Gases stoichiometric calculations

Stoichiometric calculations always require amounts in moles. For gases, amounts In moles are usually calculated from the ideal gas equation. Example shows how to do this. 

Any of the types of problems discussed in Chapters 3 and 4 can involve gases. The strategy for doing stoichiometric calculations is the same whether the species involved are solids, liquids, or gases. In this chapter, we add the ideal gas equation to our equations for converting measured quantities into moles. Example is a limiting reactant problem that involves a gas. 

Since the element of time is usually involved as die basis of a stoichiometric calculation, proper quantitative deductions often depend on adequate knowledge of other laws or principles, such as those governing rates of reaction and those pertaining to chemical equilibria. When materials in die gaseous state are involved, die general gas laws are of great utility. 

The methyl esters can be also determined by GC-FID. Using a 30 m x 0.32 mm ID x 0.25 pm (film thickness) capillary column, such as DB-1701 or equivalent, the compounds can be adequately separated and detected by FID. The recommended carrier gas (helium) flow rate is 35 cm/s, while that of the makeup gas (nitrogen) is 30 cm/min. All of the listed herbicides may be analyzed within 25 min. The oven temperature is programmed between 50 and 260°C, while the detector and injector temperatures should be 300 and 250°C, respectively. The herbicides may alternatively converted into their trimethylsilyl esters and analyzed by GC-FID under the same conditions. FID, however, gives a lower response as compared with ECD. The detection level ranges from 50 to 100 ng. For quantitation, either the external standard or the internal standard method may be applied. Any chlorinated compound stable under the above analytical conditions, which produces a sharp peak in the same RT range without coeluting with any analyte, may be used as an internal standard for GC-ECD analysis. U.S. EPA Method 8151 refers the use of 4,4,-dibromooctafluorobiphenyl and 1,4-dichlorobenzene as internal standards. The quantitation results are expressed as acid equivalent of esters. If pure chlorophenoxy acid neat compounds are esterified and used for calibration, the results would determine the actual concentrations of herbicides in the sample. Alternatively, if required, the herbicide acids can be stoichiometrically calculated as follows from the concentration of their methyl esters determined in the analysis ... 

In Chapter 12, you will find out about the ideal gas law. This law covers the many different gas laws you explored in this chapter. You will also discover a practical application for Dalton s law of partial pressures. You will learn how to do stoichiometric calculations for reactions that consume or produce a gas. In the laboratory, you will have a chance to produce and collect a gas. At the end of the next chapter, you will examine some of the chemistry that takes place in our atmosphere. 

Na20). Stoichiometric calculations are needed to determine the precise quantity of sodium azide that will produce the volume of nitrogen gas required to inflate the air bag. If too much gas is produced, the air bag may be so rigid that hitting it would be the same as hitting a solid wall. 

To do stoichiometric calculations that involve both gas volumes and masses, you must know the balanced equation for the reaction involved, at least one mass or volume value for a reactant or product, and the conditions under which the gas volumes have been measured. Then the ideal gas law can be used along with volume or mole ratios to complete the calculation. 

Use the ideal gas law to relate pressure, volume, temperature, and nnmber of moles of an ideal gas and to do stoichiometric calculations involving gases (Section 9.3, Problems 19-32). 

The molar volume of a gas is the volume that a mole of a gas occupies at a pressure of one atmosphere (equal to 101 kPa) and a temperature of 0 00°C Under these conditions of STP, the volume of 1 mol of any gas is 22.4 L, as shown in Figure 12.7. Like the molar mass, the molar volume is used in stoichiometric calculations. 

For stoichiometric calculations we would read this equation as 2 moles of carbon monoxide gas combine with 1 mole of oxygen gas to form 2 moles of carbon dioxide... 

We have seen in this chapter just how useful the ideal gas equation is. For example, if we know the pressure, volume, and temperature for a given sample of gas, we can calculate the number of moles present n = PV/RT. This fact makes it possible to do stoichiometric calculations for reactions involving gases. 

So far we have used moles or concentrations in stoichiometric calculations. However, it is equally valid to use pressures for a gas-phase system at constant... 

Largely theoretical stoichiometric calculations of the toxic combustion products should not replace direct gas analyses under the proper experimental conditions. 

When we discussed quantitative aspects of chemical reactions in Chapter 4, we emphasized the importance of ratios of moles. The ideal gas law provides a relationship between the number of moles of a gas and some easily measurable properties pressure, volume, and temperature. So when gases are involved in a chemical reaction, the ideal gas law often provides the best way to determine the number of moles. Using the ideal gas law in a stoichiometry problem really doesn t involve any new ideas. It just combines two kinds of calculations that you ve already been doing. We ll still do the stoichiometric calculation in terms of mole ratios, as always, and we ll use the gas law to connect the number of moles of a gas with its temperature, pressure, and volume. 

We are asked to find the volume of a gas, and we are given its pressure and temperature. We ll assume that the gas behaves ideally. So if we knew the number of moles, we could easily use the gas law to get the volume we need. Looking a little closer, we should recognize this as a reaction stoichiometry problem because it asks us how much CO2 will be produced. The new wrinkle here is that it asks us to express the answer as a volume rather than as a mass or a number of moles. So we will first do a stoichiometric calculation to find the number of moles of CO2 produced and then use the gas law to find the volume of that amount of gas at the indicated temperature and pressure. As in any stoichiometry problem, we ll need to start with a balanced equation for the reaction to be sure we use the correct mole ratio. 

Thus, this equation can also be read as 1 mole of N2 gas combines with 3 moles of H2 gas to form 2 moles of NH3 gas. In stoichiometric calculations, we say that three moles of H2 are equivalent to two moles of NH3, that is,... 

Stoichiometric problems involving gas volumes can be solved by the general mole-ratio method outlined in Chapter 9. The factors 1 mol/22.4 L and 22.4 L/1 mol are used for converting volume to moles and moles to volume, respectively. (See Figure 12.16.) These conversion factors are used under the assumption that the gases are at STP and that they behave as ideal gases. In actual practice, gases are measured at other than STP conditions, and the volumes are converted to STP for stoichiometric calculations. 

Gases in Chemical Reactions Stoichiometric calculations involving gases are similar to those that do not involve gases in that the coefficients in a balanced chemical equation provide conversion factors among moles of reactants and products in the reaction. For gases, the amoimt of a reactant or product is often specified by the volume of reactant or product at a given temperature and pressiue. The ideal gas law is then used to convert from these quantities to moles of reactant or product. Alternatively at standard temperature and pressure, volume can be converted directly to moles with ffie equality ... 

As we discussed in Chapter 7, many chemical reactions take place in aqueous solutions. Precipitation reactions, neutralization reactions, and gas evolution reactions, for example, all occur in aqueous solutions. Chapter 8 describes how we use the coefficients in chemical equations as conversion factors between moles of reactants and moles of products in stoichiometric calculations. These conversion factors are often used to determine, for example, the amount of product obtained in a chemical reaction based on a given amount of reactant or the amount of one reactant needed to completely react with a given amount of another reactant. The general solution map for these kinds of calculations is ... 

In reactions involving gaseous reactant or products, we often specify the quantity of a gas in terms of its volume at a given temperature and pressure. As we have seen, stoichiometry involves relationships between amounts in moles. For stoichiometric calculations involving gases, we can use the ideal gas law to determine the amounts in moles from the volumes, or to determine the volumes from the amounts in moles. 

In Section 5.5 we saw that under standard temperature and pressure, 1 mol of an ideal gas occupies 22.4 L. Consequently, if a reaction occurs at or near standard temperature and pressure, we can use 1 mol = 22.4 L as a conversion factor in stoichiometric calculations, as shown in Example 5.13. 

EXAMPLE 5.13 Using Molar Volume in Gas Stoichiometric Calculations... 

In Chapter 13, you learned how to use moles and molar mass along with a balanced chemical equation to calculate the masses of reactants and products in a chemical reaction. Now that you know how to relate volumes, masses, and moles for a gas, you can do stoichiometric calculations for reactions involving gases. 

Let us compare computations of the effectiveness factor, using each of the three approximations we have described, with exact values from the complete dusty gas model. The calculations are performed for a first order reaction of the form A lOB in a spherical pellet. The stoichiometric coefficient 10 for the product is unrealistically large, but is chosen to emphasize any differences between the different approaches. 

Formulations should be based on stoichiometric considerations. Based on a knowledge of the hydroxyl value of the polyol the amount of isocyanate necessary to cause chain growth should be calculated. The gas evolved will depend on the water content and additional isocyanate must be incorporated corresponding to the water present. When the isocyanate used equals the theoretical amount the system is said to have a TDI index of 100. In practice a slight excess of isocyanate is used (TDI index 105-110) to ensure complete... 

Analysis had shown that the fuel behaved like ethylene-air mixture and the cloud could be so large that it could fill the whole calculation domain up to about 20 m high. The ethylene-air gas cloud was assumed to be a homogeneous stoichiometric mixture with the shape of a box. The following two cloud assumptions were chosen ... 

Adiabatic Reaction Temperature (T ). The concept of adiabatic or theoretical reaction temperature (T j) plays an important role in the design of chemical reactors, gas furnaces, and other process equipment to handle highly exothermic reactions such as combustion. T is defined as the final temperature attained by the reaction mixture at the completion of a chemical reaction carried out under adiabatic conditions in a closed system at constant pressure. Theoretically, this is the maximum temperature achieved by the products when stoichiometric quantities of reactants are completely converted into products in an adiabatic reactor. In general, T is a function of the initial temperature (T) of the reactants and their relative amounts as well as the presence of any nonreactive (inert) materials. T is also dependent on the extent of completion of the reaction. In actual experiments, it is very unlikely that the theoretical maximum values of T can be realized, but the calculated results do provide an idealized basis for comparison of the thermal effects resulting from exothermic reactions. Lower feed temperatures (T), presence of inerts and excess reactants, and incomplete conversion tend to reduce the value of T. The term theoretical or adiabatic flame temperature (T,, ) is preferred over T in dealing exclusively with the combustion of fuels. 

For most compounds detailed flammability zone data are not available. In this case an estimate can be made of the location of point S, as shown in Figure AC-6. Point S can be approximated by a line starting at the pure air point and connecting through a point at the intersection of the LFL with the stoichiometric line. Equation AC-7 can be used to determine the gas composition at point S. Referring to Figure AC-2, we know the gas composition at points R and M and wish to calculate the gas composition at point S. Let A represent the fuel and C the oxy-... 

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