Gas Laws

Gas Laws

Since the days of Aristotle, all substances have been classified into one of three physical states. A substance having a fixed volume and shape is a solid. A substance, which has a fixed volume but not a fixed shape, is a liquid; liquids assume the shape of their container but do not necessarily fill it. A substance having neither a fixed shape nor a fixed volume is a gas; gases assume both the shape and the volume of their container. The structures of gases, and their behavior, are simpler than the structures and behavior of the two condensed phases, the solids and the liquids

Pressure and the Law of Boyle

Quantitative measurements on gases were first made in a rational manner by the English chemist Robert Boyle (1627 - 1691). The instruments used by Boyle to measure pressure were two: the manometer, which measures differences in pressure, and the barometer, which measures the total pressure of the atmosphere.

A manometer is simply a bent piece of tubing, preferably glass with one end closed.

When the liquid level in both arms is the same, the pressure of the sample of gas inside the closed end must equal the pressure of the external atmosphere since the downward force on the two columns of liquid is then equal. When the liquid levels are unequal, the pressures must differ. The difference in pressure can be measured in units of length of the vertical column of liquid. The mm Hg, or its modern version the torr, originated in this use of the manometer. Mercury is particularly convenient for use in manometers (and barometers) because at room temperature it has low vapor pressure, does not wet glass, and has a high density. Other liquids such as linseed oil or water have also been used in manometers.

The barometer is a device for measuring the total pressure of the atmosphere. A primitive barometer can easily be constructed by taking a glass tube about a meter long, sealing one end, filling the tube completely with mercury, placing your thumb firmly over the open end, and carefully inverting the tube into an open dish filled with mercury. The mercury will fall to a height independent of the diameter of the tube and a vacuum will be created above it.

The height of the mercury column will be the height which the atmospheric pressure can support. The standard atmospheric pressure, one atmosphere (atm), is 760 mm Hg but the actua...

... middle of paper ...

... taking enough chemistry, you will see it showing up over and over and over.

The Numerical Value for R

R's value can be determined many ways. This is just one way:

Assume we have 1.000 mol of a gas at STP. The volume of this amount of gas under the conditions of STP is known to a high degree of precision. We will use the value of 22.414 L.

By the way, 22.414 L at STP has a name. It is called "molar volume." It is the volume of ANY ideal gas at standard temperature and pressure. (Siebring, Richard, Page 54)

Let's plug our numbers into the equation:

(1.000 atm) (22.414 L) = (1.000 mol) (R) (273.15 K)

Notice how atmospheres were used as well as the exact value for standard temperature.

Solving for R gives 0.08206 L atm / mol K, when rounded to four significant figures. This is usually enough. Remember the value. You'll need it for problem solving.

Notice the weird unit on R: say out loud "liter atmospheres per mole Kelvin."

This is not the only value of R that can exist. It depends on which units you select. Those of you that take more chemistry than high school level will meet up with 8.3145 Joules per mole Kelvin, but that's for another time.