Reactions That Involve a Limiting Reactant

Chemical Reactions That Involve a Limiting Reactant 

Suppose, however, that the amounts of both CU2S and O2 are given in the problem, and we need to find out how much SO2 forms. We first have to determine whether CU2S or O2 is the limiting reactant (that is, which one is completely used up) because the amount of that reactant limits how much SO2 can form. The other reactant is in excess, and whatever amount of it is not used is left over. 

To clarify the idea of a limiting reactant, let s consider a situation from real life. A car assembly plant has 1500 car bodies and 4000 tires. How many cars can be made with the supplies on hand Does the plant manager need to order more car bodies or more tires Obviously, 4 tires are required for each car body, so the balanced equation is 

How much product (cars) can we make from the amount of each reactant  

The number of tires limits the number of cars because less product (fewer cars) can be produced from the available tires. There will be 1500 — 1000 = 500 car bodies in excess, and they cannot be turned into cars until more tires are delivered. 

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Another example of a reaction that involves a limiting reactant is the manufacture of the pure silicon that is used in computer chips or solar cells (Figure... 

Stoichiometrically Equivalent Molar Ratios from the Balanced Equation 89 Reactions That Involve a Limiting Reactant 93... 

One of the tasks closely related to documentation is simple calculations that have to be performed to prepare an experiment. The number of calculations performed, for instance, in the organic synthesis laboratory is quite small, but those calculations required are very important. The calculations associated with conversion of the starting materials to the product are based on the assumption that the reaction will follow simple ideal stoichiometry. In calculating the theoretical and actual yields, it is assumed that all of the starting material is converted to the product. The first step in calculating yields is to determine the limiting reactant. The limiting reactant in a reaction that involves two or more reactants is usually the one present in lowest molar amount based on the stoichiometry of the reaction. This reactant will be consumed first and will limit any additional conversion to product. These calculations, which are simple rules of proportions, are subject to calculation errors due to their multiple dependencies. 

The criterion for a successful enzymatic resolution is that one enantiomer be a preferred substrate for the enzyme. Generally speaking, the enantioselectivity is quite high, since enzyme-catalyzed reactions typically involve a specific fit of the reactant (substrate) into the catalytically active site. The same necessity for a substrate fit, however, is the primary limitation on enzymatic resolution. The compound to be... 

The amount of a product formed when the limiting reactant is completely consumed is called the theoretical yield of that product. In Example 3.17, 10.6 grams of nitrogen represents the theoretical yield. This is the maximum amount of nitrogen that can be produced from the quantities of reactants used. Actually, the amount of product predicted by the theoretical yield is seldom obtained because of side reactions (other reactions that involve one or more of the reactants or products) and other complications. The actual yield of product is often given as a percentage of the theoretical yield. This is called the pereent yield ... 

Physical state of the reactants. Reactants must come together to react. The more readily reactant molecules collide with one another, the more rapidly they react. Most of the reactions we consider are homogeneous, involving either all gases or all liquids. When reactants are in different phases, however, we have heterogeneous conditions, and the reaction is limited by the area of contact of the reactants. Thus, heterogeneous reactions that involve solids tend to proceed faster if the surface area of the solid is increased. For example, a medicine in the form of a fine powder dissolves in the stomach and enters the blood more quickly than the same medicine in the form of a tablet. 

Using molar ratios from the balanced equation, we calculate the amount of one substance from the amount of any other involved in the reaction. During a typical reaction, one substance (the limiting reactant) is used up, so it limits the amount of product that can form the other reactantfs) is (are) in excess. The theoretical yield, the amount indicated by the balanced equation, is never obtained in the lab because of competing side reactions, incompleteness of the main reaction, and inability to collect all of the product. (Section 3.4)... 

In summary, the groups of Espenson and Loh observe catalysis of Diels-Alder reactions involving monodentate reactants by Lewis acids in water. If their observations reflect Lewis-acid catalysis, involvirg coordination and concomitant activation of the dienophile, we would conclude that Lewis-acid catalysis in water need not suffer from a limitation to chelating reactants. This conclusion contradicts our observations which have invariably stressed the importance of a chelating potential of the dienophile. Hence it was decided to investigate the effect of indium trichloride and methylrhenium trioxide under homogeneous conditions. 

As is clear from the preceding examples, there are a variety of overall reactions that can be initiated by photolysis of ketones. The course of photochemical reactions of ketones is veiy dependent on the structure of the reactant. Despite the variety of overall processes that can be observed, the number of individual steps involved is limited. For ketones, the most important are inter- and intramolecular hydrogen abstraction, cleavage a to the carbonyl group, and substituent migration to the -carbon atom of a,/S-unsaturated ketones. Reexamination of the mechanisms illustrated in this section will reveal that most of the reactions of carbonyl compounds that have been described involve combinations of these fundamental processes. The final products usually result from rebonding of reactive intermediates generated by these steps. 

Rate constants for a large number of atmospheric reactions have been tabulated by Baulch et al. (1982, 1984) and Atkinson and Lloyd (1984). Reactions for the atmosphere as a whole and for cases involving aquatic systems, soils, and surface systems are often parameterized by the methods of Chapter 4. That is, the rate is taken to be a linear function or a power of some limiting reactant - often the compound of interest. As an example, the global uptake of CO2 by photosynthesis is often represented in the empirical form d[C02]/df = —fc[C02] ". Rates of reactions on solid surfaces tend to be much more complicated than gas phase reactions, but have been examined in selected cases for solids suspended in air, water, or in sediments. 

Many semibatch reactions involve more than one phase and are thus classified as heterogeneous. Examples are aerobic fermentations, where oxygen is supplied continuously to a liquid substrate, and chemical vapor deposition reactors, where gaseous reactants are supplied continuously to a solid substrate. Typically, the overall reaction rate wiU be limited by the rate of interphase mass transfer. Such systems are treated using the methods of Chapters 10 and 11. Occasionally, the reaction will be kinetically limited so that the transferred component saturates the reaction phase. The system can then be treated as a batch reaction, with the concentration of the transferred component being dictated by its solubility. The early stages of a batch fermentation will behave in this fashion, but will shift to a mass transfer limitation as the cell mass and thus the oxygen demand increase. 

A table of amounts is a convenient way to organize the data and summarize the calculations of a stoichiometry problem. Such a table helps to identify the limiting reactant, shows how much product will form during the reaction, and indicates how much of the excess reactant will be left over. A table of amounts has the balanced chemical equation at the top. The table has one column for each substance involved in the reaction and three rows listing amounts. The first row lists the starting amounts for all the substances. The second row shows the changes that occur during the reaction, and the last row lists the amounts present at the end of the reaction. Here is a table of amounts for the ammonia example ... 

Physical methods involve the measurement of a physical property of the system as a whole while the reaction proceeds. The measurements are usually made in the reaction vessel so that the necessity for sampling with the possibility of attendant errors is eliminated. With physical methods it is usually possible to obtain an essentially continuous record of the values of the property being measured. This can then be transformed into a continuous record of reactant and product concentrations. It is usually easier to accumulate much more data on a given reaction system with such methods than is possible with chemical methods. There are certain limitations on physical methods, however. There must be substantial differences in the contributions of the reactants and products to the value of the particular physical property used as a measure of the reaction progress. Thus one would not use pressure measurements to follow the course of a gaseous reaction that does not... 

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