Stoichiometry Problems Involving Gas Volumes

In Chapter 3 you learned how to find the mass of one substance in a chemical reaction from the mass of another substance in the reaction. Now that you know how to use the ideal gas law, we can extend these types of problems to include gas volumes. 

Consider the following reaction, which is often nsed to generate small qnantities of oxygen gas  

Suppose you heat O.OlOO mol of potassium chlorate, KCIO3, in a test tube. How many liters of oxygen can you produce at 298 K and 1.02 atm  

You solve such a problem by breaking it into two problems, one involving stoichiometry and the other involving the ideal gas law. You note that 2 mol KCIO3 yields 3 mol O2. Therefore, 

Now that you have the moles of oxygen produced, you can use the ideal gas law to calculate the volume of oxygen under the conditions given. You rearrange the ideal gas law, PV = nRT, and solve for the volume. 

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Stoichiometry Problems Involving Gas Volumes 53 Gas Mixtures Law of Partial Pressures... 

Solving stoichiometry problems involving gas volumes Given the volume (or mass) of one substance in a reaction,... 

Be sure, especially in stoichiometry problems involving gases, that you are calculating the values such as volume and pressure of the correct gas. You can avoid this mistake by clearly labeling your quantities that means, mol of 02 instead of just mol. 

In reaction stoichiometry problems involving gases, the ideal gas law provides a means to compute moles from pressure or volume data. 

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 ... 

There are ways other than density to include volume in stoichiometry problems. For example, if a substance in the problem is a gas at standard temperature and pressure (STP), use the molar volume of a gas to change directly between volume of the gas and moles. The molar volume of a gas is 22.41 L/mol for any gas at STP. Also, if a substance in the problem is in aqueous solution, then use the concentration of the solution to convert the volume of the solution to the moles of the substance dissolved. This procedure is especially useful when you perform calculations involving the reaction between an acid and a base. Of course, even in these problems, the basic process remains the same change to moles, use the mole ratio, and change to the desired units. 

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. 

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. 

When working stoichiometry problems like the one in the preceding section involving the decomposition of potassium chlorate, the oxygen is normally collected over water by displacement and the volume is then measured. However, in order to get the pressure of just the oxygen, you have to subtract the pressure due to the water vapor. You have to mathematically dry out the gas. 

To solve a stoichiometry problem that involves a gas whose volume is measured at STP, simply use 22.4 L/mol where you would have used molar mass if the amount had been given in grams. 

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. 

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