# Law of the conservation of mass

*The scientifically correct term for the subject of this article is***mass**, which is not, strictly speaking, the same as**weight**. But, for all practical purposes, the two can be considered to be the same. It's just what a scale would tell you if you weigh something.

The **Law of Mass Conservation** states that the total mass in an isolated sysstem remains constant, regardless of the processes taking place in that system.

This is intuitively obvious for simple mechanical actions: If you take a coffee maker apart, the pieces weigh as much as the original coffee maker. For chemical transformations, this is not so obvious.

This law was a development of research in the 18th and 19th centuries, notably Antoine Lavoisier's experimental discovery that, when all substances were properly accounted for—specifically gases, during the process of combustion—the total weight of a closed system is not changed by a chemical reaction. A great deal of careful research went into this law—gases are not easy to weigh. Note that *volume* is not preserved in chemical reactions (or in taking apart a coffee maker). But *mass* was found to be preserved.

As an example of this in the field of chemistry, the combination of 22.99 grams of Sodium with 35.45 grams of Chlorine (those quantities are one mole each, or Avogadro's number of atoms) yields 58.44 grams of Sodium Chloride.

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## Radioactivity and Nuclear Physics

Over time, the understanding of this principle has developed. But in the early twentieth century it became clear that radioactivity seemed to violate both the Law of Mass Conservation and the classic "Law of Conservation of Elements". It was found that small changes in mass occur when elements undergo radioactive disintegration. The effect was only observed for nuclear transformations. For a while this led to the belief that the law does not apply to nuclear reactions, and holds only for other phenomena. This false notion may still be taught to some elementary-school children.

That notion is not true. It would imply that nuclear phenomena involve a different sort of fundamental physics (laws of motion, etc.) from other phenomena. But that isn't so—the fundamental laws of physics at are the same for all phenomena.

The explanation relates to potential energy. Recall that, from the Law of Energy Conservation, energy is conserved. Kinetic energy (the energy of motion that you can "see" such as a ball falling) may seem to disappear, but it is really only turning into potential energy. That "hidden" potential energy can be turned back into kinetic energy. The sum of potential energy and kinetic energy is constant.

Here are the important points:

**Potential energy has mass.**

**When potential energy is converted to kinetic energy, that mass simply disappears. Conversely, when kinetic energy is converted to potential energy, that mass comes into existence. The Law of Mass Conservation does not cover that potential-energy-equivalent mass, though you could weigh it on a scale.**

**The conversion factor is 1.1110**^{-17}kilograms per Joule.

That conversion factor is so tiny that the scientific community can be forgiven for not noticing the effect for so long. For example, the chemical reaction of Sodium and Chlorine to create Sodium Chloride is exothermic and releases a few hundred thousand Joules per mole. (The exact amount depends on details of temperature and pressure that are not relevant here.) So the loss of that potential energy leads to a loss of a few nanograms in mass, a quantity that is for all practical purposes unmeasurable.

But when analyzing nuclear reactions, the potential-energy-equivalent mass becomes (barely) measurable, and, when methods of measuring atomic weights became sufficiently accurate in the 1910s and 1920s, it was noticed.

For example, a Radium atom has a mass (atomic weight) of 226.0254098 amu (atomic mass units). It decays by alpha decay into a Radon atom (222.0175777 amu) and a Helium atom (alpha particle, 4.0026033 amu.) The discrepancy is .0052288 amu. This is the potential-energy-equivalent mass of the Radium atom. That is, .0052288 amu of the Radium atom's mass was this potential-energy-equivalent mass. It disappeared when the potential energy was converted into kinetic energy. The various conversion factors among amu, kilograms, Joules, and electron volts, along with the conversion factor of 1.1110^{−17} given above, yields a potential energy loss of 4.870596 MeV. This got converted into the kinetic energy of both the alpha particle and the recoiling Radon atom. Using the laws of conservation of Energy and of momentum, one can calculate the ratio of alpha energy to recoil energy; it is the same as the ratio of Radon atom mass to Helium atom mass—55.5 to 1. Hence the recoil energy of the Radon atom is expected to be about 0.0868 Mev, and the expected alpha particle kinetic energy is 4.784 MeV. This is the observed alpha particle energy.

## Background Theory

The "lost" mass in radioactive decays and also in nuclear fusion can be explained using relativity and Einstein's famous equation, E=mc^{2}. From this equation, it is clear that the conversion factor from earlier should be equal to .

## Application to the origins of the universe

The Law of Mass Conservation is believed by some to be in conflict with religious sensibilities, apparently relating to the initial creation of the universe, or its ultimate fate. While the exact circumstances and causes of the "big bang" are discussed by cosmologists and philosophers, the Law of Mass Conservation is accepted for everything in between.