Mole Relationships in Chemical Equations

LEARNING GOAL Define the terms oxidation and reduction identify the reactants oxidized and reduced. 

41 In each of the following reactions, identify the reactant that is oxidized and the reactant that is reduced  

In the mitochondria of human cells, energy is provided by the oxidation and reduction reactions of the iron ions in the cytochromes in electron transport. Identify each of the following reactions as an oxidation or reduction  

Chlorine (CI2) is a strong germicide used to disinfect drinking water and to kill microbes in swimming pools. If the product is Cr, was the elemental chlorine oxidized or reduced  

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Mole Relationships in Chemical Equations LEARNING GOAL... 

I he previous chapters showed how the laws of conservation of mass and con--1- servation of atomic identity, together with the concept of the mole, determine quantitative mass relationships in chemical reactions. That discussion assumed prior knowledge of the chemical formulas of the reactants and products in each equation. The far more open-ended questions of which compounds are found in nature (or which can be made in the laboratory) and what types of reactions they undergo now arise. Why are some elements and compounds violently reactive and others inert Why are there compounds with chemical formulas H2O and NaCl, but never H3O or NaCli Why are helium and the other noble gases monatomic, but molecules of hydrogen and chlorine diatomic All of these questions can be answered by examining the formation of chemical bonds between atoms. 

This relationship between moles of gas and liters gives you a way to convert the gas from a mass to a volume. For example, suppose that you have 50.0 grams of oxygen gas (O2), and you want to know its volume at STP. You can set up the problem like this (see Chapters 10 and 11 for the nuts and bolts of using moles in chemical equations) ... 

Stoichiometry is the quantitative study of reactants and products in a chemical reaction. Although amounts in chemical reactions can be measured in many different units, such as grams, liters, or moles, a chemical equation can only tell us the relative numbers of atoms (or moles) that are produced and consumed in a reaction. Therefore, no matter in what units the initial amounts are given, they must be converted to moles before the chemical equation can be used to determine the quantitative relationships between reactants and products. For example, the combustion of carbon monoxide gas in air produces carbon dioxide according to the chemical equation... 

Sections 2- and 3- describe how to use the relationships among atoms, moles, and masses to answer how much questions about individual substances. Combining these ideas with the concept of a balanced chemical equation lets us answer how much questions about chemical reactions. The study of the amounts of materials consumed and produced in chemical reactions is called stoichiometry. 

A chemical equation describes a chemical reaction in many ways as an empirical formula describes a chemical compound. The equation describes not only which substances react, but the relative number of moles of each undergoing reaction and the relative number of moles of each product formed. Note especially that it is the mole ratios in which the substances react, not how much is present, that the equation describes. In order to show the quantitative relationships, the equation must be balanced. That is, it must have the same number of atoms of each element used up and produced (except for special equations that describe nuclear reactions). The law of conservation of mass is thus obeyed, and also the "law of conservation of atoms. Coefficients are used before the formulas for elements and compounds to tell how many formula units of that substance are involved in the reaction. A coefficient does not imply any chemical bonding between units of the substance it is placed before. The number of atoms involved in each formula unit is multiplied by the coefficient to get the total number of atoms of each element involved. Later, when equations with individual ions are written (Chap. 9), the net charge on each side of the equation, as well as the numbers of atoms of each element, must be the same to have a balanced equation. The absence of a coefficient in a balanced equation implies a coefficient of 1. 

This balanced equation can be read as 4 iron atoms react with 3 oxygen molecules to produce 2 iron(III) oxide units. However, the coefficients can stand not only for the number of atoms or molecules (microscopic level) but they can also stand for the number of moles of reactants or products. So the equation can also be read as 4 mol of iron react with 3 mol of oxygen to produce 2 mol ofiron(III) oxide. In addition, if we know the number of moles, the number of grams or molecules may be calculated. This is stoichiometry, the calculation of the amount (mass, moles, particles) of one substance in the chemical equation from another. The coefficients in the balanced chemical equation define the mathematical relationship between the reactants and products and allow the conversion from moles of one chemical species in the reaction to another. 

In this chapter, you learned how to balance simple chemical equations by inspection. Then you examined the mass/mole/particle relationships. A mole has 6.022 x 1023 particles (Avogadro s number) and the mass of a substance expressed in grams. We can interpret the coefficients in the balanced chemical equation as a mole relationship as well as a particle one. Using these relationships, we can determine how much reactant is needed and how much product can be formed—the stoichiometry of the reaction. The limiting reactant is the one that is consumed completely it determines the amount of product formed. The percent yield gives an indication of the efficiency of the reaction. Mass data allows us to determine the percentage of each element in a compound and the empirical and molecular formulas. 

The relationship above gives a way of converting from grams to moles to particles, and vice versa. If you have any one of the three quantities, you can calculate the other two. This becomes extremely useful in working with chemical equations, as we will see later, because the coefficients in the balanced chemical equation are not only the number of individual atoms or molecules at the microscopic level, but also the number of moles at the macroscopic level. 

In the reaction, one mole of hydroxide generates one mole of alcohol and one mole of carboxylate ion from one mole of ester. Based on this stoichiometry (the mole relationship as defined by the balanced chemical equation), if the number of moles of base is known, then the amount of ester is known. 

Having a balanced chemical equation and knowing the relationship between mass and moles allows us to predict how much reactant is necessary to yield a certain amount of product. This knowledge has important applications in industrial chemistry, environmental chemistry, nutrition, and in any situation where reactions take place. The balanced equation is a recipe for a chemical reaction. Just as it is necessary to know the amount of eggs, flour, sugar, and salt to bake a cake, we need to know the amount of ingredients that go into a chemical reaction. The balanced chemical equation gives the quantities of different reactants that are required to produce a specific amount of product. 

There are four undetermined quantities Apfx, (Apf ), pf, and (pf) and two equations. We must, therefore, define two of the four quantities, which in turn determines the other two quantities and the relationship between them. We can define the reference states for the component and the species. The difference between the standard chemical potential of the component and that of the species is then expressed in terms of the mole fractions in the reference state. The problem is the determination of this difference. The different species may be known from our knowledge of the chemical system, or they may be assumed. However, a definite decision must be made concerning the species, and all calculations must be carried out based upon this decision. Several examples concerning reference and standard states are discussed here and in the following sections. 

You can get the same kind of information from a balanced chemical equation. In Chapter 4, you learned how to classify chemical reactions and balance the chemical equations that describe them. In Chapters 5 and 6, you learned how chemists relate the number of particles in a substance to the amount of the substance in moles and grams. In this section, you will use your knowledge to interpret the information in a chemical equation, in terms of particles, moles, and mass. Try the following Express Lab to explore the molar relationships between products and reactants. 

In this Express Lab, you will determine the mole relationships between the products and reactants in the reaction. Then you will compare the mole relationships with the balanced chemical equation. 

You can use your understanding of the relationship between moles and number of particles to see how chemical equations communicate information about how many moles of products and reactants are involved in a reaction. 

So the chemical equation N2(g) + 3H2(g) -> 2NH3(g) also means that 1 mol of nitrogen molecules reacts with 3 mol of hydrogen molecules to form 2 mol of ammonia molecules. The relationships between moles in a balanced chemical equation are called mole ratios. For example, the mole ratio of nitrogen to hydrogen in the equation above is 1 mol N2 3 mol H2. The mole ratio of hydrogen to ammonia is 3 mol H2 2 mol NH3. 

Mole ratios You have seen that the coefficients in a chemical equation indicate the relationships among moles of reactants and products. For example, return to the reaction between iron and oxygen described in Table 12-1. The equation indicates that four moles of iron react with three moles of oxygen. It also indicates that four moles of iron react to produce two moles of iron(III) oxide. How many moles of oxygen react to produce two moles of iron(III) oxide You can use the relationships between coefficients to write conversion factors called mole ratios. A mole ratio is a ratio between the numbers of moles of any two substances in a balanced chemical equation. As another example, consider the reaction shown in Figure 12-2. Aluminum reacts with bromine to form aluminum bromide. Aluminum bromide is used as a catalyst to speed up a variety of chemical reactions. 

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 solve the problem, you need to know how the unknown moles of hydrogen are related to the known moles of potassium. In Section 12.1 you learned to use the balanced chemical equation to write mole ratios that describe mole relationships. Mole ratios are used as conversion factors to convert a known number of moles of one substance to moles of another substance in the same chemical reaction. What mole ratio could be used to convert moles of potassium to moles of hydrogen In the correct mole ratio, the moles of unknown (H2) should be the numerator and the moles of known (K) should be the denominator. The correct mole ratio is... 

Note that the first two lines must add to give the third. We use the relationships built into the balanced chemical equation to fill in the blanks in the table. Because this is the only reaction taking place, every mole of COCI2 produced consumes exactly 1 mol of CO and... 

The relationship AH = AE + P AV is valid for any process that takes place at constant temperature and pressure. It is very useful for physical changes that involve volume changes, such as expansion or compression of a gas. When a chemical reaction occurs and causes a change in the number of moles of gas, it is more convenient to use the relationship in the form AH = AE + (An)RT. You should always remember that An refers to the change in number of moles of gas in the balanced chemical equation. 

The number in front of each chemical formula can be read as a number of atoms and molecules (2 atoms of A1 and 3 molecules of Brg form 1 molecule of Al2Br6). It can refer equally as well to number of moles. Thus, the balanced equation for the reaction of aluminum and bromine tells us that 2 mol of solid aluminum reacts with 3 mol of liquid bromine to produce 1 mol of solid AlgBr . The relationship between the quantities of chemical reactants and products is called stoichiometry (pronounced stoy-key-AHM-uh-tree ), and the coefficients in a balanced equation are the stoichiometric coefficients. 

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