Law of Conservation of Mass

Weigh a sealed flask before a reaction and weigh it again after — no matter how violent the chemistry inside, the reading on the balance does not move. This simple, stubborn fact is the law of conservation of mass, the very first of the laws of chemical combination and the quiet assumption behind every balanced equation you will ever write. Antoine Lavoisier established it in the late eighteenth century by weighing reactants and products in sealed vessels, ending centuries of loose talk about substances "gaining" or "losing" matter during burning and decay. Once you accept that atoms are only rearranged, never created or destroyed, a balanced chemical equation stops being a memorised ritual and becomes an obvious bookkeeping requirement. This article restates the law precisely, works through both a closed-system and an open-system example — the second is where most marks are lost — and shows exactly how the law forces every equation to balance.

The core insight

In a closed system, the total mass of reactants always equals the total mass of products, because a chemical reaction only rearranges atoms and never creates or destroys them.

The core idea

Statement of the law. In any physical or chemical change occurring in a closed system — one that neither gains nor loses matter to its surroundings — the total mass before the change equals the total mass after it:

mass of reactants=mass of products\text{mass of reactants} = \text{mass of products}

where: "reactants" and "products" mean all the substances involved, including any gases produced or consumed, not just the solids or liquids that happen to be easy to see and weigh. For a general reaction A+B→C+DA + B \rightarrow C + D carried out inside a sealed vessel so that nothing escapes and nothing enters:

mA+mB=mC+mDm_A + m_B = m_C + m_D

where: mA,mBm_A, m_B are the masses of the reactants taken and mC,mDm_C, m_D are the masses of the products formed; all four masses are measured in the same unit (typically grams).

Why "closed system" is the whole point. The equation above only holds when the container is sealed. If the reaction happens in an open vessel and a gas escapes into the air, the solid or liquid left behind will appear to have lost mass — not because the law failed, but because part of the product left the accounting unweighed. Equally, if a gas from the air (such as oxygen) joins the reaction, the visible solid product will appear to have gained mass. In both cases the law still holds perfectly once every substance that crossed the boundary of the system is included in the sum.

Why it matters for the rest of chemistry. The law is the physical reason a chemical equation must be balanced. Atoms are neither created nor destroyed in a reaction, so the same number of atoms of each element has to appear on the reactant side and the product side of every equation — that is exactly what "balancing" an equation enforces. Every mass–mass calculation performed later in the course, where a mass of one substance is used to predict the mass of another, rests on this single law.

Historical verification. Lavoisier's decisive experiments involved combustion and other reactions carried out inside sealed vessels, with reactants and products (including any gases evolved) weighed both before and after. He found that, provided nothing was allowed to enter or escape, the total mass stayed constant to within the precision of his balance — replacing older ideas (such as the "phlogiston" theory, which struggled to explain mass changes on burning) with a quantitative law.

Figure
A sealed flask balances exactly against an open flask that has lost gas showing the law only holds when nothing enters or leaves
Mass is conserved only in a closed system sealed vessel before: 10.0 g after: 10.0 g nothing enters or leaves — mass equal open vessel gas escapes solid left: only 5.6 g mass appears to fall — law not broken, just unweighed gas Total mass of reactants always equals total mass of products once every substance crossing the boundary is counted
Derivation AFinding a missing mass from the law of conservation of mass

The goal is to show, using nothing beyond simple subtraction, how the statement "total mass of reactants equals total mass of products" lets you calculate an unknown mass in a closed-system reaction whenever the other masses are known — the single most common calculation type built on this law.

Step 1. Identify the closed system. Confirm the reaction takes place in a sealed vessel, so no reactant enters and no product escapes during the change; only under this condition does the law take its simplest form, mreactants=mproductsm_{\text{reactants}} = m_{\text{products}}.

Step 2. Write the total reactant mass. If the reactants taken have masses m1,m2,…m_1, m_2, \dots, their sum is the single number mreactants=m1+m2+⋯m_{\text{reactants}} = m_1 + m_2 + \cdots, the quantity that must be conserved.

Step 3. Write the total product mass in terms of the unknown. If the products formed have masses m1′,m2′,…m_1', m_2', \dots, with one of them, say m2′m_2', unknown, write mproducts=m1′+m2′+⋯m_{\text{products}} = m_1' + m_2' + \cdots.

Step 4. Apply the law and solve. Set mreactants=mproductsm_{\text{reactants}} = m_{\text{products}} and rearrange for the unknown: m2′=mreactants−(sum of the known product masses)m_2' = m_{\text{reactants}} - (\text{sum of the known product masses}). This single subtraction is the entire calculation — the law guarantees nothing is unaccounted for as long as the system is closed.

Worked example

Problem. 10.0 g10.0\ \text{g} of calcium carbonate (CaCO3\text{CaCO}_3) is heated strongly in a sealed, evacuated container and decomposes completely into calcium oxide (CaO\text{CaO}) and carbon dioxide gas (CO2\text{CO}_2), both trapped inside. The mass of CaO\text{CaO} formed is found to be 5.6 g5.6\ \text{g}. Find the mass of CO2\text{CO}_2 produced and verify the law of conservation of mass. Then, separately, a student burns 2.4 g2.4\ \text{g} of magnesium ribbon in an open crucible in air and obtains 4.0 g4.0\ \text{g} of magnesium oxide — an apparent increase in mass. Explain whether this contradicts the law.

Step 1. Write the decomposition reaction: CaCO3(s)→CaO(s)+CO2(g)\text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g). The vessel is sealed, so it is a closed system and m(CaCO3)=m(CaO)+m(CO2)m(\text{CaCO}_3) = m(\text{CaO}) + m(\text{CO}_2).

Step 2. Substitute the known masses: 10.0=5.6+m(CO2)10.0 = 5.6 + m(\text{CO}_2), so m(CO2)=10.0−5.6=4.4 gm(\text{CO}_2) = 10.0 - 5.6 = 4.4\ \text{g}.

Step 3. Verify: total product mass =5.6+4.4=10.0 g= 5.6 + 4.4 = 10.0\ \text{g}, exactly equal to the 10.0 g10.0\ \text{g} of reactant taken — the law is confirmed for this closed system.

Step 4. Now examine the magnesium case: 2Mg(s)+O2(g)→2MgO(s)2\text{Mg}(s) + \text{O}_2(g) \rightarrow 2\text{MgO}(s). The crucible is open to air, so it is not a closed system — oxygen gas enters from the surroundings as a reactant but was never included in the "2.4 g" that was weighed. The mass of oxygen that combined is 4.0−2.4=1.6 g4.0 - 2.4 = 1.6\ \text{g}.

Step 5. Check the full accounting: total reactant mass, including the oxygen drawn in, is 2.4+1.6=4.0 g2.4 + 1.6 = 4.0\ \text{g}, exactly equal to the 4.0 g4.0\ \text{g} of MgO\text{MgO} formed. The law of conservation of mass is not violated in either case: m(CO2)=4.4 g\mathbf{m(\text{CO}_2) = 4.4\ \text{g}}, and the magnesium's apparent mass "gain" is fully explained by the 1.6 g1.6\ \text{g} of oxygen that joined the reaction from the open air.

Common traps

  • Concluding the law is "broken" whenever a solid product's mass differs from a solid reactant's mass, without checking whether gas entered or left an open system.
  • Applying the law to only the visible solid or liquid components instead of the total mass of every reactant and every product, including gases.
  • Confusing "mass" with "weight" — the law concerns mass, which is unaffected by location or gravity, unlike weight.
  • Assuming the law applies only to chemical reactions; it holds for physical changes too, such as melting, where the mass of water formed equals the mass of ice that melted.

Ask the tutor: if a reaction seems to gain or lose mass in an open container, ask the AI tutor to help identify exactly which gas was left out of the accounting.

If I weigh the reactants and products of a reaction on my kitchen scale in an open pan and the masses do not match, does that disprove the law?

No — it almost always means the system was not closed. If a gas is released (like carbon dioxide from a fizzy reaction) it escapes unweighed and the visible mass seems to fall; if a gas from the air is consumed (like oxygen during burning) the visible solid seems to gain mass. The law only makes its simple prediction, total reactant mass equals total product mass, when every substance that crosses the boundary of the system, gas included, is accounted for. A genuinely sealed, evacuated container is needed to test the law directly.

Why does a balanced chemical equation prove the law of conservation of mass rather than just look neat?

Balancing an equation means making the number of atoms of each element equal on both sides. Since atoms are neither created nor destroyed in a reaction (that is precisely what the law states), the total mass contributed by each element's atoms must also be unchanged from reactant side to product side. A balanced equation is therefore not a stylistic convention — it is the atomic-level statement of the same conservation law that Lavoisier verified by weighing.

Was Lavoisier the first person to suspect that mass is conserved in a chemical change?

Careful, quantitative proof was Lavoisier's contribution in the late 18th century, and it is his sealed-vessel weighing experiments that CBSE credits as establishing the law. Earlier chemists had informal or qualitative notions, but they lacked the precise balances and closed-vessel technique needed to rule out gases escaping or entering unnoticed — which is exactly the trap that misled the older phlogiston theory of combustion. Lavoisier's insistence on weighing everything, including gases, is what turned a guess into a law.

Before this

Where this leads