Table 7.2 Pressure Conversion Table

7.2.5 Gases, Vapors, and the Gas Laws

A vapor is a gas that is near its condensation temperature and/or pressure. At room temperature and pressure, gaseous water is a vapor; in a steel furnace, gaseous water is a gas. Some gases (hydrogen, helium, nitrogen, oxygen, and other cryogenic gases) do not have a vapor state anywhere near STP and are sometimes called permanent gases. For more information on condensation as well as evaporation and equilibrium, see Sec. 7.2.6.

Of the three states of matter (solid, liquid, and gas), only gases have radically changing distances between molecules. When the distances between the molecules of a gas are different than what is found at STP (Standard Temperature and Pressure), we have either a positive or negative pressure (compared to atmospheric).

As far as a gas is concerned, it does not make a difference whether the size of the container, the temperature of the gas, or the amount of gas has changed. All these conditions separately or together can change the pressure within a container. Analysis of contained gases led to the following gas laws, most of which go by the name of the researcher who formally identified them:

1.All gases uniformly fill all spaces within a container. This space is called the volume (V). There cannot be an independent localized collection of gases exerting uneven pressures within a container.

2.All gases exert an equal pressure on all points of a container. Regardless of the shape of the container (on a static system), there can be no variation of gas pressure from any one point to any other point within that container.

3.All gases exhibit a direct relationship between the temperature and pres-

sure for a given volume and given amount of gas. Assuming that noth-

ing else changes, if the temperature increases, the pressure will increase a directly proportional amount.

4.All gases exhibit an inverse relationship between the volume and the pressure of a gas for a given temperature and amount of gas. Assuming that nothing else changes, if the volume increases, the pressure will decrease a directly proportional amount.

Boyle's Law

5.All gases of equal volumes, at the same temperature and pressure, contain the same number of molecules. The size of a gas atom (or molecule) has no relationship to pressure, temperature, or volume.

6.All gases exhibit a uniform relationship between the pressure and volume, temperature, and number of molecules present. This relationship is represented by the gas constant R (which is = 62.4 torrliter/molK) when Pressure is in torr, Volume is in liters, Temperature is in K, and n is the number of moles.*

7.If more than one gas is in a container, and the gases are not interacting, each gas will exhibit its own characteristic pressure. The sum of these individual pressures equals the total pressure. The percentage of each partial pressure is equal to the percentage of that gas in the sample.

Laws 3,4, and 5 are pulled together to create the ideal gas law, and the effects of it are shown pictorially in Fig. 7.1, where three different approaches to doubling

*A mole is an Avogadro's number (6.023 x 1O23) of molecules. One mole is equal to one atomic mass, or the molar mass of a molecule or atom. For example, one mole of carbon (atomic mass 12) is equal to 12.01115 g.

Fig. 7.1 Notice how you can double the pressure of a container by either doubling the temperature, doubling the number of molecules, or halving the volume.

the pressure are demonstrated. In Box A we have a given number of molecules at a given temperature and pressure in a container of one unit. In Box B, we have doubled the temperature, which causes the molecules to double their activity, which doubles the pressure. For Box C we have brought the temperature back to the original temperature, but have doubled the number of molecules within the container, which causes a doubling of the pressure. Finally, in Box D we have the same original temperature and the same number of molecules as in Box A, but we have decreased the size of the box by half, which doubles the pressure.

Remember that these are ideal gas laws, and in nature, gases do not necessarily behave ideally. This is typically because some other force is preventing the ideal gas law from performing ideally. For example, the first gas law states that all gases uniformly fill a container. Yet, in Sec. 7.2.8, Barbour demonstrates that if a system does not have effective conductance, it is possible for a system to maintain unequal pressures in different sections for a considerable period of time. The first gas law is still in force, but it is prevented from performing ideally due to another physical limitation: conductance. Additionally, anyone who has forced gases into a compressed gas tank or hastily removed them would have reason to doubt the ideal gas law graphically pointed out in Fig. 7.1, Box C. When gases are rapidly compressed in a confined area, there is typically a heat rise. Conversely, when gases are rapidly removed from a confined area, there is a typically a heat loss. The ideal gas law very clearly states that if the volume is the same and you double the number of molecules, there will be a doubling of pressure. It says nothing about a change in temperature. The problem here is that independently of the ideal gas law, adiabatic compression (and expansion) is having a secondary effect on the system. The trick is, one must allow a sufficiently slow introduction or removal of gases from a confined space for the ideal gas law to predominate. The slow addition or removal of gas allows a sufficient amount of time for heat conductance through the gas, and no heat rise or loss is created.