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Avogadros number, molar mass.
In chemistry and physics, the Avogadro constant (symbols: L, NA) is defined as the number of constituent particles (usually atoms ormolecules) in one mole of a given substance. It is a dimensionless number and has the value 6.02214129(27)×1023 mol−1.[1][2][3] Changes in the SI units are proposed that will change the constant to exactly 6.02214X×1023 when it is expressed in the unit mol−1 (see New SI definitions).
In chemistry, the molar mass 
is a physical property. It is defined as the mass of a given substance (chemical element or chemical compound) divided by its amount of substance.[1] The base SI unit for molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol.
As an example, the molar mass of water is approximately: M(H2O) ≈ 18 g·mol−1
Ideal gas and its properties.
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.
An ideal gas has a number of properties; real gases often exhibit behavior very close to ideal. The properties of an ideal gas are:
1. An ideal gas consists of a large number of identical molecules.
2. The volume occupied by the molecules themselves is negligible compared to the volume occupied by the gas.
3. The molecules obey Newton's laws of motion, and they move in random motion.
4. The molecules experience forces only during collisions; any collisions are completely elastic, and take a negligible amount of time.
Ideal gas state equation.
An ideal gas is an idealized model of real gases; real gases follow ideal gas behavior if their density is low enough that the gas molecules don't interact much, and when they do interact they undergo elastic collisions, with no loss of kinetic energy.
The behavior of an ideal gas, that is, the relationship of pressure (P), volume (V), and temperature (T), can be summarized in the ideal gas law:
Ideal gas law : PV = nRT
where n is the number of moles of gas, and R = 8.31 J / (mol K) is known as the universal gas constant.
Molar mass.
An alternate way to express the ideal gas law is in terms of N, the number of molecules, rather than n, the number of moles. N is simply n multiplied by Avogadro's number, so the ideal gas law can be written as:
Gas constant.
The gas constant (also known as the molar, universal, or ideal gas constant, denoted by the symbol R or R) is a physical constant which is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy (i.e. the pressure-volume product) pertemperature increment per mole (rather than energy per temperature increment per particle).
Physically, the gas constant is the constant of proportionality that happens to relate the energy scale in physics to the temperature scale, when a mole of particles at the stated temperature is being considered. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of the energy and temperature scales, plus similar historical setting of the value of the molar scale used for the counting of particles. The last factor is not a consideration in the value of the Boltzmann constant, which does a similar job of equating linear energy and temperature scales.
The gas constant value is
[2]