## The Gas Laws

The gas laws, particularly their influence on the solution or removal of gases from liquids, are of particular significance to the environmental engineer and scientist.

Boyle's Law

Boyle's, law states: The volume of a gas varies inversely with its pressure at constant temperature. This law is so simple and usually so well understood that further elaboration seems unnecessary. Its principal application is in converting observations of gas volume from field conditions to some standard condition. This is particularly significant at high altitudes, such as at Denver and Salt Lake City.

Charles' Law

Charles' law states: The volume of gas at constant pressure varies in direct proportion to the absolute temperature. Interpretation of this law poses no problems, provided that the absolute-temperature scale is used. Charles' law finds its greatest use in the calculation of pressures in fixed-volume containers with variable temperature. In conjunction with Boyle's law, it serves as the basis for sizing gas holders.

Generalized Gas Law

For a given quantity of a gas, Boyle's law and Charles' law can be combined in the form

where jS = constant proportional to weight of gas P = pressure of gas V = volume of gas T = absolute temperature of gas

It has been shown that the constant ¡3 is a function of the number of moles of gas present, and that a more universal, idealized gas law (termed the ideal gas law) which is quite general for any gas can be expressed as

where n equals the number of moles of gas in the particular sample and J? is a universal constant for all gases. The numerical value for R depends on the units chosen for the measurement of P, V, and T, A useful way to evaluate R is to remember that 1 mol of an ideal gas at 1 atm pressure occupies a volume of 22.414 liters at 273 kelvins (K). From this, R can be evaluated to be 0.082 liter atmosphere per mole per kelvin (0.082 L-atm/mol-K).

What tank volume is required to hold :10,000/kg of methane gas (CH4) at.25 degrees'Cek ; | EXAMPLE 2.6 sius (°C) and 2 atm pressure?

The molecular weight of CH4 gas is 12 + 4(1) = 16 g. The number of moles in ,. 10,(300 kg is 10,600,000/16 = the general gas law, \ .; /

; ^^ps' '^ith yol umfc of- r7.<54 ><:; : liters or .2.7; -X; 10?. ;cubic feet wpul<i bfe

Dalton's Law of Partial Pressures

This law has been presented in a number of ways, but in essence it may be stated as follows: In a mixture of gases, such as air, each gas exerts pressure independently of the others. The partial pressure of each gas is proportional to the amount (percent by volume) of that gas in the mixture, or in other words, it is equal to the pressure that gas would exert if it were the sole occupant of the volume available to the mixture. The basic concept of this law, in combination with Henry's law, serves in many engineering considerations and calculations.

Henry's Law

Henry's law states: The mass of any gas that will dissolve in a given volume of a liquid, at constant temperature, is directly proportional to the pressure that the gas exerts above the liquid. In equation form, p

Cequil where Ccqliji = concentration of gas dissolved in liquid at equilibrium Pgas = partial pressure of gas above liquid Kh - Henry's law constant for gas at given temperature

Henry's law is undoubtedly the most important of all the gas laws in problems involving liquids. With a firm knowledge of Dalton's and Henry's laws, one should be capable of coping with all problems involving gas transfer into and out of liquids. As an example, the Henry's law constant, KH, for oxygen in water at 20°C is 0.73 atm-m3/mol. Since air contains 21 percent by volume of oxygen, the partial pressure of oxygen in air according to Dalton's law would be 0.21 atm when the total air pressure is 1 atm. Therefore, the equilibrium concentration of oxygen in water at 20°C and in the presence of 1 atm of air would be 0.21/0.73 = 0.288 mol/m3 or 0.288(32,000)/1000 = 9.2 mg/L.

In the environmental engineering field, many of the problems related to the transfer of gases into liquids involve addition of oxygen by aeration to maintain aerobic conditions. The removal of gases from liquids is also accomplished by aeration devices of one sort or another. Usually the processes involve gas transfer at or near atmospheric pressure from air bubbles passing through a liquid, liquid drops falling through air, or thin films of liquid flowing over surfaces exposed to the air. Although Henry's law is an equilibrium law and is not directly concerned with the kinetics of gas transfer, it serves to indicate how far a liquid-gas system is from equilibrium, which in turn is a factor in the rate of gas transfer. Thus, the rate of dissolution of oxygen is proportional to the difference between the equilibrium concentration as given by Henry's law and the actual concentration in the liquid:

This concept serves as the basis for calculations in aerobic methods of waste treatment, such as the activated sludge process, and in the evaluation of the reaeration capacity of lakes and streams.

The removal of undesirable gases, such as carbon dioxide, hydrogen sulfide, hydrogen cyanide, and a wide variety of volatile organic compounds, such as trichloroethene and carbon tetrachloride, from liquids is also commonly accomplished by some form of aeration. The general principles involved are the same as in the transfer of gases into the liquid. However, in this case the normal partial pressure of the gas in air is very low or zero, so based on Henry's law, Ceqilii is also low and much less than Cactua!. Thus, the rate of transfer given by the above equation is negative, and the gas leaves rather than enters the solution. The same principles apply to the removal of any volatile substance dissolved in water as long as it exerts a significant vapor pressure at the temperature involved. Examples and discussion are given in Sec. 5.34.

Graham's Law

Graham's law is concerned with the diffusion of gases, and it states: The rates of effusion (escape of a gas through a tiny hole) of gases are inversely proportional to the square roots of their molecular masses. This law can be illustrated by a comparison of the rates of diffusion of hydrogen, oxygen, chlorine, and bromine, which have molecular weights of approximately 2, 32,71.5, and 160, respectively. On the basis of Graham's law, oxygen diffuses about one-fourth, chlorine about one-sixth, and bromine about one-ninth as fast as hydrogen. This law finds its greatest application in the field of industrial hygiene and air pollution control. Molecular mass is also important in the rate of gas transfer into (e.g., oxygen for aeration processes) and out of (e.g., removal of contaminant gases from water) aqueous solution.

Gay-Lussac's Law of Combining Volumes

Gay-Lussac's law is basic to an understanding of gas analysis. The law states: The volumes of all gases that react and that are produced during the course of a reaction are related, numerically, to one another as a group of small, whole numbers. This law may be illustrated as follows:

One volume of oxygen combines with carbon (a solid) to yield 1 volume of carbon dioxide, or

Two volumes of oxygen combine with 1 volume of methane to form 1 volume of carbon dioxide. If the temperature of the system is held above 100°C, 2 volumes of water vapor will result. Usually the temperature of the system is brought back to room temperature, the water vapor condenses, and the volume of water is considered zero because it is segregated from the gaseous phase and does not interfere with measurement of the volume of gaseous products.

## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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