Stoichiometric Calculations Using Mole Ratios

Sample Problem C What mass of carbon dioxide, in grams, is needed to react with 3.00 mol H O in the photosynthetic reaction described in Sample Problem B  

Two conversion factors are needed—the mole ratio of CO2 to H2O and the molar mass factor of CO2. 

The answer is rounded correctly to three significant figures to match those in 3.00 mol H2O. The units cancel to leave g CO2, which is the unknown. The answer is close to an estimate of 120, which is 3 x 40. 

When magnesium bums in air, it combines with oxygen to form magnesium oxide according to the following equation. 

What mass in grams of magnesium oxide is produced from 2.00 mol of magnesium  

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The process of using a chemical equation to calculate the relative amounts of reactants and products involved in the reaction is called doing stoichiometric calculations. To convert between moles of reactants and moles of products, we use mole ratios derived from the balanced equation. 

The net ionic equation, like all balanced chemical equations, gives the ratio of moles of each substance to moles of each of the others. It does not immediately yield information about the mass of the entire salt, however. (One cannot weigh out only Ba2+ ions.) Therefore, when masses of reactants are required, the specific compound used must be included in the calculation. The use of net ionic equations in stoichiometric calculations will be more important after study of molarity (Chap. 10). 

Figure 2 shows a few of the tanks used to store the millons of metric tons of ammonia made each year in the United States. Stoichiometric calculations are used to determine how much of the reactants are needed and how much product is expected. However, the calculations do not start and end with moles. Instead, other units, such as liters or grams, are used. Mass, volume, or number of particles can all be used as the starting and ending quantities of stoichiometry problems. Of course, the key to each of these problems is the mole ratio. 

Recall that stoichiometry is the study of quantitative relationships between the amounts of reactants used and the amounts of products formed by a chemical reaction. What are the tools needed for stoichiometric calculations All stoichiometric calculations begin with a balanced chemical equation, which indicates relative amounts of the substances that react and the products that form. Mole ratios based on the balanced chemical equation are also needed. You learned to write mole ratios in Section 12.1. Finally, mass-to-mole conversions similar to those you learned about in Chapter 11 are required. 

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. 

I Mole ratios derived from the balanced chemical equation are used in stoichiometric calculations. 

For your chosen reaction in POST-LABORATORY QUESTION 5, calculate an approximate enthalpy change, AHj-xn mole of S2O32-, using the maximum temperature rise for the experimentally determined stoichiometric mole ratio. Assume that the density of your reaction mixture is 1.08 g/mL and that the specific heat of your reaction mixture is 3.9 J/g °C. 

When doing stoichiometric calculations, mole ratios are very often written to look like fractions. They are used analogously to unit conversion factors, relating the amount of one substance to that of another ... 

Notice that the stoichiometric calculation is done using the mole ratio from the balanced equation, just as in all of our earlier examples. Only the conversions to and from numbers of moles have changed because this reaction is in solution. 

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. 

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. 

The mole ratio method greatly simplifies stoichiometric calculations. It can even be used to relate relative quantities of reaction participants in a series of reactions. For example, if a particular quantity of reactant is involved in a reaction followed by one or more additional reactions, the amount of a product in the final reaction is readily calculated by the mole ratio method. 

As another example of a stoichiometric calculation by the mole ratio method, consider the reaction of iron(III) sulfate, Fe(S04)3, with calcium hydroxide, Ca(OH>2. This reaction is used in water treatment processes for the preparation of gelatinous iron(III) hydroxide, Fe(OH)3, which settles in the water, carrying solid particles with it. The iron(III) hydroxide acts to remove suspended matter (turbidity) from water. The Ca(OH)2 (slaked lime) is added as a base (source of OH ion) to react with iron(III) sulfate. The reaction is... 

Similarly, we can use other ratios represented in the balanced equation as conversion factors. For example, we have 1 mol O2 — 2 mol CO2 and 2 mol CO — 1 mol O2. The corresponding conversion factors allow us to calculate the amount of CO2 produced upon reaction of a given amount of O2, and the amount of one reactant necessary to react completely with a given amount of the other. Using the preceding example, we can determine the stoichiometric amount of O2 (how many moles of O2 are needed to react with 3.82 moles of CO). 

The use of excesses of reagents and reactants to maximize reaction yield/selectivity, although a very common practice, is not part of the atom economy calculation. Reaction stoichiometry is, however, part of the calculations. This means that when 2 mol of one reactant combine with a single mole of a second reactant to form a new molecule that is either a reaction or process intermediate, the relevant stoichiometric ratio would be used to calculate the overall atom economy of the reaction. 

In a balanced equation, the number of moles of one substance is stoichiometrically equivalent to the number of moles of any other substance. The term stoichiometrically equivalent means that a definite amount of one substance is formed from, produces, or reacts with a definite amount of the other. These quantitative relationships are expressed as stoichiometrically equivalent molar ratios that we use as conversion factors to calculate these amounts. Table 3.3 presents the quantitative information contained in the equation for the combustion of propane, a hydrocarbon fuel used in cooking and water heating ... 

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. 

To determine the limiting reactant, first calculate the number of moles of each reactant present. Then determine how these numbers of moles correspond to the stoichiometric ratio indicated by the balanced chemical equation for the reaction. For each reactant, use the stoichiometric ratios from the balanced chemical equation to calculate how much of the other reactants would be required to react completely. 

To illustrate, let us consider two simple examples. First, suppose that we react completely 4.8 mol of CO with O2 to form CO2, and we want to determine how many moles of CO2 will be produced. We are given moles so we can use the chemical equation for this calculation directly. The chemical equation states that 2 mol of CO2 are formed for every 2 mol of CO reacted (that is, 2 mol CO — 2 mol CO2), giving a stoichiometric ratio of 212 = 1. The number of moles of CO2 produced is determined by multiplying the number of moles of CO reacted by the stoichiometric ratio as follows... 

The value of Q (used to heat the products to Tg) is central to explosive power. Figure 9.3 illustrated two methods of calculation of the heat of reaction, but of more interest here is gauging the relative heat generated per gram of fuel. Also, file calculations shown in that figure assume that the fuel and oxidant are in stoichiometric equivalence, meaning that file balance of concentrations of fuel and oxidant exactly match the stoichiometric balance. In the case of methane combustion (Figure 9.2), if 1.0 mole of methane was present when the reaction started, then, at stoichiometric equivalence, there would be exactly 2.0 moles of O2 present. This situation, however, is rarely encoimtered, and as a result, both the products of the reaction and the heat evolved will be affected. Therefore, a brief discussion of the stoichiometric ratio is warranted. 

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