Some facts, Information, and History of the Concept of Gases
The ideal gas equation is PV=nRT. This is derived from Boyle's Law, Charles' Law, and Avogadro's hypothesis. The standard units used for this equation include the PASCAL for pressure. Pascals (Pa) are measured in Newtons per meter squared. Also used are the ATMOSPHERE (atm), of which one atm is defined as 101.325 kPa, and the barr, which has been arbitrarily set as equal to 100 kPa. The final pressure unit is the torr, defined as one seven-hundred and sixtieth of an atmosphere, and roughly equivalent to one millimeter of Mercury on the old manometer scales. The SI unit of volume is of course the LITER, where one millileter equals the volume of one cubic centimeter. Temperature is measured by the KELVIN (note that it is not DEGREE Kelvins, only Kelvins). One Kelvin equals one degree celsius plus 273.15, and one degree celsius equals one degree fahrenheit subtracted by thirty-two degrees and then multiplied by five-nineths. This ends our discussion on the standards of working with gasses.
The experimentation leading to the Ideal Gas Law began in the seventeenth century through the work of Robert Boyle. Boyle discovered that when holding the temperature of a closed system constant, volume increased inversely to pressure (causing the graph of a hyperbola in the first quadrant). When Boyle then increased the temperature, the graph of the hyperbola shifted to the right, while a decrease shifted the graph to the left. This discovery, that pressure and volume were inversely proportional with temperature acting only as a modifier, was the first third of the ideal gas puzzle.
The next piece was assembled by Charles in the eighteenth century. Instead of holding the temperature constant for his experiments, Charles chose to make the pressure constant. In doing so he discovered that volume and temperature were directly proportional. By playing with the equation, Charles was able to determine that Volume equalled the temperature multiplied by a constant. Eventually it was realized that this equation could be further simplified to volume equals temperature times a constant divided by pressure. But what was this constant? It was a difficult number to pin down, seeming to vary in increments depending on the situation.
Eventually this constant was determined and explained through the use of n. N is defined as "the amount of substance" in PV=nRT and is usually measured in moles, where one mole is equal to the number of atoms of the most common isotope of carbon in 12.000 grams. This is called Avogadro's Constant and is 6.022 * 10^23 moles^-1. This number, discovered by Avogadro, was based on his observation that if the volume, temperature, and pressure are the same for two gasses, then n is the same for those same two gasses, leading to PV=nRT.
The next topic to be dealt with at this time involves the concept of Partial Pressures. Rarely in life does one encounter just one gas; air, for example, is approximately seventy-nine percent nitrogen, twenty percent oxygen, and less than one percent of argon, carbon dioxide, and the rest. So what exactly is "air pressure" then? The answer to this is thankfully simple. Air pressure is the cumulative sum of the pressure from all of the other gases. This can be extended to say that the pressure on any surface is equal to the pressures exerted onto it by all gases present, or the partial pressures of the gases. The partial pressure of a gas is determined through PV=nRT, just as with anything else, although here n refers specifically to the amount of only that gas present. By summing the partial pressures the total pressure is arrived at easily, and through a few simple computations so too can the molecular weight of the gas. By dividing the partial pressure by the total pressure or the partial n by the total n, a Mole Fraction, abbreviated Xi can be arrived upon. The sum of the quantities of the mole fraction multiplied by the molecular weight of the gas for which the mole fractions were calculated yields the molecular weight of the gases in question. Thust ends the first lesson.