Stoichiometry balanced equations

Consider the balanced equation for glnconeogenesis in Section 23.1. Account for each of the components of this equation and the indicated stoichiometry. 

When we do not know the changes, write one of them as x or a multiple of x and then use the stoichiometry of the balanced equation to express the other changes in terms of that x. 

Most students demonstrated the abihty to translate from the sub-micro to the symbolic level by writing a balanced equation for the reaction in the question shown in Fig. 8.8. In determining the hmiting reagent, however, there were a lower number of correct responses than for the question in Fig. 8.9 based on stoichiometry. The difference in performance is even greater for part (c) of both questions... 

All changes are related by stoichiometry. Each ratio of changes in amount equals the ratio of stoichiometric coefficients in the balanced equation. In the example above, the changes in amounts for H2 and N2 are in the ratio 3 1, the same as the ratio for the coefficients of H2 and N2 in the balanced equation. 

The balanced equation shows that three molecules of oxygen are consumed for every two molecules of propene and two molecules of ammonia. Thus, the rate of C3 Hg and NH3 consumption is only two-thirds the rate of O2 consumption. Those seven molecules of starting materials produce two molecules of CH2 CHCN and six molecules of H2 O. Thus, CH2 CHCN is produced at the same rate as C3 Hg is consumed, whereas H2 O is produced three times as fast as CH2 CHCN is. The link between relative reaction rates and reaction stoichiometry is Equation. Therefore,... 

According to the mass balance Equation 3.28, the expression in parentheses is Mi. Further, the charge Z, on a species component is the same as the charge z, on the corresponding basis species, since components and species share the same stoichiometry. Substituting, the electroneutrality condition becomes,... 

Attempts to define operationally the rate of reaction in terms of certain derivatives with respect to time (r) are generally unnecessarily restrictive, since they relate primarily to closed static systems, and some relate to reacting systems for which the stoichiometry must be explicitly known in the form of one chemical equation in each case. For example, a IUPAC Commission (Mils, 1988) recommends that a species-independent rate of reaction be defined by r = (l/v,V)(dn,/dO, where vt and nf are, respectively, the stoichiometric coefficient in the chemical equation corresponding to the reaction, and the number of moles of species i in volume V. However, for a flow system at steady-state, this definition is inappropriate, and a corresponding expression requires a particular application of the mass-balance equation (see Chapter 2). Similar points of view about rate have been expressed by Dixon (1970) and by Cassano (1980). 

One of the most useful tools for design and analysis of performance is the balance equation. This type of equation is used to account for a conserved quantity, such as mass or energy, as changes occur in a specified system element balances and stoichiometry, as discussed in Section 1.4.4, constitute one form of mass balance. 

Fermentation systems obey the same fundamental mass and energy balance relationships as do chemical reaction systems, but special difficulties arise in biological reactor modelling, owing to uncertainties in the kinetic rate expression and the reaction stoichiometry. In what follows, material balance equations are derived for the total mass, the mass of substrate and the cell mass for the case of the stirred tank bioreactor system (Dunn et ah, 2003). 

Stoichiometry Calculate reactant and product masses using the balanced equation and molar... 

This is a critical chapter in your study of chemistry. Our goal is to help you master the mole concept. You will learn about balancing equations and the mole/mass relationships (stoichiometry) inherent in these balanced equations. You will learn, given amounts of reactants, how to determine which one limits the amount of product formed. You will also learn how to determine the empirical and molecular formulas of compounds. All of these will depend on the mole concept. Make sure that you can use your calculator correctly. If you are unsure about setting up problems, refer back to Chapter 1 of this book and go through Section 1-4, on using the Unit Conversion Method. Review how to find atomic masses on the periodic table. Practice, Practice, Practice. 

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. 

We have seen how analytical calculations in titrimetric analysis involve stoichiometry (Sections 4.5 and 4.6). We know that a balanced chemical equation is needed for basic stoichiometry. With redox reactions, balancing equations by inspection can be quite challenging, if not impossible. Thus, several special schemes have been derived for balancing redox equations. The ion-electron method for balancing redox equations takes into account the electrons that are transferred, since these must also be balanced. That is, the electrons given up must be equal to the electrons taken on. A review of the ion-electron method of balancing equations will therefore present a simple means of balancing redox equations. 

In a stoichiometry calculation, the weight of one substance involved in a chemical reaction (reactant or product) is converted to the weight of another substance (reactant or product) appearing in the same reaction. The balanced equation is the basis for the calculation, and the formula weights of the reactant and product involved are needed. In the following general example,... 

A considerable improvement over purely graph-based approaches is the analysis of metabolic networks in terms of their stoichiometric matrix. Stoichiometric analysis has a long history in chemical and biochemical sciences [59 62], considerably pre-dating the recent interest in the topology of large-scale cellular networks. In particular, the stoichiometry of a metabolic network is often available, even when detailed information about kinetic parameters or rate equations is lacking. Exploiting the flux balance equation, stoichiometric analysis makes explicit use of the specific structural properties of metabolic networks and allows us to put constraints on the functional capabilities of metabolic networks [61,63 69]. 

Each of these dissociation reactions also specifies a definite equilibrium concentration of each product at a given temperature consequently, the reactions are written as equilibrium reactions. In the calculation of the heat of reaction of low-temperature combustion experiments the products could be specified from the chemical stoichiometry but with dissociation, the specification of the product concentrations becomes much more complex and the s in the flame temperature equation [Eq. (1.11)] are as unknown as the flame temperature itself. In order to solve the equation for the n s and T2, it is apparent that one needs more than mass balance equations. The necessary equations are found in the equilibrium relationships that exist among the product composition in the equilibrium system. 

In general, concentrations of the products are divided by the concentrations of the reactants. In the case of gas-phase reactions, partial pressures cire used instead of molar concentrations. Multiple product or reactant concentrations are multiplied. Each concentration is raised to an exponent equal to its stoichiometric coefficient in the balanced reaction equation. (See Chapters 8 and 9 for details on balanced equations and stoichiometry.)... 

Use the balanced equation and basic stoichiometry to determine how many moles of the mystery substance being neutralized are present (see Chapter 9 for details on stoichiometry). 

While linear algebraic methods are present in almost every problem, they also have a number of direct applications. One of them is formulating and solving balance equations for extensive quantities such as mass and energy. A particularly nice application is stoichiometry of chemical systems, where you will discover most of the the basic concepts of linear algebra under different names. 

We saw in Section 3.3 that the coefficients in a balanced equation tell the numbers of moles of substances in a reaction. In actual laboratory work, though, it s necessary to convert between moles and mass to be sure that the correct amounts of reactants are used. In referring to these mole-mass relationships, we use the word stoichiometry (stoy-key-ahm-uh-tree from the Greek stoicheion, "element," and metron, "measure"). Let s look again at the reaction of ethylene with HC1 to see how stoichiometric relationships are used. 

We need to calculate the amount of methyl tert-bu tyl ether that could theoretically be produced from 26.3 g of isobutylene and compare that theoretical amount to the actual amount (32.8 g). As always, stoichiometry problems begin by calculating the molar masses of reactants and products. Coefficients of the balanced equation then tell mole ratios, and molar masses act as conversion factors between moles and masses. 

Complex stoichiometry problems should be worked slowly and carefully, one step at a time. When solving a problem that deals with limiting reactants, the idea is to find how many moles of all reactants are actually present and then compare the mole ratios of those actual amounts to the mole ratios required by the balanced equation. That comparison will identify the reactant there is too much of (the excess reactant) and the reactant there is too little of (the limiting reactant). 

Solving stoichiometry problems always requires finding the number of moles of the first reactant, using the coefficients of the balanced equation to find the number of moles of the second reactant, and then finding the amount of the second reactant. The flow diagram in Figure 3.5 summarizes the situation. 

The chemical equation for an elementary reaction is a description of an individual molecular event that involves breaking and/or making chemical bonds. By contrast, the balanced equation for an overall reaction describes only the stoichiometry of the overall process, but provides no information about how the reaction occurs. The equation for the reaction of N02 with CO, for example, does not tell us that the reaction occurs by direct transfer of an oxygen atom from an N02 molecule to a CO molecule. 

Suppose that we have an equilibrium mixture of 0.50 M N2,3.00 M H2, and 1.98 M NH3 at 700 K, and that we disturb the equilibrium by increasing the N2 concentration to 1.50 M. Le Chatelier s principle tells us that reaction will occur to relieve the stress of the increased concentration of N2 by converting some of the N2 to NH3. As the N2 concentration decreases, the H2 concentration must also decrease and the NH3 concentration must increase in accord with the stoichiometry of the balanced equation. These changes are illustrated in Figure 13.8. 

The equilibrium problem matrix. The information concerning components, stoichiometry and formation constants can be written in the form of a table which for the purposes of this chapter will be referred to as the equilibrium problem matrix (EPM). An example of an EPM table for the monomeric A1 species is shown in Table 5.6. The EPM is a logical and compact format for summarising all the information required for solving equilibrium problems. Reading across the rows of the table the information needed to formulate the mass action expressions is contained. Down each component column are the coefficients with which the concentration of each species should be multiplied to formulate the mass balance equation (MBE). Therefore, once given the chemical problem in an EPM format the nature of the mass action equations, formation constants and mass balances considered can all be deduced. 

The mole is the chemist s counting unit. Working with the mole should be second nature to students, so let s review grams to mole calculations since they are very important in mass-mass stoichiometry and the balanced equations provides mole ratios not mass ratios. 

Stoichiometry, Chemical Recipes, an Integration of Moles, and Balanced Equations... 

Stoichiometry is the technical word for the relationships among balanced equations, moles, and grams. Stoichiometry is to chemists what cooking and recipes are to cooks. 

The balanced equation that we will use for this stoichiometry explanation is the recipe for the manufacture of ammonia (NH3). This reaction was so important that the chemist responsible for it, Fritz Haber, was awarded the Nobel Prize. Ammonia is a gateway step in the manufacture of fertilizers, and its manufacture was a giant step in solving the problem of providing food to a world population growing at an exponential rate. The equation for the Haber process is... 

The correct answer is (A). When you see two masses in a stoichiometry problem, you should be alerted that you are dealing with a limiting reactant problem. This problem will have two stages—the first is to determine the limiting reactant, and the second to determine the mass of the hydrogen gas. Before we do anything, we need to see the balanced equation for the reaction ... 

Compare molar amounts using stoichiometry ratios from the balanced equation. Solve for the unknown molar amount. 

The best way to find out how to do a stoichiometry problem using the ideal gas law is to study an example. In the following Sample Problem, you will use a balanced equation and the ideal gas law to find the volume of a gas produced. (Refer to Chapter 4, section 4.1, if you want to review how to write balanced equations.)... 

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. 

Stoichiometry involves the calculation of quantities of any substances involved in a chemical reaction from the quantities of the other substances. The balanced equation gives the ratios of formula units of all the substances in a chemical reaction. It also gives the corresponding ratios of moles of the substances. These relationships are shown in Figure 10.1. For example, one reaction of phosphorus with chlorine gas is governed by the equation... 

The first step, as in most stoichiometry problems, is to write a balanced equation for the reaction ... 

As was mentioned earlier in this section, heat is a reactant or product in most chemical reactions. It is possible for us to indicate the quantity of heat in the balanced equation and to treat it with the rules of stoichiometry that we already know. 

We next develop the mass balance equations for the gaseous reactant (oxygen) and the product (sulfur dioxide). The gas flow in the reactor is assumed to be in plug flow and hence the concentration of these gases will depend only on the height H, in the bed above the distributor plate. The rate of consumption of oxygen by reactions 1, 2 and 3 can be obtained from Eqs. 43 and 80 and the stoichiometry of these reactions. We will first examine Eq. 43 which may be rewritten as follows after appropriate substitutions. 

In Chapter 3 we covered the principles of chemical stoichiometry the procedures for calculating quantities of reactants and products involved in a chemical reaction. Recall that in performing these calculations, we first convert all quantities to moles and then use the coefficients of the balanced equation to assemble the appropriate molar ratios. In cases in which reactants are mixed, we must determine which reactant is limiting, since the reactant that is consumed first will limit the amounts of products formed. These same principles apply to reactions that take place in solutions. However, there are two points about solution reactions that need special emphasis. The first is that it is sometimes difficult to tell immediately which reaction will occur when two solutions are mixed. Usually we must think about the various possibilities and then decide what will happen. The first step in this process always should be to write down the species that are actually present in the solution, as we did in Section 4.5. 

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