Stoichiometric Calculations Amounts of Reactants and Products

As we have seen in previous sections of this chapter, the coefficients in chemical equations represent numbers of molecules, not masses of molecules. However, when a reaction is to be run in a laboratory or chemical plant, the amounts of substances needed cannot be determined by counting molecules directly. Counting is always done by weighing. In this section we will see how chemical equations can be used to determine the masses of reacting chemicals. 

To develop the principles for dealing with the stoichiometry of reactions, we will consider the reaction of propane with oxygen to produce carbon dioxide and water. We will consider the question What mass of oxygen will react with 96.1 grams ofpropane In doing stoichiometry, the first thing we must do is write the balanced chemical equation for the reaction. In this case the balanced equation is 

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A consumer typicaiiy is faced with three choices of gasoiine, with octane ratings of 87 (reguiar), 89 (midgrade), and 93 (premium). But if you happen to travei or iive in the 

This equation means that 1 mole of C3He reacts with 5 moles of O2 to produce 3 moles of CO2 and 4 moles of H2O. To use this equation to find the masses of reactants and products, we must be able to convert between masses and moles of substances. Thus we must first ask How many moles ofpropane are present in 96.1 grams ofpropane The molar mass of propane to three significant figures is 44.1 (that is, 3 X 12.01 + 8 X 1.008). The moles of propane can be calculated as follows  

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At higher elevations the air is less dense—the volume of oxygen per unit volume of air is smaller. Most engines are designed to achieve a 14 1 oxygen-to-fuel ratio in the cylinder prior to combustion. If less oxygen is 

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Before doing any calculations involving a chemical reaction, be sure the equation for the reaction Is balanced. 

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You have learned how to do stoichiometric calculations, using balanced chemical equations to find amounts of reactants and products. In these calculations, you assumed that the reactants and products occurred in the exact molar ratios shown by the chemical equation. In real life, however, reactants are often not present in these exact ratios. Similarly, the amount of product that is predicted by stoichiometry is not always produced. 

When doing stoichiometric calculations, the assumption often made is that the reaction goes to completion. This is a convenient assumption when focusing on calculations involving mole ratios and limiting reagents, but there are many examples of commercially and biologically important chemical reactions that do not go to completion. Rather, appreciable amounts of reactants and products remain in the reaction mixture once equilibrium is reached. When viewed macroscopically, the concentrations of all reactants and products remain constant, but not necessarily equal, over time. 

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. 

Chemical equations help us plan the amounts of reactants to use in a chemical reaction without having to run the reaction in the laboratory. The reaction stoichiometry calculations described in this chapter are theoretical. They tell us the amounts of reactants and products for a given chemical reaction under ideal conditions, in which all reactants are completely converted into products. However, many reactions do not proceed such that all reactants are completely converted into products. Theoretical stoichiometric calculations allow us to determine the maximum amount of product that could be obtained in a reaction when the reactants are not pure or when by-produots are formed in addition to the expected products. 

A balanced chemical reaction indicates the quantitative relationships between the moles of reactants and products. These stoichiometric relationships provide the basis for many analytical calculations. Consider, for example, the problem of determining the amount of oxalic acid, H2C2O4, in rhubarb. One method for this analysis uses the following reaction in which we oxidize oxalic acid to CO2. 

The equation for a chemical reaction speaks in terms of molecules or of moles. It contains the basis for stoichiometric calculations. However, in the laboratory a chemist measures amounts in such units as grams and milliliters. The first step in any quantitative calculation, then, is to convert the measured amounts to moles. In mole units, the balanced reaction connects quantities of reactants and products. Finally, the result is expressed in the desired units (which may not necessarily be the same as the original 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. 

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. 

We remember from Chapter 5 that the coefficients in equations such as Equation 7.3 allow the relative number of moles of pure reactants and products involved in the reaction to be determined. These relationships coupled with the mole definition in terms of masses then yield factors that can be used to solve stoichiometric problems involving the reactants and products. Similar calculations can be done for reactions that take place between the solutes of solutions if the amount of solute contained in a specific quantity of the reacting solutions is known. Such relationships are known as solution concentrations. Solution concentrations may be expressed in a variety of units, but only two, molarity and percentage, will be discussed at this time. 

At very high concentrations, the enzyme can alter the equilibrium constant. If is calculated by determining the equilibrium concentrations of all free products and reactants, and if the products and reactants have different affinities for the free enzyme, then high [Etot] favors formation of significant amounts of EA and EP, and this may cause an apparent shift in In such instances, the enzyme is now a stoichiometric participant in the reaction, and the true equilibrium constant has to take this into account. 

The amount of Pbl2 calculated in part a, 192.71 g, is known as the theoretical yield of the substance. That is the maximum amount that can form based on the stoichiometric relationships between reactants and products. The actual reaction will more than likely produce less than this, for a variety of reasons (which are unimportant to us). 

Stoichiometry establishes the quantities of reactants (used) and products (obtained) based on a balanced chemical equation. With a balanced equation, you can compare reactants and products, and determine the amount of products that might be formed or the amount or reactants needed to produce a certain amount of a product. However, when comparing different compounds in a reaction, you must always compare in moles (i.e., the coefficients). The different types of stoichiometric calculations are summarized in Figure 5.1. 

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. 

Similar calculations are made to determine the success of chemical reactions because most reactions never succeed in producing the predicted amount of product. Although your work with stoichiometric problems so far may have led you to think that chemical reactions proceed according to the balanced equation without any difficulties and always produce the calculated amount of product, this is not the case Not every reaction goes cleanly or completely. Many reactions stop before all of the reactants are used up, so the actual amount of product is less than expected. Liquid reactants or products may adhere to the surfaces of containers or evaporate, and solid product is always left behind on filter paper or lost in the purification process. In some instances, products other than the intended ones may be formed by competing reactions, thus reducing the yield of the desired product. 

It s important to understand that reaction rates are determined experimentally by measuring the concentrations of reactants and/or products in an actual chemical reaction. Reaction rates cannot be calculated from balanced equations as stoichiometric amounts can. 

The stoichiometric amount of reactant B is determined for the specific chemical reaction or reactions under consideration. For combustion reactions, the convention is to select the chemical reactions that provide complete oxidation of all the fuel components to their highest oxidation level (all carbon atoms to CO2, all sulfur atoms to SO2, etc.). Hence, although other chemical reactions may take place during the operation, generating CO and other products, the excess oxygen is defined and calculated on the basis of complete oxidation reactions. 

One of the most important areas of chemical arithmetic is based on balanced chemical equations. Chemists call this area of endeavor stoichiometry (stoy-key-om -ah-tree), which concerns the quantitative relationships between the reactants and products in chemical reactions. Stoichiometric calculations can be used to determine the amount of one reactant needed to completely react with another, or to determine the amount of reactant needed to produce a desired amount of product. The key to understanding how this is done is found in the way balanced chemical equations can be interpreted. So that is the place to begin learning the arithmetic of balanced chemical equations. 

I Chemists use stoichiometric calculations to predict the amounts of reactants used and products formed in specific reactions. 

Theoretical and Actual Yields In many of the stoichiometric calculations you have performed, you have calculated the amount of product produced from a given amount of reactant. The answer you obtained is the theoretical yield of the reaction. The theoretical yield is the maximum amount of product that can be produced from a given amount of reactant. 

The experiments were designed to provide data on the composition of both the solution and solid phases and to permit the calculation of stoichiometric yields of the reaction products in relation to amounts of reactants consumed. The results, briefly summarized in Tables II-IV for several typical solutions, support the following conclusions ... 

As we discussed in Chapter 7, many chemical reactions take place in aqueous solutions. Precipitation reactions, neutralization reactions, and gas evolution reactions, for example, all occur in aqueous solutions. Chapter 8 describes how we use the coefficients in chemical equations as conversion factors between moles of reactants and moles of products in stoichiometric calculations. These conversion factors are often used to determine, for example, the amount of product obtained in a chemical reaction based on a given amount of reactant or the amount of one reactant needed to completely react with a given amount of another reactant. The general solution map for these kinds of calculations is ... 

The coefficients required to balance a chemical equation are called stoichiometric coefficients. These coefficients are essential in relating the amounts of reactants used and products formed in a chemical reaction, through a variety of calculations. In balancing a chemical equation, keep the following point in mind. 

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