Law of Conservation of Mass
The law of conservation of mass states that, in a closed system, total mass remains constant during a chemical reaction. A conservation of mass calculator applies this mass balance to determine an unknown mass from measured reactants, leftovers, and products.
Core definition and formulas
For two reactants A and B, the total mass before reaction equals the total mass after reaction:
\[
\begin{aligned}
m_{\text{before}} &= m_{\text{after}} \\
m_A^{(i)} + m_B^{(i)} &= m_A^{(f)} + m_B^{(f)} + m_{\text{prod}}
\end{aligned}
\]
Here \(m_A^{(i)}\) and \(m_B^{(i)}\) are the initial masses (before reaction), \(m_A^{(f)}\) and \(m_B^{(f)}\) are the unreacted (leftover) masses after the reaction, and \(m_{\text{prod}}\) is the total mass of products collected. All masses must use the same unit (commonly grams).
How to interpret results
A larger computed \(m_{\text{prod}}\) means more product mass was formed from the consumed reactants, while a smaller value indicates either limited reaction progress or larger leftover mass. When the inputs represent a true closed system, the totals should agree: \(m_A^{(i)} + m_B^{(i)}\) should match \(m_A^{(f)} + m_B^{(f)} + m_{\text{prod}}\) within normal measurement and rounding error. Typical units are \(\mathrm{g}\) or \(\mathrm{kg}\); they represent absolute mass, not moles or concentration.
- Common outputs: missing product mass, missing initial mass of a reactant, or missing leftover mass after the reaction.
- Consistency check: agreement of “total before” and “total after” supports the conservation assumption.
Common pitfalls
- Mixing units (e.g., grams and kilograms) without converting first.
- Entering negative leftovers or forgetting that “fully consumed” implies \(m^{(f)}=0\).
- Using measurements from an open system (gas escape, evaporation, splatter, leaks).
- Confusing mass balance with stoichiometry; coefficients affect moles, not the closed-system mass total.
Micro example: If \(m_A^{(i)}=0.455\,\mathrm{g}\), \(m_B^{(i)}=2.315\,\mathrm{g}\), \(m_A^{(f)}=0\), and \(m_B^{(f)}=2.015\,\mathrm{g}\), then
\(m_{\text{prod}}=0.455+2.315-0-2.015=0.755\,\mathrm{g}\).
This tool is appropriate for lab-style mass balance in a closed container or a carefully captured system with measured leftovers and products. It is not appropriate when significant mass is lost as gas to the surroundings or when the goal is to predict amounts from a balanced equation; a next-step method in those cases is stoichiometry using molar mass and limiting reactants.
