Applications of the Gas Laws

One national news story in the year 2000 involved the defect in certain brands of tires and how tread separation caused vehicle accidents leading to personal injury and in some cases deaths. One prominent aspect of the tire story involved whether the tires were properly inflated to the correct pressure. The air inside a tire can be considered an ideal gas, and we can apply the gas laws to the air inside. The inflation pressure recommendations stamped on the sides of tires call for tires to be inflated under cold conditions, or before the vehicle is driven. Because the most important aspect of tire performance is correct inflation pressure, it is important to adhere to the recommended tire pressure. Many individuals disregard this recommendation. It is not uncommon for someone to pull into a gas station and fill 

This is a relatively small change, but consider the change if you inflate the tire in a heated garage at 70°F and then drive in winter when the temperature is 10°F. In this case, the pressure drop would be approximately 5 psi. A pressure change of this much can lead to as much as a 25% reduction in fuel efficiency. Additionally, underinflated tires result in overloading and possible tire failure. Reduced tire pressures of as little as 4 psi were cited in some of the national stories involving tire failure and vehicle accidents. 

Another area in which the gas laws play a key role is in scuba diving. At the surface, we breath air at a pressure of approximately 1 atmosphere. The partial pressures of nitrogen and oxygen are 0.78 and 0.20 atmosphere, respectively. A scuba diver breaths compressed air that is delivered at a pressure that corresponds to the pressure at the depth of the diver. Because 33 feet of 

Another example of a diving problem that is a direct consequence of Dalton s Law of partial pressure concerns oxygen toxicity. The deeper a diver descends, the greater the partial pressure of oxygen. At a depth of 130 feet, the total pressure is close to 5 atmospheres and the partial pressure of oxygen will be close to 1 atmosphere (21% X 5 atmospheres). What this means is that breathing compressed air at 130 feet is like 

Both decompression sickness and air embolism can be treated by placing the victim in a hyperbaric chamber. Hyper  

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When a solid such as charcoal is exposed in a closed space to a gas or vapour at some definite pressure, the solid begins to adsorb the gas and (if the solid is suspended, for example, on a spring balance) by an increase in the weight of the solid and a decrease in the pressure of the gas. After a time the pressure becomes constant at the value p, say, and correspondingly the weight ceases to increase any further. The amount of gas thus adsorbed can be calculated from the fall in pressure by application of the gas laws if the volumes of the vessel and of the solid are known or it can be determined directly as the increase in weight of the solid in the case where the spring balance is used. 

As mentioned above, the rate of mass flux into the monitor is independent of pressure and dependent on the square root of absolute temperature. However, further corrections do exist when mass, by G.C. analysis, is converted to mg/m3 or PPM. As with rotometers and a pump, the corrections are not the simple application of the gas laws. 

In this section, you learned how to use the combined gas law for gas calculations. You also learned about natural phenomena that are related to gases. Finally, you learned about Dalton s law of partial pressures. In Chapter 12, you will learn more about gas laws. First, however, you will take a closer look at some technological applications of the gas laws. 

The compilations of CRC (1-2), Daubert and Danner (3), Dechema (15), TRC (13-14), Vargaftik (18), and Yaws (19-36) were used extensively for critical properties. Estimates of critical temperature, pressure, and volume were primarily based on the Joback method (10-12) and proprietary techniques of the author. Critical density was determined from dividing molecular weight by critical volume. Critical compressibility factor was ascertained from application of the gas law at the critical point. Estimates for acentric factor were primarily made by using the Antoine equation for vapor pressure (11-12). 

Hot air balloonists use large fans to force air into their balloons. When the balloon is about three quarters full, they turn off the fan and heat the air inside the balloon using a propane burner. As the air is heated, the balloon rises. Once airborne, the balloonist can turn off the burner and just use it occasionally to keep the balloon aloft. The heating of the air in the balloon is a practical application of the gas laws. 

One of the most important applications of the gas laws in chemistry is to calculate the volumes of gases consumed or produced in chemical reactions. If the conditions of pressure and temperature are known, the ideal gas law can be used to convert between the number of moles and gas volume. Instead of working with the mass of each gas taking part in the reaction, we can then use its volume, which is easier to measure. This is illustrated by the following example. 

This term C0 is called by Nemst (Applications of Thermodynamics to Chemistry) the chemical constant of the substance in question It must be remembered that at ordinary temperatures the gas laws only hold approximately for saturated vapour At lower temperatures, however, the application of the gas laws becomes increasingly more valid For this reason, therefore, Nemst and his pupils have in recent years earned out a considerable number of very accurate vapour pressure determinations at temperatures considerably below o° C Details of these will be found m his book already referred to (Applications of Thermodynamics to Chemistry), and also J T Barker (Zeit fur fhysik Chem, 71, 235, I910)... 

Consider forms I and II of a given substance Let us suppose that the respective solubilities in a solvent A are CIA and Cm We shall further suppose that even the saturated solutions are sufficiently dilute to justify the applicability of the gas law The maximum work obtainable on transferring 8n moles from the solid in contact with the first solution to the solid in contact with the second is—... 

Chemical equilibrium in homogeneous systems—Dilute solutions—Applicability of the Gas Laws—Thermodynamic relations between osmotic pressure and the lowering of the vapour pressure, the rise of boiling point, the lowering of freez ing point of the solvent, and change in the solubility of the solvent in another liquid—Molecular weight of dissolved substances—Law of mass action—Change of equilibrium constant with temperature and pressure... 

In equation (127), U0 denotes the heat evolution of the reaction at the absolute zero, and E the energy content of each separate gas the summation is to be taken as described on page 126. The expression in formula (128) is, however, by no means zero for T — o, i.e. our Heat Theorem in this case again does not hold, in its direct application to gases. This is, of course, not surprising because we have so far assumed the applicability of the gas laws down to the lowest temperatures, which, according to equation (126) precludes the applicability of our Heat Theorem. 

In the determination of the surface area, the amount of gas adsorbed by a fixed mass of solid at a fixed temperature is measured for different gas pressures p. Commonly, a known volume of gas is contacted with the powder, and the amount of gas adsorbed is determined from the fall in gas pressure by application of the gas laws. A graph of amount of gas adsorbed versus p (or p/po, if the gas is at a pressure below its saturation vapor pressure po), referred to as the adsorption isotherm, is plotted. In the literature, there are thousands of adsorption isotherms... 

The amount adsorbed depends upon the nature of the solid (adsorbent), and the pressure at which adsorption takes place. The amount of gas (adsorbate) adsorbed can be found by determining the increase in weight of the solid (gravimetric method) or determining the amount of gas removed from the system due to adsorption by application of the gas laws (volumetric method). 

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