Gas particles moving about at speeds of 500 meters per second.
In science, gas is a state of matter, in which the particles of its composition, i.e. atoms, molecules, or ions, etc., being characterized by weak interactions, move about in space in relatively random motions, often assumed to have non-correlation of velocities, at speeds proportional to the temperature of its volumetric containing region, tending to completely occupy the volume of any given space into which it is put. [1] The term was coined in the early 17th century by Flemish physician and chemist Johann Helmont in reference to "spirits" released during combustion. [4]

Air
To give a three-dimensional picture of a gas, a sugar-lump sized cube of the gas called “air”, for instance, which is comprised of approximately ten chemical species: nitrogen (N2) 78%, oxygen (O2) 21%, as well as argon (Ar), neon (Ne), helium (He), methane (CH4), krypton (Kr), hydrogen (H2), nitrous oxide (N2O), and xenon (Xe), in smaller percentages, at room temperature, contains 30-trillion particles.

Velocities
The average speed of gas particles is on average 500-meters per second (or 1200-mph). [2]
It was German physicist Rudolf Clausius who, in his 1857 article “On the Nature of the Motion which we call Heat”, made the first calculation of the speed of gas particles.

History
In the earlier 16th century writings of Swiss alchemist and physician Paracelsus the word khaos was used in the occult sense of "proper elements of spirits" or "ultra-rarified water". [3]

During the years 1609 to 1644, Flemish physician and chemist Johann Helmont defined the word “gas” as a type of spirit that can be reduced to liquid form and can, if produced, cause glass containing vessels to explode. [6] Helmont likely derived the term from the Greek khaos (chaos) meaning void or "empty space", being that the Dutch "g" is roughly equivalent to that of Greek "kh." The word was gas was introduced by Helmont in an experiment where he burned 62 pounds of oak after which time only one pound of ash remained. Thus, he concluded that 61-pounds (or 98%) of the material was converted into a new type of invisible air or spirit, to which he affixed the name “gas”. Specifically, in his writings, Helmont states: [4]

“The flame which is only burning smoke, perishes at once in a closed vessel, and charcoal may be heated continuously in a closed vessel without wasting … yet it 62-pounds of oak charcoal contain 1-pound of ashes, the remaining 61-pounds are “wild spirit” (spiritus silvestre), which cannot escape from the shut vessel.”

Then tells us:

“I call this spirit, hitherto unknown, by the new name of gas (Hunc spiritum, incognitum hactenus, novo nomine Gas voco), which can neither be retained in vessels nor reduced to a visible form, unless the seed is first extinguished.”

More than once, Helmont concluded that he was the “inventor” of gas. He investigated and categorized a number of gases, such as gas from eructions (belches) or CO2, poisonous red gas (NO2) that is formed when aqua fortis (HNO3) acts on silver, sulfurous gas that “flies off” burning sulfur, and others. He says that gas is composed of invisible atoms which can come together by intense cold and condense to minute liquid drops; and that gases can be contained in bodies in fixed form, and set free again by heat, fermentation, or chemical reaction. [4] In relation to combustion, he concluded that there were two classes of gas: [5]

● Gas sylvestre – one that would not burn or support combustion.
● Gas pingue – one that would burn (a combustible gas).
 The pneumatical engine, invented in 1658 by Irish scientist Robert Boyle, based on the earlier 1650 vacuum pump design of German engineer Otto Guericke, the device used to calculate Boyle's law, the first of the gas laws.

Gas laws
See main: Gas laws, Ideal gas law
In the 1834 publication Memoir on the Motive Power of Heat, French physicist Émile Clapeyron derived one of the first formulations of what is now called the “ideal gas law”. In particular, after a few substitutions in a discussion on various aspects of the Carnot cycle, Clapeyron states that Mariotte’s law (PV = k, at constant temperature) combined with that of Gay-Lussac's law (P = kT, at constant volume) gives the expression: [10]

$~ Pv = R(267 + t) ~$

Building on the work of Clapeyron, in relation to the development of the science of thermodynamics, the term “perfect gas” was defined in 1859 by Scottish engineer William Rankine as “a substance in such a condition that the total pressure exerted by any number of portions of it, at a given temperature, against the sides of a vessel in which they are enclosed, is the sum of the pressures which each portion would exert if enclosed in the vessel separately at the same temperature.” [7] By 1890, the phrase “ideal perfect gas” was being used in relation to gases that obeyed the laws of Charles and Boyle, as defined by the following “characteristic equation”:

$\frac{PV}{T} = K\,$

in which P is the pressure, V the volume, and T the absolute temperature of the gas. [8] In 1923, American chemical physicists Gilbert Lewis and Merle Randall, in their famed Thermodynamics textbook, had come to define “the perfect gas or ideal gas is an invented substance, defined by certain properties which are not possessed by any actual substance, but which are supposed to be approached by any every actual gas as its pressure is indefinitely diminished.” They continue, by stating that the perfect gas is a substance which meets the criterion that its energy is a function of temperature alone, quantified by the following function:

$\left ( \frac{{\partial E}}{{\partial T}} \right )_T = 0\,$

and that when its temperature, pressure, and volume are changed the gas obeys the relation:

$~ PV = nRT ~$

where n is the number of mols of gas and R is universal constant (8.316 joules per degree), that has the same value for all gases. [9] Into the 1950s, this latter equation, describing the state of the ideal perfect gas, had come to be commonly known as the "ideal gas law".

References
1. (a) Perrot, Pierre. (1998). A to Z of Thermodynamics, Oxford: Oxford University Press.
(b) Boltzmann, Ludwig. (1895). Lectures on Gas Theory. New York: Dover.
(c) Clark, John O.E. (2004). The Essential Dictionary of Science. Barnes & Noble.
(d) Daintith, John. (2005). Oxford Dictionary of Physics. Oxford University Press.
2. (a) Clark, John O.E. (2004). The Essential Dictionary of Science. Barnes & Noble.
(b) Air, composition of (Britannica); 2002 Deluxe Edition, CD-ROM.
3. Gas – Online Etymology Dictionary.
4. Partington, J.R. (1937). A Short History of Chemistry (pgs. 48-51). New York: Dover.
5. Gratzer, Walter. (2005). Terrors of the Table (pg. 49). Oxford University Press.
6. (a) Helmont did his chemical experiments during these years.
(b) Helmont’s writings were published posthumously in 1648 by his son Franciscus Mercurius under the title Ortus medicinae (Origins of Medicine).