Unit 4 Chemical Reactions

AP Chemistry Law of Conservation of Mass

Why mass is conserved in every reaction, how open containers seem to break the rule, and the related laws of definite and multiple proportions, in four worked examples.

The law of conservation of mass is the reason chemical equations have to balance and the reason stoichiometry works at all. It is simple to state, but lab questions test it in a tricky way: a reaction in an open beaker can gain or lose mass on the balance. This page explains the law at the atom level, works through those cases, and covers the two related laws of chemical combination.

What the Law of Conservation of Mass Says and Why It Holds

Law of conservation of mass: in a chemical reaction, the total mass of the products equals the total mass of the reactants. It is sometimes called the law of conservation of matter.

The reason is at the particle level. A reaction breaks and forms bonds, so atoms are regrouped into new substances, but no atom is created or destroyed and every atom keeps its mass. Equal atom counts on both sides therefore mean equal mass on both sides, which is exactly what a balanced equation records.

Fig. 1 · Mass and atoms before and after burning methane

Open and Closed Systems: When Mass Seems to Change

Closed system: nothing can enter or leave, such as a sealed flask or bag. The mass on the balance stays the same throughout the reaction.
Open system: gases can escape or be taken in from the air. The balance reading can go down (a gas product leaves) or up (a gas reactant such as O₂ joins the solid).

Either way, mass is still conserved; the balance just is not weighing every reactant and product. When an experiment seems to break the law, look for a gas you did not weigh.

Law of definite proportions (law of constant composition): a pure compound always has the same elements in the same mass ratio. Water is always 11.19% hydrogen by mass, whatever its source. See pure substances and mixtures.
Law of multiple proportions: when two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in a small whole-number ratio (Example 4).

Together with conservation of mass, these laws were the evidence for atomic theory: they make sense only if matter comes in whole atoms of fixed mass.

Worked Example 1: Why Burning Magnesium Gains Mass

A 10.0 g strip of magnesium burns completely in air: 2Mg + O₂ → 2MgO. Find the mass of MgO formed and explain why the product is heavier than the metal.

Moles of Mg: 10.0 g ÷ 24.31 g/mol = 0.411 mol, which gives 0.411 mol MgO.
Mass of MgO: 0.411 mol × 40.31 g/mol = 16.6 g.
Mass gained: 16.6 − 10.0 = 6.6 g, the mass of oxygen taken from the air.

The ash weighs more than the metal, yet mass is conserved: 10.0 g of Mg plus 6.6 g of O₂ equals 16.6 g of MgO. The open-air balance simply never weighed the oxygen going in.

Worked Example 2: Why Baking Soda and Vinegar Lose Mass in an Open Beaker

8.40 g of baking soda (NaHCO₃) reacts completely with excess vinegar in an open beaker: NaHCO₃ + CH₃COOH → NaCH₃COO + H₂O + CO₂. By how much does the mass on the balance drop?

Moles of NaHCO₃: 8.40 g ÷ 84.01 g/mol = 0.100 mol, so 0.100 mol of CO₂ forms.
Mass of CO₂: 0.100 mol × 44.01 g/mol = 4.40 g, which escapes as gas.
Balance reading: drops by 4.40 g.

Run the same reaction in a sealed bag and the reading does not change at all, because the CO₂ stays inside. The difference between the two set-ups is the whole point of the law.

Worked Example 3: Finding a Missing Mass in a Decomposition

Heating 25.0 g of calcium carbonate produces 14.0 g of calcium oxide: CaCO₃ → CaO + CO₂. How much carbon dioxide forms?

Conservation of mass: mass of CO₂ = 25.0 g − 14.0 g = 11.0 g.
Check with stoichiometry: 25.0 g ÷ 100.09 g/mol = 0.250 mol CaCO₃, giving 0.250 mol × 44.01 g/mol = 11.0 g CO₂.

When every product but one has been weighed, subtraction finds the last one without any mole calculation. Both routes agree, which is a good self-check on a free-response answer.

Worked Example 4: Showing Multiple Proportions in CO and CO₂

Carbon forms two oxides, CO and CO₂. Find the mass of oxygen that combines with 1.000 g of carbon in each, and compare them.

CO: 16.00 g O per 12.01 g C, so 16.00 ÷ 12.01 = 1.332 g O per gram of C.
CO₂: 32.00 g O per 12.01 g C, so 2.664 g O per gram of C.
Ratio: 2.664 ÷ 1.332 = 2.000, a small whole number.

The whole-number ratio appears because a CO₂ molecule has exactly two oxygen atoms for every one in CO. Fractional atoms would give fractional ratios, which is never observed.

Five Conservation of Mass Practice Questions With Answers

12.0 g of carbon burns completely to form 44.0 g of CO₂. How much oxygen was used?
Show answer
44.0 − 12.0 = 32.0 g of O₂.
5.00 g of H₂ and 40.0 g of O₂ react in a sealed container. What is the total mass of the contents afterward?
Show answer
45.0 g. Whatever forms and whatever is left over, nothing leaves the container.
A student heats copper powder in an open crucible and finds the mass increases. Does this break the law of conservation of mass?
Show answer
No. The copper combines with oxygen from the air to form copper oxide; the added mass is that oxygen.
Nitrogen forms NO and NO₂. Find the oxygen per gram of nitrogen in each and their ratio.
Show answer
NO: 16.00 ÷ 14.01 = 1.142 g; NO₂: 2.284 g; ratio 2.000, as the law of multiple proportions predicts.
Why does a balanced equation guarantee conservation of mass?
Show answer
It has the same number of each kind of atom on both sides, and each atom keeps its mass, so the total mass on both sides is equal.

Common Conservation of Mass Mistakes

Forgetting gases. A gas reactant or product is easy to leave off the balance and off the calculation.
Saying an open-beaker result disproves the law. The missing or extra mass is a gas entering or leaving.
Conserving moles instead of mass. Mass is conserved; the total number of moles can change (2H₂ + O₂ → 2H₂O goes from 3 mol to 2 mol).
Balancing by changing subscripts. That changes the substance; balance with coefficients so the atoms, and the mass, match.
Confusing the two proportion laws. Definite proportions is about one compound; multiple proportions compares two compounds of the same elements.
Mixing up physical and chemical changes. Mass is conserved in both; only chemical changes rearrange atoms.

Conservation of mass underlies every stoichiometry and limiting-reactant answer in Unit 4. To see how stronger Unit 4 answers would move your overall estimate, try the AP Chem Score Calculator.

Frequently Asked Questions

What is the law of conservation of mass?

In a chemical reaction, the total mass of the products equals the total mass of the reactants. Atoms are rearranged into new substances but are never created or destroyed, so the mass does not change.

Why does burning wood seem to lose mass if mass is conserved?

Because some of the products, carbon dioxide and water vapor, are gases that escape into the air. If every product and every reactant, including the oxygen used, were weighed in a sealed container, the total mass would be unchanged.

What is the law of definite proportions?

Also called the law of constant composition, it states that a pure compound always contains the same elements in the same mass ratio. Every sample of pure water is 11.19% hydrogen and 88.81% oxygen by mass.

What is the law of multiple proportions?

When two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in a small whole-number ratio. In CO and CO₂, the oxygen per gram of carbon is in a 1 : 2 ratio.

How does the law of conservation of mass relate to balancing equations?

A balanced equation has the same number of each kind of atom on both sides. Because atoms keep their masses, equal atom counts guarantee that the reactants and products have equal total mass.

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