Conservation of mass
The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. An equivalent statement is that matter changes form, but cannot be created nor destroyed. This implies that for any chemical process in a closed system, the mass of the reactants must equal the mass of the products. In chemistry, so long as no nuclear reactions take place, a special form the conservation of mass also holds in regard to the conservation of the mass (and number of atoms) of each chemical element. In most basic chemical reactions and equations, no atoms of any element may be created or destroyed. They must only come out exactly as found in the reactant side of an equation, with a different location in regard to their new chemical formula, as may be found on the product side of an equation.
The conservation of mass is widely used in many fields such as chemistry, mechanics, and fluid dynamics. According to special relativity, the conservation of mass is a statement of conservation of energy. The invariant mass of a system of particles is equivalent to its center of momentum frame energy. Energy is conserved according to any inertial frame and so this system mass defined this way is conserved even under nuclear reactions. It is the sum of the masses of a system's constituent particles that is changed in such a reaction. The decrease in the sum of the masses of the constituent particles becomes an increase in the kinetic energies of the constituents which is what is referred to as a mass-energy conversion, but although the sum of (rest) masses is not conserved - the system's mass which includes the kinetic energies of the constituents according to the center of momentum frame is conserved.
Also, for example, several forms of radiation are popularly said to show mass to energy conversion in which matter may be converted into kinetic energy/potential energy and vice versa. Calculating that the net mass changes in such situations, results from the Newtonian addition of rest masses (see "mass defect" in binding energy), to get total mass--an operation not allowed once the system's mass has been defined relativistically as its center of momentum frame energy, instead of the sum of the constituent masses. The entire system in such conversions continues to have mass, and this mass is conserved in nuclear reactions, unless energy is allowed to escape.
Tiny amounts of mass are thus gained or lost from systems when they lose or gain heat, or any kind of radiation, and this gain or loss may not be taken into account. However, in many practical (low-energy and chemical) contexts, the assumption of conservation of mass is true to a high degree of approximation, even for systems that are not closed to radiation.
Historical development and importance
The law of conservation of mass (which is effectively conservation of weight when weights are properly taken) was clearly formulated by Antoine Lavoisier in 1789, who is often for this reason (see below) referred to as the father of modern chemistry. However, Mikhail Lomonosov (1748) had previously expressed similar ideas and proved them in experiments. Historically, the conservation of mass and weight was kept obscure for millennia by the buoyant effect of the Earth's atmosphere on quantities of gases, an effect not understood until the vacuum pump first allowed the effective weighing of gases using scales. Once understood, conservation of mass was of key importance in changing alchemy to modern chemistry. When scientists realized that substances never disappeared from measurement with the scales (once buoyancy had been accounted for), they could for the first time embark on quantitative studies of the transformations of substances. This in turn led to ideas of chemical elements, as well as the idea that all chemical processes and transformations (including both fire and metabolism) are simple reactions between invariant amounts/weights of these elements.
Approximate conservation vs. serious violation
Even when energy such as heat or light is allowed to enter a system, or escape it, the law of conservation of mass holds to high approximation in cases when neglected. Even in higher energy chemical reactions, the mass-energy of the reactants is huge in comparison to the energy absorbed, retained, or released when they react. By way of example, a gram of TNT releases 4.16 kJ of energy when exploded. However, the rest-energy of a gram of TNT is 90 TJ, or about 20 billion times as much. This means that even if the products of a TNT explosion were stopped and allowed to cool to the original temperature, they would only lose 1 part in 20 billion in weight. This amount would be very difficult to measure.
Serious violations
Drastic violations of the conservation of mass can occur in systems open to escape of energy, for relativistic processes involving very high speeds or very strong fields, such as nuclear and subnuclear reactions and very large astronomical objects. In these situations, whenever a system loses potential energy, and this energy is allowed to escape the system as radiation or heat, the system also loses the corresponding amount of mass with an appropriate factor of c2. Essentially, this loss in mass is ponderable in such systems, because a very great amount of radiation or heat is involved (enough to have appreciable mass). Even here, however, it must be again emphasized that the loss or gain in mass would not appear if the energy associated with it were not allowed to enter or escape the system.
From the non-system view, large violations of conservation of mass in nuclear reactions occur when the total mass of the reaction products is erroneously derived in Newtonian fashion from the sum (addition) of their "rest masses". Such derivation can be accomplished either from allowing energy to escape (i.e., being able to measure all products at "rest," or with zero momentum,okiiby using the value for the mass of each product in its own frame of rest, meaning that the observer has moved multiple times, to look at each particle). None of these operations are correct in special relativity, although they result in no great errors in Newtonian mechanics so long as speeds (and energies) are relatively small (for speeds, this means small in comparison to the speed of light).