Law of Conservation of Mass in Reactions
The law of conservation of mass in reactions states that the total mass of the reactants equals the total mass of the products in a closed system, because chemical reactions rearrange atoms without creating or destroying them. In brief: when 4.86 g of magnesium burns completely with 3.20 g of oxygen, exactly 8.06 g of magnesium oxide forms; a balanced equation shows the same number of atoms of each element on both sides.
The law is the reason why chemical equations must be balanced and why a mass calculation in chemistry works. This article applies the law to reactions. It explains the link between mass conservation and atom counting, shows how to verify the law with calculations, discusses open and closed systems, gives the experiments of Lavoisier and Landolt that tested it, explains the tiny exception that comes from relativity, and lists common mistakes.
Why is mass conserved in a reaction?
In a chemical reaction, bonds between atoms are broken and new bonds form, but the nuclei of the atoms are unchanged. The same atoms are present before and after, so the total mass is constant. The law was an important step in the development of chemistry in the 18th century, as it showed that chemical changes can be studied by weighing.
The law has two practical consequences. First, an equation must have the same number of atoms of each element on both sides. Second, if you know the mass of all reactants and all but one product, you can calculate the mass of the missing product.
How do you check with atom counting?
Count the atoms of each element on both sides of the equation, multiplying each subscript by the coefficient. For the combustion of propane, C3H8 + 5O2 → 3CO2 + 4H2O:
| Element | Atoms in reactants | Atoms in products | Balanced? |
|---|---|---|---|
| C | 3 | 3 × 1 = 3 | Yes |
| H | 8 | 4 × 2 = 8 | Yes |
| O | 5 × 2 = 10 | 3 × 2 + 4 × 1 = 10 | Yes |
Open and closed systems
The law applies to the whole system, including all gases. In an open system, matter can enter or leave, and the mass of the contents can appear to change. In a closed system, nothing enters or leaves, so the mass stays constant.
- Apparent loss: a reaction that produces gas in an open container, such as marble chips in acid, loses mass as the gas escapes.
- Apparent gain: burning magnesium in air gains mass, as it combines with oxygen from the air.
- No change: the same reaction in a sealed flask on a balance shows no change in mass.
A mass balance table
| Substance | Moles | Molar mass (g/mol) | Mass (g) |
|---|---|---|---|
| Mg (reactant) | 0.200 | 24.31 | 4.86 |
| O2 (reactant) | 0.100 | 32.00 | 3.20 |
| Total reactants | – | – | 8.06 |
| MgO (product) | 0.200 | 40.31 | 8.06 |
Worked examples
- Missing product mass. 12.0 g of calcium carbonate decomposes into calcium oxide and carbon dioxide: CaCO3 → CaO + CO2. If the solid residue (CaO) has a mass of 6.72 g, the mass of carbon dioxide released is 12.0 − 6.72 = 5.28 g.
- Check against the equation. 12.0 g of CaCO3 (100.09 g/mol) is 0.1199 mol. The equation gives 0.1199 mol of CaO (56.08 g/mol), which is 6.72 g, and 0.1199 mol of CO2 (44.01 g/mol), which is 5.28 g. The values agree with example 1.
- Gain in mass on burning. 2.43 g of magnesium (0.100 mol) burns in air to give 4.03 g of MgO (0.100 mol). The mass of oxygen that combined is 4.03 − 2.43 = 1.60 g, which corresponds to 0.0500 mol of O2, in agreement with the 2 : 1 ratio.
- Open flask. A flask containing 100.00 g of acid and a 5.00 g marble chip has a total mass of 105.00 g. After the reaction in an open flask, the mass is 102.80 g. The lost mass of 2.20 g is carbon dioxide, which corresponds to 2.20 ÷ 44.01 = 0.0500 mol, in agreement with 5.00 g of CaCO3 (0.0500 mol).
- Atom count for a larger equation. 2C4H10 + 13O2 → 8CO2 + 10H2O. Carbon: 2 × 4 = 8 on the left and 8 on the right. Hydrogen: 2 × 10 = 20 and 10 × 2 = 20. Oxygen: 13 × 2 = 26 and 8 × 2 + 10 = 26. The equation is balanced.
Which experiments tested the law?
The Russian scientist Mikhail Lomonosov described the idea in 1748 and carried out experiments in sealed vessels in 1756. Antoine Lavoisier performed careful experiments in the 1770s and 1780s. In one of them he heated mercury in a closed volume of air for several days. A red powder (mercury oxide) formed and a part of the air was used up, and the mass of the red powder was equal to the mass of the mercury plus the oxygen taken from the air. He then heated the red powder and recovered the mercury and the oxygen. Around 1908, the German chemist Hans Landolt repeated such experiments in sealed glass vessels with a precision of about 1 part in 10 million and found no change in mass.
Is the law exact?
According to Einstein’s equation E = mc2, a change in energy is accompanied by a change in mass. When a reaction releases energy, the products have slightly less mass than the reactants. For chemical reactions the effect is far too small to measure. Burning 1 mol of methane releases 890 kJ. The mass change is Δm = E ÷ c2 = 890,000 J ÷ (2.998 × 108 m/s)2 = 9.9 × 10−12 kg, or about 1 × 10−8 g. Compared with the 16 g of methane and 64 g of oxygen, this is about 1 part in 1010, much smaller than the precision of any balance. In nuclear reactions the energy changes are about a million times larger, and the mass change can be measured.
Which mistakes are common?
Mistake 1: Balancing by changing the subscripts
Changing a subscript changes the substance. Only coefficients may be adjusted.
Mistake 2: Forgetting the gases in the mass balance
Gaseous reactants and products must be included. They may come from or escape into the air.
Mistake 3: Assuming that the number of molecules is conserved
Mass and the number of atoms of each element are conserved. The number of molecules can change: 3 molecules (2H2 + O2) give 2 molecules (2H2O).
Mistake 4: Applying the law to volume
Volume is not conserved. Gases can expand or contract, and mixing liquids can change the total volume.