Applications of the Ideal Gas Law

Worst-case atmospheric conditions occur to maximize (C). This occurs with minimum dispersion coefficients and minimum wind speed u within a stability class. By inspection of Figs. 26-54 and 26-55 and Table 26-28, this occurs with F-stability and u = 2 m/s. At 300 m = 0.3 km, from Figs. 26-54 and 26-55, <3 = 11m and <3 = 5 m. The concentration in ppm is converted to kg/m by application of the ideal gas law. A pressure of 1 atm and temperature of 298 K are assumed. 

Specific volume is determined by application of the ideal gas law. One pound mole of air occupies a volume of 359 cubic feet at standard conditions, hence ... 

Equation 3-7 is converted to the more convenient concentration units of ppm by direct application of the ideal gas law. Let m represent mass, p represent density, and the subscripts v and b denote the volatile and bulk gas species, respectively. Then ... 

Solution Successive applications of the ideal gas law allow us to calculate the desired quantities. 

Most gas calculations are just applications of the ideal gas law in which three of the variables P, V, T, and n are known, and the fourth variable must be calculated. For example, the reaction used in the deployment of automobile air bags is the high-temperature decomposition of sodium azide, NaN3, to produce N2 gas. (The sodium is then removed by a subsequent reaction.) How many liters of N2 at 1.15 atm and 30°C are produced by decomposition of 145 g of NaN3 ... 

Still other applications of the ideal gas law make it possible to calculate such properties as density and molar mass. Densities are calculated by weighing a known volume of a gas at a known temperature and pressure, as shown in Figure 9.10. Using the ideal gas law to find the volume at STP and then dividing the measured mass by the volume gives the density at STP. Worked Example 9.7 gives a sample calculation. 

Figure 12.10 Mole Conversions, Including Application of the Ideal Gas Law to Determine the Number of Moles of a Gaseous Reactant or Product The green boxes represent the new additions to concepts already learned.

Another application of the ideal gas law arises when one is interested in converting a mass (or molar) flowrate to a volumetric flowrate (actual or standard), or vice versa. The ideal gas equation is rearranged and solved for one variable in terms of the others. For example, the volume of 1 Ibmol of ideal gas is given by... 

The laws discussed above are strictly valid only for ideal gases. The very fact that all gases can be liquefied if they are compressed and cooled sufficiently is an indication that all gases become nonideal at high pressures and low temperatures. The ideal properties are observed at low pressures and high temperatures, conditions far removed from those of the liquid state. At pressures below a few atmospheres practically all gases are sufficiently dilute for the application of the ideal gas laws with a reliability of a few percent or better. 

The concentration of a substance in the vapour phase (saturated vapour concentration, SVC) may be calculated from the SVP of the substance. This may be done to a useful level of accuracy by the simple application of the ideal gas law. Table 3 specifies the symbols and units of the parameters used in the calculation. 

The quantitative relationship of reactants and products is called stoichiometry. Stoichiometric problems require you to calculate the amounts of reactants required for certain amounts of products, or amounts of products produced from certain amounts of reactants. If, in a chemical reaction, one or more reactants or products are gases, gas laws must be considered for the calculation. Usually, the applications of the ideal gas law give results within 5% precision. 

Identify the region of applicability of the ideal-gas law and the truncated virial equation. 

Throughout this textbook, the application of the ideal gas law will come up again and again in one form or another. While you have almost certainly encountered the ideal gas law many times already, it is worth briefly reviewing it here. The ideal gas law is most commonly expressed as... 

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