Gases mole problems

Ans. Ideal gas law problems involve moles. If the number of moles of gas is given or asked for, or if a quantity that involves moles is given or asked for, the problem is most likely an ideal gas law problem. Thus, any problem involving masses of gas (which can be converted to moles of gas) or molecular weights (grams per mole) or numbers of individual molecules (which can be converted to moles) and so forth is an ideal gas law problem. Problems that involve an unchanging mass of gas are most likely not ideal gas law problems. 

Our goal in this chapter is to assist you in learning the concepts of gases and gas laws. Be sure that you know how to properly use your calculator and, if you need to, refer to Chapter 3 on the mole concept. It s especially true with gas law problems that the only way to master them is to Practice, Practice, Practice. 

Gas law problems, like all problems, begin with isolating the variables and the unknown from the question. The usual suspects in gas law problems are pressure, volume, temperature, and moles. You will need to deal with at least two of these properties in every problem. 

Another type of gas law problem involves stoichiometry. Gas stoichiometry problems are just like all other stoichiometry problems—you must use moles. In addition, one or more gas laws are necessary. Let s look at a gas stoichiometry problem. What volume, in liters of oxygen gas, collected over water, forms when 12.2 g ofKCl03 decompose according to the following equation ... 

Since the number of moles of reactant gas equals the number of moles of product gas, moles may be used in place of concentrations (as in Problem 16-12), and Kp = K. 

The compound balances are in moles. Gas combustion problems can be presented in tabular form for convenience and to save space. The balances can be written as... 

In gas stoichiometry problems, what is the bridge between amount in moles and volume ... 

For more practice with ideal gas law problems that use moles, go to Supplemental Practice Problems in Appendix A. 

P4-7. A gas phase reaction with a change in the total number of moles] volumetric flow rate v. If either P4-4 or P4-5 is assigned at the same tii this problem, I would suggest assigning only parts (a) and (b) and pel part (e). In part (e) they must solve for X and different temperatures loi the optimum- (A/se see CDP F for a gas phase reaction with a chan the total number of moles. Problem CDP4 F r which was often S5( from the second edition, is straight forward and reinforces the principles and can be alternated form year to year with P4-7 problem.)... 

In Chapters 3 and 4, we encountered many reactions that involved gases as reactants (e.g., combustion with O2) or as products (e.g., a metal displacing H2 from acid). From the balanced equation, we used stoichiometrically equivalent molar ratios to calculate the amounts (moles) of reactants and products and converted these quantities into masses, numbers of molecules, or solution volumes (see Figure 3.10). Figure 5.11 shows how you can expand your problem-solving repertoire by using the ideal gas law to convert between gas variables (F, T, and V) and amounts (moles) of gaseous reactants and products. In effect, you combine a gas law problem with a stoichiometry problem it is more realistic to measure the volume, pressure, and temperature of a gas than its mass. 

Problem Hot H2 can reduce copper(II) oxide, forming the pure metal and H2O. What volume of H2 at 765 torr and 225°C is needed to reduce 35.5 g of copper(II) oxide Plan This is a stoichiometry and gas law problem. To find Fh we first need h,. We write and balance the equation. Next, we convert the given mass of CuO (35.5 g) to amount (mol) and use the molar ratio to find moles of H2 needed (stoichiometry portion). Then, we use the ideal gas law to convert moles of H2 to liters (gas law portion). A roadmap is shown, but you are familiar with all the steps. 

Gas absorption and liquid-liquid extraction are analogous in that in each there are two carrier streams and at least one solute to be partitioned between them. The following example illustrates the application of the McCabe-Thiele graphical method to a gas absorption problem. Mole units are used. 

To avoid using the units of / as a fraction, we will use it as follows R = 0.0821 L atm K mol. Note carefully the units of R pressure is in atmospheres, temperature in kelvins, volume in liters, and n in moles. To use this equation for solving gas law problems you must pay strict attention to all units. 

The solution to this problem requires an analysis of multiple gas-phase reactions in a differential plug-flow tubular reactor. Two different solution strategies are described here. In both cases, it is important to write mass balances in terms of molar flow rates and reactor volume. Molar densities and residence time are not appropriate for the convective mass-transfer-rate process because one cannot assume that the total volumetric flow rate is constant in the gas phase, particularly when the total number of moles is not conserved. In each reaction, 2 mol of reactants generates 1 mol of product. Furthermore, an overall mass balance suggests that the volumetric flow rate is constant only when the overall mass density does not change. This is a reasonable assumption for liquid-phase reactors but not for gas-phase problems when the total volume is not restricted. The exception is a constant-volume batch reactor. 

Tliis is a gas stoichiometry problem that requires knowledge of Avogadro s law to solve. Avogadro s law states that the volume of a gas is directly proportional to the number of moles of gas at constant temperatiue and pressure. 

The stoichiometry path may be summarized as given quantity mol given mol wanted wanted quantity. In a gas stoichiometry problem, the first or third step in the path is a conversion between moles and liters of gas at a given temperature and pressure. If you are given volume, you must convert to moles if you find moles of wanted substance, you must convert to volume. These conversions are made with the ideal gas equation, PV = nRT. You have already made conversions like these. For example, in Example 14.3, you calculated the volume occupied by 0.393 mol N2 at 24°C and 0.971 atm. You used the ideal gas equation solved for V. 

Be sure to match the units of the known quantities and the units of R. In this book, you will be using R = 0.0821 L atm/(mol K). Your first step in solving any ideal gas law problem should be to check the known values to be sure you are working with the correct units. If necessary, you must convert volumes to liters, pressures to atmospheres, temperatures to kelvins, and masses to numbers of moles before using the ideal gas law. 

One approach to the problem of retrieval of gas profiles by inversion is linearization and iteration. The unknown profile is expressed in terms of a set of discrete parameters these may consist of the values of the gas mole fraction at the quadrature points used in the numerical integrations required to calculate the radiance... 

Next to sales contract specifications, coiTosion protection ranks highest among the reasons for the removal of acid gases. The partial pressure ol the acid gases may be used as a measure to determine whether treatment IS required. The partial pressure of a gas is defined as the total pressure of the system times the mole % of the ga,seous component. Where ( 02 is present with free water, a partial pres.sure ot. hi psia or greater would indicate that CO2 corrosion should be expected. If CO2 is not removed, inhibition and special metallurgy may be required. Below 15 psia, COt corrosion is not normally a problem, although inhibition may be required. 

Diethanolamine Systems. Diethanolamine (DEA) is a secondary amine that has in recent years replaced MEA as the most common chemical solvent., s a secondary amine, DEA is a weaker base than MEA, and therefore DEA systems do not typically suffer the same corrosion problems. In addition, DEA has lower vapor loss, requires less heat for regeneration per mole of acid gas removed, and does not require a reclaimei. DEA reacts with H iS and COt as follows ... 

PROBLEM What is the amount of heat which must be removed in cooling one pound mole of 0.6 Sp. Gravity gas at 120 Absolute from 300°F to 100°F ... 

An examination of some laboratory runs with diluted C150-1-02 catalyst can illustrate this problem. In one run with 304°C at inlet, 314 °C at exit, and 97,297 outlet dry gas space velocity, the following results were obtained after minor corrections for analytical errors. Of the CO present (out of an inlet 2.04 mole % ), 99.9885% disappeared in reaction while the C02 present (from an initial 1.96%) increased by over 30%. Equilibrium carbon oxides for both methanation reactions were essentially zero whereas the equilibrium CO based on the water-gas shift reaction at the exit composition was about one-third the actual CO exit of 0.03 mole %. From these data, activities for the various reactions may be estimated on the basis of various assumptions (see Table XIX for the effect of two different assumptions). 

Solution The obvious way to solve this problem is to choose a pressure, calculate Oq using the ideal gas law, and then conduct a batch reaction at constant T and P. Equation (7.38) gives the reaction rate. Any reasonable values for n and kfCm. be used. Since there is a change in the number of moles upon reaction, a variable-volume reactor is needed. A straightforward but messy approach uses the methodology of Section 2.6 and solves component balances in terms of the number of moles, Na, Nb, and Nc-... 

The problem asks about the fraction of gas in the larger tank. This fraction is the ratio of the number of moles in the larger tank to the total number of moles in both tanks. Because n j V is constant, we can large tank ... 

We have a mixture of two gases in a container whose volume and temperature are known. The problem asks for pressures and mole tractions. Because molecular interactions are negligible, each gas can be described independently by the ideal gas equation. As usual, we need molar amounts for the calculations. 

In any stoichiometry problem, work with moles. This problem involves gases, so use the ideal gas equation to convert P-V-T information into moles. 

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. 

In this form Eq. (86) cannot be integrated without a relation between P and V, because die second term on the right-hand side involves both variables. However, in the special case in which the gas is ideal, PV = RT for one mole and (dEfdV)r = 0 (see problem 6). The latter relation implies the absence of intermolecular forces. Then, Eq. (86) becomes... 

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