# Law of Conservation of Mass | History, Formula, Example

## Definition of Law of Conservation of Mass

The law of conservation of mass states that, “The mass in an isolated system can neither be created nor be destroyed but can be transformed from one form to another”.

According to the law of conservation of mass, the mass of the reactants must be equal to the mass of the products for a low-energy thermodynamic process.

## Assumptions of Law of Conservation of Mass

• It is believed that there are a few assumptions from classical mechanics which define mass conservation.
• Later the law of conservation of mass was modified with the help of quantum mechanics and special relativity that energy and mass are one conserved quantity.
• In 1789, Antoine Laurent Lavoisier discovered the law of conservation of mass. The law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy. The mass of the system must remain constant over time. As the system’s mass cannot change, so the quantity can neither be added nor be removed. Therefore, the quantity of mass is conserved over time.
• The law implies that mass can neither be created nor destroyed. Although it may be rearranged in space, or the entities associated with it may be changed in form.

## The Law of Conservation of Mass-Energy

This law was later amended by Einstein in the law of conservation of mass-energy. Which describes the fact that the total mass and energy in a system remain constant. This amendment incorporates the fact that mass and energy can be converted from one to another.

However, the law of conservation of mass remains a useful concept in chemistry. Since the energy produced or consumed in a typical chemical reaction accounts for a minute amount of mass.

Therefore, we can visualize chemical reactions as the rearrangement of atoms and bonds. While the number of atoms involved in a reaction remains unchanged.

This assumption allows us to represent a chemical reaction as a balanced equation, in which the number of moles of any element involved is the same on both sides of the equation.

An additional useful application of this law is the determination of the masses of gaseous reactants and products. If the sums of the solid or liquid reactants and products are known, any remaining mass can be assigned to gas.

## History

An important idea in ancient Greek philosophy was that “Nothing comes from nothing”. So that what exists now has always existed: no new matter can come into existence where there was none before.

An explicit statement of this, along with the further principle that nothing can pass away into nothing, is found in Empedocles. “For it is impossible for anything to come to be from what is not, and it cannot be brought about or heard of that what should be utterly destroyed.”

A further principle of conservation was stated by Epicurus around 3rd century BC, who, describing the nature of the Universe, wrote that “the totality of things was always such as it is now, and always will be.” Jain philosophy, a non-creationist philosophy based on the teachings of Mahavira (6th century BC), states that the Universe and its constituents, such as matter, cannot be destroyed or created.

The Jain text Tattvarthasutra (2nd century AD) states that a substance is permanent, but its modes are characterized by creation and destruction.

Nasir al-Din al-Tusi (around the 13th century AD) also stated a principle of the conservation of matter.

He wrote, “A body of matter cannot disappear completely. It only changes its form, condition, composition, color, and other properties and turns into a different complex or elementary matter”.

## Discoveries of law of conservation of mass in Chemistry

• By the 18th century, the principle of conservation of mass during chemical reactions was widely used. It was an important assumption during experiments, even before a definition was formally established, as can be seen in the works of Joseph Black, Henry Cavendish, and Jean Rey.
• The first to outline the principle was Mikhail Lomonosov in 1756. He might have demonstrated it by experiments and certainly had discussed the principle in 1748 in correspondence with Leonhard Euler, though his claim on the subject is sometimes challenged. According to the soviet physicist Yaakov Dorfman:
• Lomonosov formulated the universal law based on general philosophical materialistic considerations. It was never questioned or tested by him, but on the contrary. It served him as a solid starting position in all research throughout his life.
• A more refined series of experiments were later carried out by Antoine Lavoisier. Who expressed his conclusion in 1773 and popularized the conservation of mass. The demonstrations of the principle disproved the then-popular phlogiston theory that claimed mass could be gained or lost in combustion and heat processes.
• The conservation of mass was obscure for millennia because of the buoyancy effect of the Earth’s atmosphere on the weight of gases. For example, a piece of wood weighs less after burning; this seemed to suggest that some of its mass disappears or is transformed or lost. This was not disproved until careful experiments were performed in which chemical reactions such as rusting were allowed to take place in sealed glass ampoules; it was found that the chemical reaction did not change the weight of the sealed container and its contents. Weighing of gases using scales was not possible until the invention of the vacuum pump in the 17th century.

## Importance of Law of Conservation of Mass

• The Discovery of the law of conservation of mass helped turn chemistry into the respectable science it is today. Chemistry has its foundations in alchemy, a protoscience that put much stock into magic and mysticism. With the advent of the law of conservation of mass, chemists took the mystery and illusion of alchemy and brought predictability and reliability to chemistry.
• The law of conservation of mass is fundamental to the study and production of chemical reactions. If scientists know the quantities and identities of reactants for a particular reaction. Then they can predict the amounts of products made. Chemical manufacturers can increase efficiency by applying the law of conservation of mass to their laboratory practices.

## Formula of Law of Conservation of Mass

Law of conservation of mass can be expressed in the differential form using the continuity equation in fluid mechanics and continuum mechanics as:

∂ρ / ∂t+▽(ρv) = 0

where,

• ρ is the density.
• t is the time.
• v is the velocity.
• ▽ is the divergence.

## Examples

### Combustion Process

Burning of wood is a conservation of mass as wood-burning involves Oxygen, Carbon dioxide, water vapor, and ashes.

### Chemical Reactions:

To get one molecule of H2O (water) with the molecular weight of 10, Hydrogen with molecular weight 2 is added with Oxygen whose molecular weight is 8, thereby conserving the mass.

• A similar law of conservation of mass example is the image of a burning candle. For this example, picture a regular candle with wax and a wick. Once the candle completely burns down, though, you can see that there is far less wax than there was before you lit it. This means that some of the wax (not all of it, as you’ve likely noticed with candles you’ve lit in real life!) has been transformed into gases—namely, water vapor and carbon dioxide. As the previous example with the bonfire has shown, no matter (and therefore no mass) is lost through the process of burning.

## Questions Based on the Law of Conservation of Mass

Here are some questions based on the law of conservation of mass

### Question-1

grams of calcium carbonate (CaCO3) produces 3.8 grams of carbon dioxide (CO2) and 6.2 grams of calcium oxide (CaO). Represent this reaction in terms of law of conservation of mass.

Solution:

According to law of conservation of mass:

Mass of reactants = Mass of products

∴ 10 gram of CaCO3 = 3.8 grams of CO2 + 6.2 grams of CaO

10 grams of reactant = 10 grams of products

Hence, it is proved that the law of conservation of mass is followed by the above reaction.

### Question-2

Potassium hydroxide ( KOH) readily reacts with carbon dioxide (CO2) to produce potassium carbonate (K2CO3) and water (H2O). How many grams of potassium carbonate are produced if 224.4 g of KOH reacts with 88.0 g of CO2 ? The reaction also produces 36.0 g of water.

Solution:

The Law is also applicable to both chemical and physical changes. For example, if you have an ice cube that melts into a liquid and you heat that liquid up, it becomes a gas. It will appear to have disappeared, but is still there.