The Ideal Gas Law and Reaction Stoichiometry

SAMPLE PROBLEM 5.11 Using Gas Variables to Find Amounts 

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. 

Check One way to check the answer is to compare it with the molar volume of an ideal gas at STP (22.4 L at 273.15 K and 1 atm). One mole of H2 at STP occupies about 22 L, so less than 0.5 mol occupies less than 11 L. 7 is less than twice 273 K, so V should be less than twice 11 L. 

Comment The main point here is that the stoichiometry provides one gas variable (n), two more are given, and the ideal gas law is used to find the fourth. 

FOLLOW-UP PROBLEM 5.11 Sulfuric acid reacts with sodium chloride to form aqueous sodium sulfate and hydrogen chloride gas. How many milliliters of gas form at STP when 0.117 kg of sodium chloride reacts with excess sulfuric acid  

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The equation is rendered integrable by application of the stoichiometry of the reaction, the ideal gas law, and, for instance, the power law for rate of reaction. Some details are shown in Table 7-9. 

We can use the gas law relationships, especially the ideal gas law and the combined gas law, in reaction stoichiometry problems. For example, suppose you have 2.50 g of an impure sample of KC103 and you want to determine how many grams of pure KC103 are present. You heat the mixture and the KC103 decomposes according to the equation ... 

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. 

The conservation equations of 9.6 and 9.7 have been written with the assumption of constant fluid velocity. If there is a net change in the number of moles due to the reaction, or if there is a significant change in the reactor temperature or pressure, the velocity cannot be considered constant. This change in velocity can be accounted for with the aid of the ideal gas law and the reaction stoichiometry ... 

Although the temperature and pressure of the gas are given, the number of moles of gas is not. Can we get it somewhere The chemical reaction of KCIO, yields the oxygen, and the rules of stoichiometry (Chap. 8) may be used to calculate the number of moles of gas. Note that the number of moles of KCIO, is not used in the ideal gas law equation. 

In this chapter, you learned about the properties of gases. You learned that you can use the combined gas law, the ideal gas law, or the individual gas laws to calculate certain gas quantities, such as temperature and pressure. You also learned that these equations could also be useful in reaction stoichiometry problems involving gases. You learned the postulates of the Kinetic-Molecular... 

You have already learned that the ideal gas law can be used to solve for different variables in several different types of situations. As you may recall, the term stoichiometry" refers to the relationship between the number of moles of the reactants and the number of moles of the products in a chemical reaction. In this section, you will learn how to use Gay-Lussac s law of combining volumes and the ideal gas law to solve stoichiometric problems that involve gases. 

Section 12.1 introduces the concept of pressure and describes a simple way of measuring gas pressures, as well as the customary units used for pressure. Section 12.2 discusses Boyle s law, which describes the effect of the pressure of a gas on its volume. Section 12.3 examines the effect of temperature on volume and introduces a new temperature scale that makes the effect easy to understand. Section 12.4 covers the combined gas law, which describes the effect of changes in both temperature and pressure on the volume of a gas. The ideal gas law, introduced in Section 12.5, describes how to calculate the number of moles in a sample of gas from its temperature, volume, and pressure. Dalton s law, presented in Section 12.6, enables the calculation of the pressure of an individual gas—for example, water vapor— in a mixture of gases. The number of moles present in any gas can be used in related calculations—for example, to obtain the molar mass of the gas (Section 12.7). Section 12.8 extends the concept of the number of moles of a gas to the stoichiometry of reactions in which at least one gas is involved. Section 12.9 enables us to calculate the volume of any gas in a chemical reaction from the volume of any other separate gas (not in a mixture of gases) in the reaction if their temperatures as well as their pressures are the same. Section 12.10 presents the kinetic molecular theory of gases, the accepted explanation of why gases behave as they do, which is based on the behavior of their individual molecules. 

Gases that are involved in chemical reactions obey the same laws of stoichiometry that apply to substances in any other state, as described in Chapters 8 and 10. Therefore, the ideal gas law can be used to calculate the quantities of gaseous substances involved in a reaction and then those results used to find the quantities of other substances. Figure 12.10 presents the conversions allowed by the ideal gas law (with green backgrounds), in addition to those originally shown in earlier figures. 

The molar mass of glueose is 180.15 g mol". From this, we ean ealculate the number of moles of glucose formed and, using the reaction stoichiometry, determine the number of moles of CO2 needed. With that information and the other information provided in the problem, we ean use the ideal gas law to ealculate the volume of air that is needed ... 

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. 

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. 

In dealing with the stoichiometry of reactions involving gases, it is useful to define the volume occupied by 1 mole of a gas under certain specified conditions. For 1 mole of an ideal gas at 0 C (273 K) and 1 atm, the volume of the gas given by the ideal gas law is... 

Rearrangements of the ideal gas law are used to calculate the density and molar mass of a gas and the partial pressure of each gas in a gas mixture (Dalton s law). We use gas variables (P, V, and T) in stoichiometry problems to find the amounts (n) of gaseous reactants or products in a reaction. (Section 5.4)... 

Because this example is a bit more complicated, let us map out a strategy before we begin. We assume that some of the molecular iodine will dissociate—call the amount x— and the amount of atomic iodine, given by the stoichiometry of the reaction, will be +2x. In a volume of 1.00 L at 1000 K, we can use the ideal-gas law to determine partial pressures. We have to constrain any possible answer to the fact that pi + Pi must equal 0.750 atm. 

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. 

For a quantitative description of the behavior of gases, we will employ some simple gas laws and a more general expression called the ideal gas equation. These laws will be explained by the kinetic-molecular theory of gases. The topics covered in this chapter extend the discussion of reaction stoichiometry from the previous two chapters and lay some groundwork for use in the following chapter on thermochemistry. The relationships between gases and the other states of matter— liquids and solids—are discussed in Chapter 12. 

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. 

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