Mass Conservation

Total System Mass Stays Constant

When a chemical reaction happens, atoms do not vanish or appear from nothing. They are rearranged into new substances. That is why the mass of the whole system before a reaction equals the mass of the whole system after the reaction.

m_{\text{system before}} = m_{\text{system after}}

The system boundary determines what is included in the mass. In a closed container, every substance remains inside the part being weighed. In an open container, gas may leave that boundary. The balance then shows less mass because the escaped gas is no longer on it. the total amount of matter stays the same during chemical and physical changes, so the reading dropped while the matter did not disappear.

Measurements by Lavoisier

Before modern chemistry, combustion was often explained with phlogiston, as if something left a material when it burned. Antoine Lavoisier challenged that idea through careful weighing. He tracked the mass of reactants and products, including gases, and showed that combustion involves a reaction with oxygen.

Lavoisier helped establish the law of conservation of mass and connected combustion with oxygen.

Closed System Balance

Compare a closed system with an open system. Conservation of mass includes every substance. In the open-system model, sulfur that crosses the container boundary still exists, but it no longer contributes to the balance reading.

System Balance

Compare what the balance reads when all sulfur stays in the container and when one modeled portion crosses the boundary before reacting.

In a closed system, products and leftover reactants stay inside the part being weighed.

What is counted: The container, products, and leftover reactants are one system.
Mass reading: $10.00 + 2.00 = 6.08 + 5.92$ , so the total mass stays $12.00\ \mathrm{g}$ .

Mass Balance in an Open System

The open view starts with the same $10.00\ \mathrm{g}$ of zinc and $2.00\ \mathrm{g}$ of sulfur. It then models $1.00\ \mathrm{g}$ of sulfur crossing the boundary as vapor before it reacts. The 2024 abridged standard atomic weights are $A_r(\mathrm{Zn})=65.38$ and $A_r(\mathrm{S})=32.06$ . With these values, the remaining sulfur reacts with about $2.04\ \mathrm{g}$ of zinc.

\begin{aligned} &m_{\mathrm{ZnS}} \approx 2.04 + 1.00 = 3.04\ \mathrm{g} \\ &m_{\mathrm{Zn\ left}} \approx 10.00 - 2.04 = 7.96\ \mathrm{g} \\ &m_{\mathrm{on\ balance}} \approx 3.04 + 7.96 = 11.00\ \mathrm{g} \\ &m_{\mathrm{enlarged\ system}} = 11.00 + 1.00 \\ &= 12.00\ \mathrm{g} \end{aligned}

The balance measures only the matter that remains inside the chosen boundary, so it reads $11.00\ \mathrm{g}$ after $1.00\ \mathrm{g}$ of sulfur vapor leaves. If the escaping vapor is included in the system, the total mass remains $12.00\ \mathrm{g}$ .

Zinc and Sulfur

In one experiment, $10.00\ \mathrm{g}$ of zinc is heated with $2.00\ \mathrm{g}$ of sulfur. After the reaction, $6.08\ \mathrm{g}$ of zinc sulfide forms and $5.92\ \mathrm{g}$ of zinc remains unreacted.

The particle-level stoichiometric shorthand is:

\mathrm{Zn(s)} + \mathrm{S(s)} \rightarrow \mathrm{ZnS(s)}

The equation states a ratio of one zinc atom for each sulfur atom incorporated into zinc sulfide. This simplified notation is used to calculate the atomic ratio in the reaction. It does not display the particle structure of bulk elemental sulfur.

The product mass does not have to equal the mass of every starting substance if one reactant is left over. First count only the zinc that actually reacted.

\begin{aligned} &m_{\mathrm{Zn\ reacted}} = 10.00 - 5.92 = 4.08\ \mathrm{g} \\ &m_{\mathrm{reactants\ reacted}} = 4.08 + 2.00 \\ &= 6.08\ \mathrm{g} \\ &m_{\mathrm{product}} = 6.08\ \mathrm{g} \end{aligned}

In this example, mass conservation holds for the part that reacts: the mass of zinc that reacts plus the mass of sulfur equals the mass of zinc sulfide formed.

If the whole container is counted, the mass is also unchanged:

\begin{aligned} m_{\mathrm{before}} &= 10.00 + 2.00 = 12.00\ \mathrm{g} \\ m_{\mathrm{after}} &= 6.08 + 5.92 = 12.00\ \mathrm{g} \end{aligned}

Three Mass Quantities in the Calculation

Keep three questions separate.

What is the product mass? Only the new product counts, so it is $6.08\ \mathrm{g}$ of zinc sulfide.
Is the system mass conserved? Yes, when the product and leftover reactant are counted together.
Can the reading appear lower? Yes, if gas leaves an open container and is not weighed.

Chemical equations must be balanced because both sides contain the same number of atoms of each element. Mass calculations follow conservation of matter.

The law of constant composition answers a different question. When two elements form the same compound, does their mass ratio stay fixed?