Chemical equations as conversion factors

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 ... 

Reaction Stoichiometry Chemical Equations as Conversion Factors... 

Fig. 8-1 The conversion of moles of one reagent to moles of another, using a ratio of the coefficients of the balanced chemical equation as a factor label...

A chemical equation tells us the relations between the amounts (in moles) of each reactant and product. By using the molar masses as conversion factors, we can express these relations in terms of masses. 

Consider the reaction of phosphorus with chlorine as shown in the previous equation. Of course, the chemist is not required to place exactly 2 mol of P and 3 mol of CI2 in a reaction flask. The equation gives the reacting ratio. Ratios of coefficients from balanced chemical equations can be used as conversion factors for solving problems. 

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. 

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... 

Determine the moles of the unknown substance from the moles of the given substance. Use the appropriate mole ratio from the balanced chemical equation as the conversion factor. 

The coefficients in a chemical equation can be used as conversion factors in calculations much as the subscripts in a chemical formula were used previously. These calculations are important because they allow us to predict how much of a particular reactant might be needed in a particular reaction, or how much of a particular product will be formed. For example, one of the gases that contribute to global warming is carbon dioxide (COj). Carbon dioxide is a product of the combustion of fossil fuels such as methane, the primary component of natural gas. From the previous section, the chemical equation for the combustion of methane is as follows ... 

Using Chemical Equation Coefficients as Conversion Factors (Moles to Moles)... 

Given the chemical equation Na2C03(aqf) + Ca(OH)2 —> 2NaOH(at/) + CaC03(s), determine to two decimal places the molar masses of all substances involved. Then, write the molar masses as conversion factors. 

In Section 4.2 we discussed how the coefficients in chemical equations are used as conversion factors between the amounts of reactants (in moles) and the amounts of products (in moles). In aqueous reactions, quantities of reactants and products are often specified... 

QA First, determine the mass of iron that has reacted as Fe2+ with the titrant. The balanced chemical equation provides the essential conversion factor. 

Stoichiometry is the series of calculations on the basis of formulas and chemical equations and will be covered in Chapter 4. The use of conversion factors is common even when the relative proportions are not fixed by a chemical formula. Consider a silver alloy used for jewelry production. (Alloys are mixtures of metals and, as mixtures, may be produced in differing ratios of the metals.) A particular alloy contains 86 percent silver. Factors based on this composition, such as... 

The coefficients in a balanced chemical equation show the relative numbers of moles of the substances in the reaction. As a result, you can use the coefficients in conversion factors called mole ratios. Mole ratios bridge the gap and can convert from moles of one substance to moles of another, as shown in Skills Toolkit 1. 

Does the chemical equation tell you anything about the masses of the reactants and products Not directly. But as you learned in Chapter 11, the mass of any substance can be determined by multiplying the number of moles of the substance by the conversion factor that relates mass and number of moles, which is the molar mass. Thus, the mass of the reactants can be calculated in this way. 

Most chemical reactions that occur on the earth s surface, whether in living organisms or among inorganic substances, take place in aqueous solution. Chemical reactions carried out between substances in solution obey the requirements of stoichiometry discussed in Chapter 2, in the sense that the conservation laws embodied in balanced chemical equations are always in force. But here we must apply these requirements in a slightly different way. Instead of a conversion between masses and number of moles, using the molar mass as a conversion factor, the conversion is now between solution volumes and number of moles, with the concentration as the conversion factor. 

As part of our calculation, we convert from moles of one substance (P4O10) to moles of another (H2O), so we need a conversion factor that relates the numbers of particles of these substances. The coefficients in the balanced chemical equation provide us with information that we can use to build this conversion factor. They tell us that six molecules of H2O are needed to react with one molecule of P4O10 in order to produce four molecules of phosphoric acid ... 

Thinking it Through It is not a common practice on ACS exams, but do not assume that all information provided in a question is actually essential to its solution. Rather, decide on a route to the solution that will be the most expedient. Given that 6.25 L of Ni(CO)4fgJ form at standard temperature and pressure conditions, the molar volume of 22.4 L can be used as a conversion factor to find the number of moles of Ni(CO>4 present. Then the coefficients in the balanced chemical equation can be applied, observing that one mole of Ni(CO)4 reacts to produce one mole of Ni. The atomic molar mass for nickel can then be used to find the number of grams of Ni present. 

Because an elementary reaction occurs on a molecular level exactly as it is written, its rate expression can be determined by inspection. A unimolecular reaction is a first-order process, bimolecular reactions are second-order, and termolecular processes are third-order. However, the converse statement is not true. Second-order rate expressions are not necessarily the result of an elementary bimolecular reaction. While a stoichiometric chemical equation remains valid when multiplied by an arbitrary factor, a mechanistic eqnation loses its meaning when multiplied by an arbitrary factor. Whereas stoichiometric coefficients and reaction orders may be integers or nonintegers, the molecularity of a reaction is always an integer. The following examples indicate the types of rate expressions associated with various molecularities. Unimolecular ... 

Eq. (2) for the gas phase, but with its chemical potential p,° defined at atmospheric pressure p = 1.0 atm. Equation (3) expresses then the chemical potential of the (pure) solvent vapor over the solution. Note, that in these expressions one always uses atm as unit of pressure, a non-SI unit of pressure (see Fig. 2.3, for conversion factors see Sect 4.5.1). At equilibrium, the two logarithmic terms in Eqs. (1) and (3) must be equal, Pi = pP, and produce Raoult s law. Raoult s law is indicated by the diagonal in the graph of Fig. 7.3. At concentrations approaching the pure solvent, Xj - 1.0, this equation must always hold. 

You should recognize this as a reaction stoichiometry problem because it is asking us how much CaC03 will be produced. As for any stoichiometry problem, we should write a balanced chemical equation for the reaction. Then convert the volume of gas into moles and proceed as usual. Because the gas volume given is at STP, we can use the molar volume we calculated above as a conversion factor. 

Figures. Summary of amount-mass-number relationships in a chemical equation. Start at any box (known) and move to any other (unknown) by using the conversion factor on the arrow. As always, convert to amount (mol) first.

We may want to calculate how much COj is emitted into the atmosphere as a result of methane combustion. The total amount of methane used is known because gas companies keep accurate records. What we need is a conversion factor between the amount of methane used and the amount of carbon dioxide produced. The chemical equation gives us this conversion factor. 

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