Conversion Factors from a Chemical Equation

I Given a chemical equation, or a reaction for which the equation is known, and the number of moles of one species in the reaction, calculate the number of moles of any other species. 

In Section 8.4 we introduced the three levels on which a chemical equation may be interpreted particulate, molar, and macroscopic. Let s briefly review the particulate and molar interpretations of an equation. Consider the equation 

On the particulate level, this equation is read, Four NH3 molecules react with 5 O2 molecules to produce 4 NO molecules and 6 HjO molecules. If we have 40 NH3 molecules—10 times as many—how many O2 molecules are required for the reaction The answer is again ten times as many, or 50. But what if we have 308 NH3 molecules How many O2 molecules are required for the reaction This answer is less obvious. 

The coefficients in a chemical equation give us the conversion factors to get from the number of particles of one substance to the number of particles of another substance in a reaction. For example. Equation 10.1 shows that 5 molecules of O2 are needed to react with every 4 molecules of NH3. In other words, the reaction uses 5 

Let s return to the question we asked before How many O2 molecules are required to react with 308 NH3 molecules The answer to this question comes from applying the Per relationship  

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Conversion Factors from a Chemical Equation Mass-Mass Stoichiometry Percent Yield Limiting Reactants ... 

The balanced chemical equation for a reaction is used to set up the conversion factor from one substance to another and that conversion factor, the mole ratio for the reaction, is applied to the moles given to calculate the moles required. 

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. 

Draw a solution map beginning with the number of moles of the given substance and then use the conversion factor from the balanced chemical equation to determine the number of moles of the substance you are trying to find. 

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 ... 

The dimensions of permeabiUty become clear after rearranging equation 1 to solve for P. The permeabiUty must have dimensions of quantity of permeant (either mass or molar) times thickness ia the numerator with area times a time iaterval times pressure ia the denomiaator. Table 1 contains conversion factors for several common unit sets with the permeant quantity ia molar units. The unit nmol/(m-s-GPa) is used hereia for the permeabiUty of small molecules because this unit is SI, which is preferred ia current technical encyclopedias, and it is only a factor of 2, different from the commercial permeabihty unit, (cc(STP)-mil)/(100 in. datm). The molar character is useful for oxygen permeation, which could ultimately involve a chemical reaction, or carbon dioxide permeation, which is often related to the pressure in a beverage botde. 

C03-0042. Diagram the process for converting from the mass of a compound of a known chemical formula to the number of atoms of one of its constituent elements. Include all necessary equations and conversion factors. 

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. 

The balanced equation expresses quantities in moles, but it is seldom possible to measure out quantities in moles directly. If the quantities given or required are expressed in other units, it is necessary to convert them to moles before using the factors of the balanced chemical equation. Conversion of mass to moles and vice versa was considered in Chapter 6. Not only mass, but any measurable quantity that can be converted to moles may be treated in this manner to determine the quantity of product or reactant involved in a reaction from the quantity of any other reactant or product. 

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 ... 

Example 10.1 shows how the coefficients in a balanced chemical equation provide a number of conversion factors that allow us to convert from moles of any reactant or product to moles of any other reactant or product. 

To see how molarity can be used in equation stoichiometry problems, let s take a look at the thought process for calculating the number of milliliters of 1.00 M AgN03 necessary to precipitate the phosphate from 25.00 mL of0.500 M Na3P04. The problem asks us to convert from amount of one substance in a chemical reaction to amount of another substance in the reaction, so we know it is an equation stoichiometry problem. The core of our setup will be the conversion factor for changing moles of sodium phosphate to moles of silver nitrate. To construct it, we need to know the molar ratio of AgN03 to Na3P04, which comes from the balanced equation for the reaction. 

We then strategize by drawing a solution map that begins with mol N2 and ends with mol NH3. The conversion factor comes from the balanced chemical equation. 

Gases in Chemical Reactions Stoichiometric calculations involving gases are similar to those that do not involve gases in that the coefficients in a balanced chemical equation provide conversion factors among moles of reactants and products in the reaction. For gases, the amoimt of a reactant or product is often specified by the volume of reactant or product at a given temperature and pressiue. The ideal gas law is then used to convert from these quantities to moles of reactant or product. Alternatively at standard temperature and pressure, volume can be converted directly to moles with ffie equality ... 

Solving any reaction stoichiometry problem requires the use of a mole ratio to convert from moles or grams of one substance in a reaction to moles or grams of another substance. A mole ratio is a conversion factor that relates the amounts in moles of any two substances involved in a chemical reaction. This information is obtained directly from the balanced chemical equation. Consider, for example, the chemical equation for the electrolysis of melted aluminum oxide to produce aluminum and oxygen. 

This problem requires one conversion factor—the mole ratio of LiOH to CO2. The mole ratio is obtained from the balanced chemical equation. Because you are given moles of CO2, select a mole ratio that vwill cancel mol CO2 and give you mol LiOH in your final answer. The correct ratio has the following units. 

A mole ratio is the conversion factor that relates the amount in moles of any two substances in a chemical reaction. The mole ratio is derived from the balanced equation. 

The convention is to express rates in terms of reactants as negative, because the concentrations of reactants are decreasing as the reaction progresses. Conversely, rates expressed in terms of products are positive, because product amounts are increasing as the reaction proceeds. To remind ourselves of these facts, we write the -and -I- signs explicitly in equation 20.3. The brackets [ ] imply amounts, usually moles or molarity (that is, concentration) units. The coefficients a, b, c, or d in the denominators are the scaling factors from the stoichiometry of the balanced chemical equation. These allow a rate to be expressed as the same numerical value no matter which change in amount is used to express the rate. 

Example 8.13 is an example of a mole-to-mole conversion—one in which moles of one chemical involved in a chemical reaction are converted to moles of another. The conversion factor is always the mole ratio, as determined from the balanced equation. 

Equation (6.5) can be used to calculate the half-life of a chemical in the bloodstream when the first-order elimination rate constant is known. Conversely, it can be used to calculate the first-order elimination rate constant when the half-life is known. The half-life can also be determined graphically from the time-concentration curve in Figure 6.8 by picking any two serum concentrations in the curve s second phase that differ by a factor of two, then determining the difference between the times on the x-axis that correspond to the two concentrations. A chemical s half-life generally reflects the combined rate of its clearance from the bloodstream by the kidneys and the liver for some chemicals, other organs may contribute to elimination, as well, for example, the lungs. The faster a chemical is cleared, the shorter is its half-life. 

We can use this ratio to determine how many moles of CO2 form when a given number of moles of CgHig bums. Suppose that we bum 22.0 moles of CgHig how many moles of CO2 form We use the ratio from the balaneed chemical equation in the same way that we used the ratio from the pizza recipe. The ratio acts as a conversion factor between the amount in moles of the reactant (CgHig) and the amount in moles of the product (CO2) ... 

Such problems as this one involve many steps or conversions. Try to break the problem into simpler ones involving fewer steps or conversions. It may also help to remember that solving a stoichiometry problem involves three steps (1) converting to moles, (2) converting between moles, and (3) converting from moles. Use molarities and molar masses to carry out volume-mole conversions and gram-mole conversions, respectively, and stoichiometric factors to carry out mole-mole conversions. The stoichiometric factors are constructed from a balanced chemical equation. 

The molar mass of NaN3 is used for the first conversion. The second conversion makes use of a stoichiometric factor constructed from the coefficients of the chemical equation. The ideal gas equation is used to complete the final conversion. 

Using the various simplifications above, we have arrived at a model for reaction 11.9 in which only one step, the chemical conversion occurring at the active site of the enzyme characterized by the rate constant k3, exhibits the kinetic isotope effect Hk3. From Equations 11.29 and 11.30, however, it is apparent that the observed isotope effects, HV and H(V/K), are not directly equal to this kinetic isotope effect, Hk3, which is called the intrinsic kinetic isotope effect. The complexity of the reaction may cause part or all of Hk3 to be masked by an amount depending on the ratios k3/ks and k3/k2. The first ratio, k3/k3, compares the intrinsic rate to the rate of product dissociation, and is called the ratio of catalysis, r(=k3/ks). The second, k3/k2, compares the intrinsic rate to the rate of the substrate dissociation and is called forward commitment to catalysis, Cf(=k3/k2), or in short, commitment. The term partitioning factor is sometimes used in the literature for this ratio of rate constants. 

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