Chemical reactions & conservation of mass

What you will learn

state the Law of Conservation of Mass,
write a word equation, then a symbol equation for a reaction,
balance chemical equations by inspecting atom counts,
use conservation of mass to calculate an unknown mass,
recognise the common reaction types: synthesis, decomposition, displacement, combustion.

Worked example 0 Real-world example: why a rusted car weighs more

A $5\,000$ g steel plate is left in the rain. After three years it has corroded. Mass of rust collected: $5\,300$ g. Where did the extra $300$ g come from? Does this violate the Law of Conservation of Mass?

Rust is iron(III) oxide, written Fe $_2$ O $_3 \cdot x$ H $_2$ O. The iron combines with oxygen from the air and water from the rain.
Reaction: $4\text{Fe} + 3\text{O}_2 \to 2\text{Fe}_2\text{O}_3$ .
The $300$ g of extra mass is oxygen (and water) that joined the solid from the atmosphere.
If you weighed the air + steel + water system as a whole, the total mass would be unchanged. Nothing was created — oxygen moved from gas into solid.

Key idea: mass is conserved across the whole system, including gases you cannot see. Apparent gains and losses come from gases entering or leaving.

1. Word and symbol equations

A word equation names reactants and products:

\text{methane} + \text{oxygen} \to \text{carbon dioxide} + \text{water}.

A symbol equation uses chemical formulas:

\text{CH}_4 + 2\text{O}_2 \to \text{CO}_2 + 2\text{H}_2\text{O}.

Numbers in front of formulas are called coefficients. They multiply the whole formula, not just one element.

Worked example 1 Word to symbol

Convert this word equation to a symbol equation: “sodium + chlorine $\to$ sodium chloride”.

Sodium is Na; chlorine gas is Cl $_2$ ; sodium chloride is NaCl.
Unbalanced: $\text{Na} + \text{Cl}_2 \to \text{NaCl}$ .
Count atoms: LHS has $1$ Na, $2$ Cl. RHS has $1$ Na, $1$ Cl. Not balanced.
Balance Cl: put coefficient $2$ in front of NaCl $\to$ $\text{Na} + \text{Cl}_2 \to 2\text{NaCl}$ .
Now Na: LHS $1$ , RHS $2$ . Put $2$ in front of Na: $2\text{Na} + \text{Cl}_2 \to 2\text{NaCl}$ . Balanced.

2. Balancing chemical equations — step by step

Strategy:

Write the unbalanced equation.
Count atoms of each element on both sides.
Balance one element at a time, leaving H and O until last.
Use coefficients only — never change a formula (subscripts).
Re-check every element at the end.

Worked example 2 Balancing methane combustion

Balance: $\text{CH}_4 + \text{O}_2 \to \text{CO}_2 + \text{H}_2\text{O}$ .

Carbon: $1$ on each side — balanced.
Hydrogen: LHS $4$ , RHS $2$ . Put $2$ in front of H $_2$ O: $\text{CH}_4 + \text{O}_2 \to \text{CO}_2 + 2\text{H}_2\text{O}$ .
Oxygen: LHS $2$ , RHS $2 + 2 = 4$ . Put $2$ in front of O $_2$ : $\text{CH}_4 + 2\text{O}_2 \to \text{CO}_2 + 2\text{H}_2\text{O}$ .
Re-check: C $1 = 1$ ; H $4 = 4$ ; O $4 = 4$ . Balanced.

Worked example 3 Balancing a tricky one

Balance: $\text{Fe} + \text{O}_2 \to \text{Fe}_2\text{O}_3$ .

Iron: LHS $1$ , RHS $2$ . Put $2$ in front of Fe: $2\text{Fe} + \text{O}_2 \to \text{Fe}_2\text{O}_3$ .
Oxygen: LHS $2$ , RHS $3$ . Need a common multiple of $2$ and $3$ : use $6$ .
Put $3$ in front of O $_2$ (gives $6$ ) and $2$ in front of Fe $_2$ O $_3$ (gives $6$ O): $2\text{Fe} + 3\text{O}_2 \to 2\text{Fe}_2\text{O}_3$ .
Now Fe: LHS $2$ , RHS $4$ . Adjust Fe: $4\text{Fe} + 3\text{O}_2 \to 2\text{Fe}_2\text{O}_3$ .
Check: Fe $4 = 4$ ; O $6 = 6$ . Balanced.

3. Conservation of mass calculations

Because atoms are only rearranged, the total mass of reactants equals the total mass of products.

Worked example 4 Finding an unknown product mass

In the reaction $2\text{H}_2 + \text{O}_2 \to 2\text{H}_2\text{O}$ , $4$ g of hydrogen reacts with $32$ g of oxygen. What mass of water is formed?

Mass of reactants: $4 + 32 = 36$ g.
By conservation of mass, mass of products $= 36$ g.
Mass of water formed $= 36$ g.

Worked example 5 Losing apparent mass to a gas

$50$ g of calcium carbonate is heated: $\text{CaCO}_3 \to \text{CaO} + \text{CO}_2$ . The solid remaining in the test tube has mass $28$ g. How much CO $_2$ gas escaped?

Mass before: $50$ g.
Mass after (solid): $28$ g.
Mass lost as gas: $50 - 28 = 22$ g of CO $_2$ .
This matches conservation: no mass is missing; it just left as invisible gas.

4. Types of chemical reactions

Synthesis (combination): $A + B \to AB$ . E.g. $2\text{H}_2 + \text{O}_2 \to 2\text{H}_2\text{O}$ .
Decomposition: $AB \to A + B$ . E.g. $2\text{H}_2\text{O}_2 \to 2\text{H}_2\text{O} + \text{O}_2$ .
Displacement: a more reactive element pushes a less reactive one out. E.g. $\text{Zn} + \text{CuSO}_4 \to \text{ZnSO}_4 + \text{Cu}$ .
Combustion: a fuel burns in oxygen to release CO $_2$ and water (if it contains C and H).

Worked example 6 Predicting a displacement product

Predict the products of $\text{Mg} + \text{FeSO}_4 \to$ . Write a balanced equation.

Magnesium is more reactive than iron, so Mg will displace Fe from the sulfate.
Products: MgSO $_4$ and Fe metal.
Equation: $\text{Mg} + \text{FeSO}_4 \to \text{MgSO}_4 + \text{Fe}$ . Balanced as written.

Practice: Year 10

Fluency

Word and symbol equations

State the Law of Conservation of Mass in one sentence.
Write a word equation for the burning of hydrogen in oxygen.
Write the symbol equation for the decomposition of water by electricity into hydrogen and oxygen gas.
Identify the reactants and products in: $\text{Zn} + 2\text{HCl} \to \text{ZnCl}_2 + \text{H}_2$ .
What does the coefficient " $2$ " mean in " $2\text{H}_2\text{O}$ "?

Fluency

Balancing

Balance each equation.

$\text{H}_2 + \text{Cl}_2 \to \text{HCl}$ .
$\text{Na} + \text{O}_2 \to \text{Na}_2\text{O}$ .
$\text{Al} + \text{O}_2 \to \text{Al}_2\text{O}_3$ .
$\text{Mg} + \text{HCl} \to \text{MgCl}_2 + \text{H}_2$ .
$\text{C}_2\text{H}_6 + \text{O}_2 \to \text{CO}_2 + \text{H}_2\text{O}$ .
$\text{Fe}_2\text{O}_3 + \text{C} \to \text{Fe} + \text{CO}_2$ .

Fluency

Conservation of mass

$8$ g of sulfur reacts completely with $8$ g of oxygen. What is the mass of sulfur dioxide produced?
$10$ g of limestone (CaCO $_3$ ) decomposes to give $5.6$ g of calcium oxide. How much CO $_2$ was released?
A $3$ g magnesium ribbon burns in air and forms $5$ g of magnesium oxide. How much oxygen reacted?
$4.6$ g of sodium combines with $3.55$ g of chlorine gas. What mass of sodium chloride forms?
$20$ g of iron rusts completely by combining with oxygen to form $28.6$ g of iron(III) oxide. How much oxygen was used?

Reasoning

Reaction types and explain

Classify each: (a) $2\text{H}_2 + \text{O}_2 \to 2\text{H}_2\text{O}$ ; (b) $\text{CaCO}_3 \to \text{CaO} + \text{CO}_2$ ; (c) $\text{Cu} + 2\text{AgNO}_3 \to \text{Cu(NO}_3)_2 + 2\text{Ag}$ ; (d) $\text{C}_3\text{H}_8 + 5\text{O}_2 \to 3\text{CO}_2 + 4\text{H}_2\text{O}$ .
A student tries to balance $\text{H}_2 + \text{O}_2 \to \text{H}_2\text{O}_2$ by changing the water formula. Why is this wrong?
When iron rusts, the mass of the object appears to increase. Does this violate conservation of mass? Explain.
A candle burns and loses mass. Explain where the mass went.
Photosynthesis: $6\text{CO}_2 + 6\text{H}_2\text{O} \to \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2$ . If $88$ g of CO $_2$ and $36$ g of water react, what is the combined mass of glucose and oxygen produced?

Problem solving

Real reactions

When $5$ g of copper carbonate decomposes, $3.2$ g of copper oxide remains. What mass of CO $_2$ escaped? Write the balanced equation.
A zinc strip placed in copper sulfate solution gradually becomes coated in copper. Write the balanced equation and classify the reaction.
Write and balance the symbol equation for the complete combustion of butane (C $_4$ H $_{10}$ ) in oxygen.
Sodium metal reacts vigorously with water to produce hydrogen gas and sodium hydroxide. Write the balanced equation.

Challenge

Reasoning

Harder reasoning

$10.0$ g of CaCO $_3$ is heated in an open crucible. The decomposition reaction produces CaO and CO $_2$ . Explain how you could verify conservation of mass despite CO $_2$ escaping.
A sealed glass ampoule contains $3.0$ g of hydrogen and $24.0$ g of oxygen. After ignition all the hydrogen is consumed. What is the mass of water formed, and what is left in the ampoule?
Derive the balanced equation for the combustion of ethanol (C $_2$ H $_5$ OH) in oxygen, and use atom counting to verify the equation.
Antoine Lavoisier weighed reactants and products in sealed vessels to prove conservation of mass. Why would open-vessel experiments of the day fail to reveal this law? Give two examples where an open vessel would give misleading mass readings.