

• H = 2
• Cl = 2

Products:

• H = 1
• Cl = 1

Place 2 before HCl:

H₂ + Cl₂ → 2HCl

Now:

Reactants:

• H = 2
• Cl = 2

Products:

• H = 2
• Cl = 2

Balanced.

---

Example 5: Aluminium Oxide

Start:

Al + O₂ → Al₂O₃

This is more challenging.

Oxygen appears as:

2 atoms in O₂

and:

3 atoms in Al₂O₃

The smallest common multiple of 2 and 3 is:

6

Use:

3O₂

to give 6 oxygen atoms.

Use:

2Al₂O₃

to give 6 oxygen atoms.

Now:

Al + 3O₂ → 2Al₂O₃

The products contain:

4 Al atoms

So place 4 before Al:

4Al + 3O₂ → 2Al₂O₃

Balanced.

---

Using Multiples When Balancing

The aluminium oxide example demonstrates an important strategy.

If one side contains oxygen in groups of 2 and the other in groups of 3:

2, 4, 6, 8...

and:

3, 6, 9, 12...

the first common value is:

6

This tells us useful coefficients are:

3O₂

and:

2Al₂O₃

Recognizing common multiples can make balancing much faster.

---

Example 6: Iron and Oxygen

Start:

Fe + O₂ → Fe₂O₃

As before, oxygen appears in groups of 2 and 3.

Use 6 oxygen atoms:

Fe + 3O₂ → 2Fe₂O₃

Now the products contain:

4 Fe

So:

4Fe + 3O₂ → 2Fe₂O₃

Balanced.

---

Example 7: Methane Combustion

Methane reacts with oxygen to produce carbon dioxide and water.

Start:

CH₄ + O₂ → CO₂ + H₂O

Balance carbon:

C is already balanced.

Balance hydrogen:

Reactants have:

4 H

Place 2 before water:

CH₄ + O₂ → CO₂ + 2H₂O

Now count oxygen on the product side:

CO₂ contains 2 O.

2H₂O contains 2 O.

Total:

4 O atoms

Therefore use:

2O₂

Balanced equation:

CH₄ + 2O₂ → CO₂ + 2H₂O

---

Example 8: Propane Combustion

Start:

C₃H₈ + O₂ → CO₂ + H₂O

Balance carbon:

C₃H₈ + O₂ → 3CO₂ + H₂O

Balance hydrogen:

C₃H₈ + O₂ → 3CO₂ + 4H₂O

Now count oxygen on the products:

3CO₂ gives:

6 O

4H₂O gives:

4 O

Total:

10 O

Therefore:

5O₂

Balanced equation:

C₃H₈ + 5O₂ → 3CO₂ + 4H₂O

---

A Useful Order for Balancing

There is no single order that works perfectly for every equation, but a useful strategy is:

• begin with elements appearing in only one compound on each side
• leave hydrogen and oxygen until later when possible
• balance unchanged polyatomic ions as groups when appropriate
• recount everything at the end

For combustion reactions involving hydrocarbons, a useful order is often:

carbon → hydrogen → oxygen

---

Counting Atoms Carefully

Consider:

2Al₂O₃

The coefficient 2 multiplies the entire formula.

Aluminium:

2 × 2 = 4 Al

Oxygen:

2 × 3 = 6 O

So:

2Al₂O₃

contains:

• 4 aluminium atoms
• 6 oxygen atoms

This multiplication is essential when checking balanced equations.

---

Particle Relationships

Balanced equations are not just bookkeeping.

They describe particle relationships.

Consider:

N₂ + 3H₂ → 2NH₃

At the particle level:

1 N₂ molecule

reacts with:

3 H₂ molecules

to produce:

2 NH₃ molecules

The coefficients give the relative numbers of particles.

---

Ratios in Balanced Equations

Consider:

2H₂ + O₂ → 2H₂O

Coefficient ratio:

2 : 1 : 2

This means that if we double everything:

4 : 2 : 4

the reaction relationship is still correct.

Or multiply by 10:

20 : 10 : 20

The relative ratio remains:

2 : 1 : 2

---

Coefficients Do Not Usually Represent Individual Atoms

Consider:

2Na + Cl₂ → 2NaCl

At a particle level, the equation describes the relative numbers of reacting particles or formula units.

For molecular substances, we can talk about molecules.

For ionic substances such as NaCl, we normally describe formula units, because solid sodium chloride forms a giant ionic lattice rather than existing as separate NaCl molecules.

This distinction becomes increasingly important in chemistry.

---

Balanced Equations and Mass

Consider:

2H₂ + O₂ → 2H₂O

The equation conserves atoms.

Because atoms have mass, conserving the number and type of atoms also conserves total mass.

The atoms have simply changed their arrangement.

This connects the particle model directly to the law of conservation of mass.

---

Why Mass May Appear to Change

Suppose a carbonate reacts with an acid in an open flask and produces carbon dioxide gas.

If the gas escapes, the measured mass of the flask and its contents decreases.

Does this violate conservation of mass?

No.

The carbon dioxide still exists. It has simply entered the surroundings.

If the entire reaction and gas were contained in a closed system, the total mass would remain constant.

---

Reactions That Take In Gases

The opposite can also happen.

Suppose a metal reacts with oxygen from the air.

The solid product may have a greater mass than the original metal.

This does not mean mass was created.

The additional mass came from:

oxygen in the air

The total mass of the metal plus oxygen is conserved.

---

State Symbols

Chemical equations sometimes include state symbols.

These show the physical state of each substance:

(s) = solid

(l) = liquid

(g) = gas

(aq) = aqueous, dissolved in water

For example:

2Mg(s) + O₂(g) → 2MgO(s)

State symbols provide additional information but do not affect whether the equation is balanced.

---

Balancing with State Symbols

Consider:

H₂(g) + O₂(g) → H₂O(l)

First balance the formulas exactly as before:

2H₂(g) + O₂(g) → 2H₂O(l)

The state symbols remain attached to their substances.

Do not count state symbols as atoms.

---

Word Equations and Symbol Equations

A word equation shows substance names:

magnesium + oxygen → magnesium oxide

A symbol equation uses chemical formulas:

Mg + O₂ → MgO

A balanced symbol equation shows correct formulas and conserved atoms:

2Mg + O₂ → 2MgO

These forms communicate increasingly detailed information.

---

Checking Whether an Equation Is Balanced

Consider:

2Na + Cl₂ → 2NaCl

Count atoms.

Left:

• Na = 2
• Cl = 2

Right:

• Na = 2
• Cl = 2

Therefore:

balanced

Now consider:

Na + Cl₂ → NaCl

Left:

• Na = 1
• Cl = 2

Right:

• Na = 1
• Cl = 1

Therefore:

not balanced

---

Worked Example 1

Balance:

H₂ + Br₂ → HBr

Count:

Left:

• H = 2
• Br = 2

Right:

• H = 1
• Br = 1

Add coefficient 2:

H₂ + Br₂ → 2HBr

Balanced.

---

Worked Example 2

Balance:

K + O₂ → K₂O

Balance oxygen first:

K + O₂ → 2K₂O

Now the products contain:

4 K

Therefore:

4K + O₂ → 2K₂O

Balanced.

---

Worked Example 3

Balance:

Ca + H₂O → Ca(OH)₂ + H₂

Start by examining Ca.

Ca is already balanced.

Ca(OH)₂ contains:

• 2 O
• 2 H in the hydroxide groups

Use 2H₂O:

Ca + 2H₂O → Ca(OH)₂ + H₂

Count:

Left:

• Ca = 1
• H = 4
• O = 2

Right:

• Ca = 1
• H = 4
• O = 2

Balanced.

---

Worked Example 4

Balance:

Na + H₂O → NaOH + H₂

Start by balancing sodium and the water relationship:

2Na + 2H₂O → 2NaOH + H₂

Count:

Left:

• Na = 2
• H = 4
• O = 2

Right:

• Na = 2
• H = 4
• O = 2

Balanced.

---

Worked Example 5

Balance:

CaCO₃ → CaO + CO₂

Count:

Left:

• Ca = 1
• C = 1
• O = 3

Right:

CaO gives:

• Ca = 1
• O = 1

CO₂ gives:

• C = 1
• O = 2

Total right-side oxygen:

3

The equation is already balanced:

CaCO₃ → CaO + CO₂

Not every equation needs additional coefficients.

---

Worked Example 6

Balance:

Fe + HCl → FeCl₂ + H₂

Fe is already balanced.

The product contains:

2 Cl

Therefore use:

2HCl

Equation:

Fe + 2HCl → FeCl₂ + H₂

Count hydrogen:

Left = 2 H

Right = 2 H

Balanced.

---

Worked Example 7

Balance:

P₄ + O₂ → P₂O₅

Balance phosphorus:

P₄ + O₂ → 2P₂O₅

Products now contain:

10 O

Therefore use:

5O₂

Final equation:

P₄ + 5O₂ → 2P₂O₅

---

Worked Example 8

Balance:

C₂H₆ + O₂ → CO₂ + H₂O

Balance carbon:

C₂H₆ + O₂ → 2CO₂ + H₂O

Balance hydrogen:

C₂H₆ + O₂ → 2CO₂ + 3H₂O

Products contain:

4 + 3 = 7 oxygen atoms

This initially gives:

7/2 O₂

Fractions can be useful during working:

C₂H₆ + 7/2O₂ → 2CO₂ + 3H₂O

Multiply every coefficient by 2:

2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O

Now all coefficients are whole numbers.

---

Smallest Whole-Number Coefficients

Consider:

4H₂ + 2O₂ → 4H₂O

This equation is balanced.

However, all coefficients can be divided by 2:

2H₂ + O₂ → 2H₂O

Chemical equations are normally written using the smallest whole-number ratio.

---

Particle Diagrams and Balanced Equations

A particle diagram should agree with its balanced equation.

For:

2H₂ + O₂ → 2H₂O

a correct particle model should show:

Before:

• 2 H₂ particles
• 1 O₂ particle

After:

• 2 H₂O particles

Count the atoms in the picture:

Before:

• 4 H
• 2 O

After:

• 4 H
• 2 O

The visual model confirms conservation of atoms.

---

From Particle Diagram to Equation

Suppose a particle diagram shows:

Before:

• 1 N₂ molecule
• 3 H₂ molecules

After:

• 2 NH₃ molecules

The corresponding equation is:

N₂ + 3H₂ → 2NH₃

Particle diagrams can therefore be translated directly into coefficients.

---

What Balanced Equations Do Not Tell Us

A balanced chemical equation provides important information, but it does not automatically tell us:

• how quickly the reaction occurs
• how much energy is released
• the reaction temperature
• the reaction mechanism
• whether the reaction will happen easily
• the actual amount used in a particular experiment

A balanced equation primarily describes:

which substances react and their relative particle relationships.

---

Common Mistakes

Mistake 1: Changing subscripts

Incorrect:

H₂ + O₂ → H₂O₂

if the intended product is water.

Changing the subscript changes the substance.

---

Mistake 2: Forgetting that coefficients multiply the whole formula

For:

3CO₂

there are:

3 C and 6 O

not 3 C and 2 O.

---

Mistake 3: Balancing only one element

Every element must have the same number of atoms on both sides.

---

Mistake 4: Forgetting diatomic elements

Some elements commonly appear as diatomic molecules, including:

H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂

For example, elemental oxygen is normally written:

O₂

not:

O

---

Mistake 5: Not reducing coefficients

4H₂ + 2O₂ → 4H₂O

is balanced, but:

2H₂ + O₂ → 2H₂O

is the preferred simplest ratio.

---

Error Analysis

A student balances:

Mg + O₂ → MgO

as:

Mg + O₂ → MgO₂

The student has changed the chemical formula.

That changes magnesium oxide into a different formula rather than balancing the original reaction.

Correct approach:

2Mg + O₂ → 2MgO

---

Another Error Analysis

A student writes:

2H₂ + O₂ → 2H₂O

and counts:

Products:

H = 2

O = 1

This ignores the coefficient.

The coefficient multiplies the entire formula.

For:

2H₂O

Hydrogen:

2 × 2 = 4

Oxygen:

2 × 1 = 2

Therefore the equation is balanced.

---

Why Balanced Equations Matter

Balanced equations are fundamental to chemistry because they allow chemists to:

• represent chemical reactions accurately
• demonstrate conservation of mass
• compare quantities of reactants and products
• predict particle relationships
• perform chemical calculations
• plan laboratory reactions
• calculate expected product quantities
• understand industrial chemical processes

Balanced equations provide the foundation for stoichiometry, where these particle ratios are used to calculate actual amounts of substances.

---

A Final Balancing Checklist

Before deciding that an equation is balanced, check:

1. Are all chemical formulas correct?

2. Have only coefficients been changed?

3. Is every element present in equal numbers on both sides?

4. Have coefficients been applied to the entire formula?

5. Are the coefficients whole numbers?

6. Are they in the smallest whole-number ratio?

7. Does the equation make sense as a particle relationship?

If the answer to all seven is yes, the equation is properly balanced.

---

Did You Know?

Chemical equations are a symbolic way of representing events happening on an enormous particle scale.

A balanced equation such as:

2H₂ + O₂ → 2H₂O

does not mean chemists normally react only two hydrogen molecules.

A laboratory sample contains enormous numbers of particles.

The equation tells us the ratio in which those particles react.

Whether we imagine:

2 : 1 : 2

or:

2,000 : 1,000 : 2,000

or enormously larger quantities, the same particle relationship applies.

---

Key Terms

• Chemical reaction: Process in which substances are transformed into new substances.
• Chemical equation: Symbolic representation of a chemical reaction.
• Reactant: Starting substance in a chemical reaction.
• Product: Substance formed during a chemical reaction.
• Law of conservation of mass: Mass is not created or destroyed during an ordinary chemical reaction.
• Balanced equation: Chemical equation containing equal numbers of each type of atom on both sides.
• Coefficient: Number placed before a chemical formula showing the relative number of particles or formula units.
• Subscript: Small number in a chemical formula showing the number of atoms of an element within the formula.
• Molecule: Discrete group of covalently bonded atoms.
• Formula unit: Simplest whole-number ratio represented by an ionic compound's formula.
• Closed system: System in which matter cannot enter or leave.
• Open system: System in which matter can enter or leave.
• State symbol: Symbol showing whether a substance is solid, liquid, gas, or aqueous.
• Particle ratio: Relative numbers of particles represented by coefficients.
• Stoichiometry: Quantitative study of reactants and products using balanced chemical equations.

---

Key Rules

Conservation of mass:

total mass of reactants = total mass of products

For every element:

number of atoms before reaction = number of atoms after reaction

When balancing equations:

Change coefficients only.

Never change subscripts.

Coefficients multiply:

the entire chemical formula

Balanced equations should normally use:

the smallest whole-number coefficients

---

Key Takeaways

• Chemical reactions rearrange atoms into new combinations.
• Atoms are not created or destroyed during ordinary chemical reactions.
• The law of conservation of mass explains why chemical equations must be balanced.
• In a closed system, the total mass before and after a chemical reaction remains constant.
• Apparent mass loss can occur in an open system when a gaseous product escapes.
• Apparent mass gain can occur when a substance reacts with matter from the surroundings, such as oxygen.
• Reactants appear on the left side of a chemical equation.
• Products appear on the right side.
• The reaction arrow means "reacts to form" or "produces."
• Subscripts describe the composition of a chemical substance.
• Coefficients describe relative numbers of particles or formula units.
• A coefficient multiplies every atom in the formula following it.
• Chemical formulas must not be changed when balancing equations.
• Changing a subscript changes the identity of the substance.
• Equations are balanced by changing coefficients.
• Each element must have the same number of atoms on both sides of a balanced equation.
• Common multiples can help balance elements appearing in different numerical groups.
• Equations should normally be reduced to the smallest whole-number coefficient ratio.
• Particle diagrams provide a visual way to check conservation of atoms.
• Balanced equations describe particle relationships as ratios.
• Molecular substances can be interpreted in terms of molecules.
• Ionic substances are more appropriately described using formula units.
• State symbols provide information about physical state but do not affect atom balancing.
• A balanced equation does not automatically describe reaction rate, energy change, or reaction conditions.
• Balanced equations provide the foundation for quantitative chemical calculations and stoichiometry.
• A final atom count is one of the most reliable ways to check that an equation has been balanced correctly.