Law of Conservation of Mass: Definition, History, Formula, Examples

Law of Conservation of Mass: Do burning destroy matter? It may seem so, but the same amount, or mass, of the matter, still exists even after the combustion process. When a log of wood burns, it combines with oxygen and forms carbon dioxide, water vapour, and ashes. The gases disappear into the air, leaving behind just the ashes. Taking the oxygen used and the gases produced by the fire into account and measuring the mass of the wood before and after the burning process, we would find that the total mass of matter after the fire is the same as the total mass of matter before the fire. This illustrates the Law of conservation of mass. Let’s explore it more in this article.

History of the Law of the Conservation of Mass

The ancient Greeks first proposed the idea that the total amount of matter in the universe is constant. However, in \(1789\), the father of modern chemistry, Antoine Lavoisier, described the constant nature of matter in his law of conservation of mass (or the principle of mass/matter conservation).

The Law of conservation of mass states that, in a chemical reaction or physical transformation, the mass of the participating species is conserved, i.e., it can neither be created nor destroyed within an isolated system. In simple words, the mass of the products formed in a chemical reaction will always be equal to the mass of the reactants.

Law of Conservation of Mass

The Law of conservation of mass was designed by the French chemist Antoine Lavoisier in \(1789\). According to this Law, matter can neither be created nor destroyed in a chemical reaction.

For example, when a candle melts, the mass of the soot and gases equals the original mass of the wax and the oxygen when it first reacted. Hence, the mass of the substances is equal before and after a chemical reaction. i.e. the mass of the products formed is equal to the mass of the reacting species.

 A reactant is a substance that participates in a chemical reaction to form two or more new substances known as the product.

Hence, chemical reactions can be visualised as rearranging atoms and bonds of reactants to form products, while the number of atoms involved in a reaction remains unchanged. The Law of Conservation of mass allows us to represent a chemical reaction as a balanced equation, in which the number of moles of any element on the reactant side is the same as that on the product side. This Law also helps us to determine the masses of gaseous reactants and products. With the sum of the masses of the solid or liquid reactants and products, any remaining mass can be assigned to gas.

Formula of Law of Conservation of Mass

The Law of Conservation of mass can be expressed as-
Mass of products \(=\) mass of reactants

Law of Conservation of Mass Examples

According to the Law of conservation of mass- the number of atoms participating in a chemical reaction to form new products must be the same, i.e. the number of atoms on the reactant must always be equal to the number of atoms on the product side.

For example-

1. In the formation of a water molecule, hydrogen combines with oxygen in a \(2:1\) ratio to form \(2\) moles of the water molecule.

In this case, the total mass of the reactants \(=\) is the total mass of the products. Also, the number of atoms of oxygen and hydrogen in the reactants side and the products side are equal.

2. Carbon combines with oxygen in a \(2:1\) ratio to form two moles of carbon monoxide.

In this case, the total mass of reactants and products also are equal. The number of atoms at the beginning and the end is equal as well.

3. Hydrochloric acid reacts with sodium hydroxide in a \(1:1\) ratio to form one mole of sodium chloride and one mole of the water molecule.

Law of Conservation of Energy

The Law of conservation of energy is similar to that of the Law of conservation of mass. According to the Law of conservation of energy, the total energy of a closed system (a system isolated from its surroundings) is conserved. This means energy can neither be created nor be destroyed. It can only be transformed from one form to another. All forms of energy follow the law of conservation of energy.

The amount of Energy in any system is given by:

\({{\rm{U}}_{\rm{T}}}{\rm{ = }}{{\rm{U}}_{\rm{i}}}{\rm{ + W + Q}}\)

\({{\rm{U}}_{\rm{T}}}\) is the total Energy of a system
\({{\rm{U}}_{\rm{i}}}\) is the initial Energy of a system
\({\rm{Q}}\) is the heat added or removed from the system
\({\rm{W}}\) is the work done by or on the system

The law of conservation of mass and the law of conservation of energy was later amended by Einstein as the Law of conservation of mass energy, which describes that the total mass and energy in a closed system remains constant. Hence mass and energy can be converted from one form to another.

Law of Conservation of Momentum

The Law of conservation of momentum states that the total momentum of an isolated system consisting of two bodies acting upon each other remains constant unless an external force is applied. This means momentum can neither be created nor be destroyed. It is a direct consequence of Newton’s Third Law of motion.

Derivation of Conservation of Momentum

According to Newton’s Third Law, when a force is applied by object \({\rm{A}}\) on object \({\rm{B}}\), then object \({\rm{B}}\) exerts back an equal and opposite force on object \({\rm{A}}\). This idea was the underlying principle behind the Law of conservation of momentum.

Let us consider two particles, \({\rm{A}}\) and \({\rm{B}}\), with masses \({{\rm{m}}_{\rm{1}}}\) and \({{\rm{m}}_{\rm{2}}}\) colliding with each other at time \({\rm{t}}\).

Change in momentum of particle \({\rm{A = }}{{\rm{m}}_{\rm{1}}}\left( {{{\rm{v}}_{\rm{1}}}{\rm{ – }}{{\rm{u}}_{\rm{1}}}} \right)\)
Change in momentum of particle \({\rm{B = }}{{\rm{m}}_{\rm{2}}}\left( {{{\rm{v}}_{\rm{2}}}{\rm{ – }}{{\rm{u}}_{\rm{2}}}} \right)\)

Where, \({{{\rm{u}}_{\rm{1}}}}\) and \({{{\rm{v}}_{\rm{1}}}}\) are the initial and final velocities of \({\rm{A}}\) and \({{{\rm{u}}_{\rm{2}}}}\) and \({{{\rm{v}}_{\rm{2}}}}\) are the initial and final velocities of \({\rm{B}}\).

According to Newton’s Third Law-

\({{\rm{F}}_{{\rm{BA}}}}{\rm{ = – }}{{\rm{F}}_{{\rm{AB}}}}\)

\({{\rm{F}}_{{\rm{BA}}}}{\rm{ = }}{{\rm{m}}_{\rm{2}}}{\rm{ \times }}{{\rm{a}}_{\rm{2}}}{\rm{ = }}\frac{{{{\rm{m}}_{\rm{2}}}\left( {{{\rm{v}}_{\rm{2}}}{\rm{ – }}{{\rm{u}}_{\rm{2}}}} \right)}}{{\rm{t}}}\)

\({{\rm{F}}_{{\rm{AB}}}}{\rm{ = }}{{\rm{m}}_{\rm{1}}}{\rm{ \times }}{{\rm{a}}_{\rm{1}}}{\rm{ = }}\frac{{{{\rm{m}}_{\rm{1}}}\left( {{{\rm{v}}_{\rm{1}}}{\rm{ – }}{{\rm{u}}_{\rm{1}}}} \right)}}{{\rm{t}}}\)

Applying Newton’s third law we get,

\(\frac{{{{\rm{m}}_{\rm{2}}}\left( {{{\rm{v}}_{\rm{2}}}{\rm{ – }}{{\rm{u}}_{\rm{2}}}} \right)}}{{\rm{t}}}{\rm{ = – }}\frac{{{{\rm{m}}_{\rm{1}}}\left( {{{\rm{v}}_{\rm{1}}}{\rm{ – }}{{\rm{u}}_{\rm{1}}}} \right)}}{{\rm{t}}}\)

\({{\rm{m}}_{\rm{2}}}\left( {{{\rm{v}}_{\rm{2}}}{\rm{ – }}{{\rm{u}}_{\rm{2}}}} \right){\rm{ = – }}{{\rm{m}}_{\rm{1}}}\left( {{{\rm{v}}_{\rm{1}}}{\rm{ – }}{{\rm{u}}_{\rm{1}}}} \right)\)

\({{\rm{m}}_{\rm{2}}}{{\rm{v}}_{\rm{2}}}{\rm{ – }}{{\rm{m}}_{\rm{2}}}{{\rm{u}}_{\rm{2}}}{\rm{ = – }}{{\rm{m}}_{\rm{1}}}{{\rm{v}}_{\rm{1}}}{\rm{ + }}{{\rm{m}}_{\rm{1}}}{{\rm{u}}_{\rm{1}}}\)

\({{\rm{m}}_{\rm{1}}}{{\rm{u}}_{\rm{1}}}{\rm{ + }}{{\rm{m}}_{\rm{2}}}{{\rm{u}}_{\rm{2}}}{\rm{ = }}{{\rm{m}}_{\rm{1}}}{{\rm{v}}_{\rm{1}}}{\rm{ + }}{{\rm{m}}_{\rm{2}}}{{\rm{v}}_{\rm{2}}}\)

The above equation is the Law of conservation of momentum, where \({{\rm{m}}_{\rm{1}}}{{\rm{u}}_{\rm{1}}}{\rm{ + }}{{\rm{m}}_{\rm{2}}}{{\rm{u}}_{\rm{2}}}\) is the total momentum of particles \({\rm{A}}\) and \({\rm{B}}\) before the collision and \({{\rm{m}}_{\rm{1}}}{{\rm{v}}_{\rm{1}}}{\rm{ + }}{{\rm{m}}_{\rm{2}}}{{\rm{v}}_{\rm{2}}}\) is the total momentum of particles \({\rm{A}}\) and \({\rm{B}}\) after collision.

Summary

Chemical reactions are usually expressed in terms of chemical equations where reactants change to form products. Chemical equations are the shorthand representation of a chemical reaction in terms of atoms and molecules. In a chemical equation, the number of atoms reacting is always equal to the number of atoms formed. This means the right and left sides of the arrow in a chemical equation should have an equal number of atoms resulting in a balanced chemical equation. A balanced chemical equation is based on the Law of conservation of mass proposed by Antoine Lavoisier. Through this article, we learned the statement, concept and examples that govern the Law of conservation of mass. We also learned the Law of conservation of mass energy, Law of conservation of momentum and its formula.

Frequently Asked Questions

Q.1. What does the law of conservation of mass mean?
Ans: The law of conservation of mass means that the mass of an isolated system always remains constant. It is neither created nor destroyed by chemical reactions or by physical transformations.

Q.2. Who proposed the law of conservation of mass?
Ans: The French chemist Antoine Lavoisier proposed the law of conservation of mass in \(1789\).

Q.3. Why there is no change in mass during chemical reactions?
Ans: There is no change in mass during chemical reactions because atoms can neither be created nor be destroyed during the course of a chemical reaction. A rearrangement of atoms or a group of atoms of reactants occurs to form products. The number of atoms and mass of the reacting species remains constant.

Q.4. State the law of conservation of mass and energy.
Ans: The law of conservation of mass and energy describes that the total mass and energy in a closed system remains constant and can only be converted from one form to another.

Q.5. If energy is neither created nor destroyed, what is the ultimate source of Energy?
Ans: The ultimate source of all forms of energy is the Sun. Energy in the universe is neither created nor destroyed. It is only converted from one form to another. For example, the energy possessed by a falling apple is converted from potential energy to kinetic energy. Similarly, when a bulb glows, electrical energy is converted to heat and light energy.

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