Conservation of mass

Burn 16.04 g of methane in 64.00 g of oxygen and you get 44.01 g of carbon dioxide and 36.03 g of water: 80.04 g before and after.

Drag to turn. Scroll or pinch to zoom.

Stacked masses before and after. Striped blocks are gases. Open the lid and the scale stops counting gases that leave or arrive.

A log weighs a few kilograms, and after it burns the ash weighs far less. A nail left outside grows heavier as it rusts. For centuries these two facts made it look as if matter could vanish in some reactions and appear in others. Both turn out to be the same mistake: the scale was not weighing the gases. Smoke and carbon dioxide leave the fire, and oxygen from the air joins the iron.

Lavoisier and the sealed flask

BackgroundThe French chemist Antoine-Laurent Lavoisier settled the question by weighing everything, including the air. In a memoir for the Academy of Sciences dated 1774 and published in 1777, he described heating tin sealed inside a glass vessel. The solids in the vessel gained mass, and the air sealed in with them lost exactly the same mass, so the vessel as a whole weighed the same as before. The extra mass of the metal had come out of the air. In his textbook Traité élémentaire de chimie of 1789 he stated the rule that in every operation an equal quantity of matter exists before and after. Lavoisier was executed in 1794 during the French Revolution, but the law outlived him.

Today the rule is called the law of conservation of mass, or of matter: there is no detectable change in the total quantity of matter when one kind of matter turns into another. A balanced equation is the same law written in atoms. Atoms are not created or destroyed in a chemical reaction, so if the atoms balance, the masses must balance too.

From atoms to grams

To turn an equation into masses, chemists count in moles. One mole is 6.02214076 × 10²³ particles, a number fixed exactly in the International System of Units. The mass of one mole of a substance, its molar mass, is the sum of the atomic weights in its formula, in grams. With IUPAC atomic weights of 1.008 for hydrogen, 12.011 for carbon and 15.999 for oxygen, methane CH₄ is 12.011 + 4 × 1.008 = 16.043 g per mole, O₂ is 31.998 g, CO₂ is 44.009 g and H₂O is 18.015 g.

Now read CH₄ + 2O₂ → CO₂ + 2H₂O in moles. One mole of methane, 16.043 g, reacts with two moles of oxygen, 63.996 g, for a total of 80.039 g. The products are one mole of CO₂, 44.009 g, and two moles of water, 36.030 g, which again adds to 80.039 g. Move the amount slider in the lab and both columns grow together; the totals never part.

Why open containers seem to break the law

Choose calcium carbonate in the lab. Heated strongly, 100.09 g of it becomes 56.08 g of calcium oxide and 44.01 g of carbon dioxide gas. In a sealed container the scale reads 100.09 g at the end. With the lid open the gas drifts away and the scale shows only 56.08 g. Baking soda and vinegar behave the same way, losing the mass of the carbon dioxide bubbles. Tin does the reverse: in an open container it takes oxygen from the air, so the solid gains mass, exactly what Lavoisier measured. In every case the missing or extra mass is a gas, and the atoms are all accounted for.

What is the molar mass of water, H₂O, to one decimal place?
16.04 g of methane burns in 64.00 g of oxygen. What is the total mass of the products in grams?
Heating 100.09 g of CaCO₃ gives 56.08 g of CaO. How many grams of CO₂ form?
Why does a burning log leave lighter ash?
- Gases such as CO₂ escape into the air
- Mass is destroyed by fire
- Heat has negative mass
- Ash is made of new atoms
Tin heated in an open container gains mass because…
- It combines with oxygen from the air
- Heat adds mass
- Tin atoms split
- Water condenses on it
In which year was Lavoisier's Traité élémentaire de chimie published?
How many particles are in one mole?
- 6.02214076 × 10²³
- 1,000
- 6.02 × 10¹⁰
- 100
2 mol of H₂ react completely with O₂ (2H₂ + O₂ → 2H₂O). About how many grams of water form?
Baking soda and vinegar react in an open cup. The scale reading afterwards is…
- Lower, because CO₂ escapes
- Higher, because foam is heavy
- Exactly the same
- Zero

Key points

Total mass is the same before and after a reaction (Lavoisier, 1789).
Molar mass = sum of atomic weights in grams; one mole is 6.02214076 × 10²³ particles.
Open containers lose or gain gases, so the scale changes while the atoms stay the same.

Sources for this course (14)

OpenStax Chemistry 2e (openstax.org/books/chemistry-2e): 1.2 law of conservation of matter, 1.3 chemical change (rust, combustion, cooking and rotting)
4.1 balancing by inspection (CH4 + 2O2, 2H2O to 2H2 + O2, 2N2 + 5O2 to 2N2O5)
4.2 precipitation (PbI2 from KI and Pb(NO3)2, AgCl insoluble)
redox (Na + Cl2, copper wire in silver nitrate)
combustion, 5.1 specific heat of water 4.184 J/g °C, 5.3 enthalpy (ΔH < 0 exothermic; ΔHc CH4 −890.8, H2 −285.8, ethanol −1366.8, methanol −726.1 kJ/mol; 1.00 L isooctane 33,100 kJ; ozone formation endothermic)
12.2 factors affecting rates (sodium and iron in air, calcium and sodium in water, sawdust, rate roughly doubles per 10 °C, phosphorus in pure oxygen, air about 20% oxygen, H2O2 decomposition)
12.5 collision theory and Arrhenius equation (R = 8.314 J/mol/K, catalytic converters)
12.7 catalysis and enzymes
NIST Chemistry WebBook methane ΔcH°gas −890.7 ± 0.4 kJ/mol (webbook.nist.gov)
NIST CODATA Avogadro constant 6.022 140 76 × 10²³ mol⁻¹ exact (physics.nist.gov)
IUPAC CIAAW abridged standard atomic weights (H 1.0080, C 12.011, N 14.007, O 15.999, Na 22.990, Ca 40.078, Fe 55.845, Sn 118.71; ciaaw.org)
ACS International Historic Chemical Landmark, The Chemical Revolution of Antoine-Laurent Lavoisier (acs.org, Traité élémentaire de chimie 1789, quotation on conservation of mass)
Lavoisier, memoir on the calcination of tin in closed vessels, Mémoires de l'Académie Royale des Sciences for 1774, published 1777 (via web.lemoyne.edu/giunta/classicalcs/lavoisier.html)
PubChem sodium bicarbonate and acetic acid pages (pubchem.ncbi.nlm.nih.gov).

Checked: 2026-10-17