Stoichiometry reactions

For a phase in which a chemical reaction occurs according to the equation 

The stoichiometric numbers provide relations among the changes in mole numbers of chemical species which occur as the result of chemical reaction. Thus, for reaction  

All these terms are equal, and they can be equated to the change in a single quantity tj, called the reaction coordinate for reaction, thereby giving 

Because the total change in mole number Atij is just the sum of the changes Any resulting from the various reactions, 

The general criterion of chemical reaction equilibria is given by Eq. (4-296). For a system in which just a single reaction occurrs, Eq. (4-361) becomes 

When you understand the weight relationships in a chemical reaction, you can do some stoichiometry problems. Stoichiometry refers to the mass relationship in chemical equations. 

When you get ready to work stoichiometry types of problems, you must start with a balanced chemical equation. If you don t have it to start with, go ahead and balance the equation. 

Look at my favorite reaction — you guessed it — the Haber process  

Suppose that you want to know how many grams of ammonia can be produced from the reaction of 75.00 grams of nitrogen with excess hydrogen. The mole concept is the key. The coefficients in the balanced equation are not only the number of individucd atoms or molecules but also the number of moles  

convert the 75.00 grams of nitrogen to moles of nitrogen. Then use the ratio of the moles of ammonia to the moles of nitrogen from the balanced equation to convert to moles of ammonia. Finally, take the moles of ammonia and convert that number to grams. The equation looks like this  

As we have discussed previously, the balanced chemical equation not only indicates which chemical species are the reactants and the products, but also indicates the relative ratio of reactants and products. Consider the balanced equation of the Haber process for the production of ammonia  

This balanced equation can be read as 1 nitrogen molecule reacts with 3 hydrogen molecules to produce 2 ammonia molecules. But as indicated previously, the coefficients can stand not only for the number of atoms or molecules (microscopic level), they can also stand for the number of moles of reactants or products. The equation can also be read as 1 mol of nitrogen molecules reacts with 3 mol of hydrogen molecules to produce 2 mol of ammonia molecules. And if the number of moles is known, the number of grams or molecules can be calculated. This is stoichiometry, the calculation of the amount (mass, moles, particles) of one substance in a chemical reaction through the use of another. The coefficients in a 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. 

Consider the Haber process above. How many moles of ammonia could be produced from the reaction of 20.0 mol of nitrogen with excess hydrogen  

Before any stoichiometry calculation can be done, you must have a balanced chemical equation  

You are starting with moles of nitrogen and want moles of ammonia, so we ll convert from moles of nitrogen to moles of ammonia by using the ratio of moles of ammonia to moles of nitrogen as defined by the balanced chemical equation  

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Rios, A. Luque de Castro, M. Valcarcel, M. Determination of Reaction Stoichiometries by Flow Injection Analysis, ... 

The amount of combustion ait is tightly controlled to maximize sulfur recovery, ie, maintaining the appropriate reaction stoichiometry of 2 1 hydrogen sulfide to sulfur dioxide throughout downstream reactors. Typically, sulfur recoveries of up to 97% can be achieved (7). The recovery is heavily dependent on the concentration of hydrogen sulfide and contaminants, especially ammonia and heavy hydrocarbons, ia the feed to the Claus unit. 

When an equilibrium reaction occurs in a vapor-hquid system, the phase compositions depend not only on the relative volatility of the components in the mixture, but also on the consumption (and production) of species. Thus, the condition for azeotropy in a nonreactive system = x, for all i) no longer holds true in a reactive system and must be modified to include reaction stoichiometry ... 

This method estimates the reaction order based on the reaction stoichiometry and assumptions concerning its mechanism. The assumed rate equation is then integrated to obtain a relation between the composition and time. The following procedures are used for determining the rate equations ... 

The overall reaction stoichiometry having been established by conventional methods, the first task of chemical kinetics is essentially the qualitative one of establishing the kinetic scheme in other words, the overall reaction is to be decomposed into its elementary reactions. This is not a trivial problem, nor is there a general solution to it. Much of Chapter 3 deals with this issue. At this point it is sufficient to note that evidence of the presence of an intermediate is often critical to an efficient solution. Modem analytical techniques have greatly assisted in the detection of reactive intermediates. A nice example is provided by a study of the pyridine-catalyzed hydrolysis of acetic anhydride. Other kinetic evidence supported the existence of an intermediate, presumably the acetylpyridinium ion, in this reaction, but it had not been detected directly. Fersht and Jencks observed (on a time scale of tenths of a second) the rise and then fall in absorbance of a solution of acetic anhydride upon treatment with pyridine. This requires that the overall reaction be composed of at least two steps, and the accepted kinetic scheme is as follows. 

For symbolic convenience we make use of the reaction variable x, which is the decrease in concentration of reactant A in time t. Because of the reaction stoichiometry, X is also the decrease in B concentration. The mass balance expressions are... 

From the reaction stoichiometry, for each mole of acetic acid one mole of oxygen was used. So the equal molar oxygen consumption is ... 

There are, however, two disadvantages associated with use of the phenyldimethylsilyl group. Based on the reaction stoichiometry, for each equivalent of substrate, one silyl group is unused, and after work-up this appears as a relatively involatile by-product. Secondly, after synthetic use of such vinylsilanes involving desilylation, a similar problem of by-product formation arises. One solution to these problems lies in the use of the tri-methylsilyl group (Chapter 8), since the by-product, hexamethyldisiloxane, is volatile and normally disappears on work-up. 

The rate is first order with respect to [C5H10NH], showing that there is an intermediate. since the kinetic stoichiometry does not match the reaction stoichiometry. The second-order rate constant does not vary too much among six different substituents, five of which represent different elements. (Some would say that a kinetic element effect is absent.) One argues, therefore, that the C-X bond likely remains intact in the interme-... 

Sometimes we need to know how much product to expect from a reaction, or how much reactant we need to make a desired amount of product. The quantitative aspect of chemical reactions is the part of chemistry called reaction stoichiometry. The key to reaction stoichiometry is the balanced chemical equation. Recall from Section H that a stoichiometric coefficient in a chemical equation tells us the relative amount (number of moles) of a substance that reacts or is produced. Thus, the stoichiometric coefficients in... 

What Do We Need to Know Already We need to be familiar with SI units (Appendix IB) and the concepts of force and energy (Section A). This chapter also develops the techniques of reaction stoichiometry (Sections L and M) by extending them to gases. 

What Do We Need to Know Already The concepts of chemical equilibrium are related to those of physical equilibrium (Sections 8.1-8.3). Because chemical equilibrium depends on the thermodynamics of chemical reactions, we need to know about the Gibbs free energy of reaction (Section 7.13) and standard enthalpies of formation (Section 6.18). Ghemical equilibrium calculations require a thorough knowledge of molar concentration (Section G), reaction stoichiometry (Section L), and the gas laws (Ghapter 4). 

The equilibrium constant of a reaction contains information about the equilibrium composition at the given temperature. However, in many cases, we know only the initial composition of the reaction mixture and are given apparently incomplete information about the equilibrium composition. In fact, the missing information can usually be inferred by using the reaction stoichiometry. The easiest way to proceed is to draw up an equilibrium table, a table showing the initial composition, the changes needed to reach equilibrium in terms of some unknown quantity x, and the final equilibrium composition. The procedure is summarized in Toolbox 9.1 and illustrated in the examples that follow. 

The composition of a reaction mixture tends to adjust until the molar concentrations or partial pressures of gases ensure that Qc = Kc and Q = K. A change in the abundance of any one component is linked to changes in the others by the reaction stoichiometry. 

We do not know the number of acid molecules that lose their protons, and so we assume that the concentration of the acid decreases by x mol-L 1 as a result of deprotonation. The reaction stoichiometry gives us the other changes in terms of x. 

First, use the reaction stoichiometry to find the amount of excess acid or base. 

Step 3 Write the chemical equation for the neutralization reaction and use the reaction stoichiometry to find the amount of H. O ions (or OH ions if the analyte is a strong base) that remains in the analyte solution after all the added titrant reacts. Each mole of H30+ ions reacts with 1 mol OH ions therefore, subtract the number of moles of H30+ or OH ions that have reacted from the initial number of moles. 

Step 3 Use the reaction stoichiometry to calculate the following amounts ... 

We can predict the pH at any point in the titration of a polyprotic acid with a strong base by using the reaction stoichiometry to recognize what stage we have reached in the titration. We then identify the principal solute species at that point and the principal proton transfer equilibrium that determines the pH. 

In the calculation in Example 13.1, we used the units micromoles per liter per second (pmol-L 1 -s 1) to report the reaction rate, but other units for time (such as minutes or even hours) are commonly encountered for slower reactions. Note, too, that, when we report a reaction rate, we must specify the species to which the rate refers. For example, the rate of consumption of HI is twice the rate of formation of H2 in the reaction in Example 13.1, because two HI molecules are used to make one H2 molecule. The various ways of reporting the rate of a given reaction are related by the reaction stoichiometry. Therefore, in our example, we conclude that... 

Basically, the oxidation of iron pyrite, FeS2, results in the production of iron(III) sulfate and sulfuric acid, H2SO4. However, two overall reaction stoichiometries are possible and each will yield a different acid generation capacity (e.g., Langmuir, 1997 Baird, 1995) ... 

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