Stoichiometry summarized

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. 

To construct an overall rate law from a mechanism, write the rate law for each of the elementary reactions that have been proposed then combine them into an overall rate law. First, it is important to realize that the chemical equation for an elementary reaction is different from the balanced chemical equation for the overall reaction. The overall chemical equation gives the overall stoichiometry of the reaction, but tells us nothing about how the reaction occurs and so we must find the rate law experimentally. In contrast, an elementary step shows explicitly which particles and how many of each we propose come together in that step of the reaction. Because the elementary reaction shows how the reaction occurs, the rate of that step depends on the concentrations of those particles. Therefore, we can write the rate law for an elementary reaction (but not for the overall reaction) from its chemical equation, with each exponent in the rate law being the same as the number of particles of a given type participating in the reaction, as summarized in Table 13.3. 

Boron carbide is a non-metallic covalent material with the theoretical stoichiometric formula, B4C. Stoichiometry, however, is rarely achieved and the compound is usually boron rich. It has a rhombohedral structure with a low density and a high melting point. It is extremely hard and has excellent nuclear properties. Its characteristics are summarized in Table 9.2. 

Mg(THF), when the stoichiometry was 1 2. Monomeric and dimeric amidinate complexes of magnesium have been studied in detail with respect to potential applications of these compounds in the chemical vapor deposition of magnesium-doped Group 13 compound semiconductor films. The reactions and products are summarized in Scheme 16. ... 

The interaction of small, well defined, rhodium clusters, Rh and Rhs, with O2 has been investigated (220) by matrix infrared, and UV-visible, spectroscopy, coupled with metal/02 concentration studies, warm-up experiments, and isotopic oxygen studies. A number of binuclear O2 complexes were identified, with stoichiometries Rh2(02)n, n = 1-4. In addition, a trinuclear species Rhs(02)m, m = 2 or 6, was identified. The infrared data for these complexes, as well as for the mononuclear complexes Rh(02)x, = 1-2 (229), are summarized in Table XI. Metal-concentration plots that led to the determination of... 

There are some exotic chemical names here, but they should not distract you from the basic principles of reaction stoichiometry. The stoichiometric coefficients state that one mole of each reactant will produce one mole of each product. A flowchart summarizes the steps used to convert the mass of geraniol into the mass of geranyl formate. 

A table of amounts is a convenient way to organize the data and summarize the calculations of a stoichiometry problem. Such a table helps to identify the limiting reactant, shows how much product will form during the reaction, and indicates how much of the excess reactant will be left over. A table of amounts has the balanced chemical equation at the top. The table has one column for each substance involved in the reaction and three rows listing amounts. The first row lists the starting amounts for all the substances. The second row shows the changes that occur during the reaction, and the last row lists the amounts present at the end of the reaction. Here is a table of amounts for the ammonia example ... 

We have data for the amounts of both starting materials, so this is a limiting reactant problem. Given the chemical equation, the first step in a limiting reactant problem is to determine the number of moles of each starting material present at the beginning of the reaction. Next compute ratios of moles to coefficients to identify the limiting reactant. After that, a table of amounts summarizes the stoichiometry. 

According to (7.8) and (7.12), the stoichiometry (m/n) can be extracted from the slope of the plots of adatom charge density versus hydrogen (or hydrogen plus anion) charge density. Some representative plots are shown in Fig. 7.3. The conclusions extracted from this kind of analysis are summarized in Tables 7.1 and 7.2 for Pt(l 11) and Pt(lOO) modified surfaces, respectively. The extension of this analysis... 

The stoichiometry of the reaction dictates that the final generated NO concentration will be equal to the concentration of SNAP in the solution. The method can be summarized as follows. Saturated cuprous chloride solution is first prepared by adding 150 mg CuCl to 500 mL distilled water. This solution is then deoxygenated by purging with pure nitrogen or argon gas for 15 min. The final, saturated CuCl solution will have a concentration of approximately 2.4 mM at room temperature. The solution is light sensitive and must therefore be kept in the dark prior to use. 

This diagram summarizes the relationship between the stoichiometry of a reaction and AH. 

The above described data have been summarized by different laboratories into structural models. In Fig. 2 the most recent proposals are shown. They all agree on the point that the minor pigment-proteins should be located in a pericentral position between the core complex and the major LHCII. Major differences are encountered in the monomeric (B) or dimeric (A, C, D) organization of the core, the stoichiometry between the core complex and LHC proteins (model in panel D uses the same stoichiometry as the one in panel A) and, finally, the possibility that CP29 and CP24 belong to the same subcomplex (A, C), as previously suggested [9, 10, 63], or are independently connected to the core complex (B, D). 

Nine studies regarding the thermochemical conversion of packed-beds of biomass have been reviewed. The review is summarized in Table 7 below. The focus of the survey has been on the theories of the methods applied to measure ignition front rate, conversion rate (combustion rate, burning rate), conversion gas stoichiometry, and air factors. 

The stoichiometry of the fast SCR reaction (Equation 13.24), is recovered once the overall readion summarizing the chemistry of the NO2-NH3 system is coupled with that describing the addition of NO to this reacting system. The proposed readion scheme accounts for the optimal equimolar NO NO2 feed ratio and also for the... 

Information about the stoichiometry of selector-selectand complex is difficult to gain from CE. However, this knowledge is useful in order to characterize the structure of intermolecular complexes as well as for the calculation of the binding constants. Previous research and review papers (3, 4,62,65) summarize the application of this technique to the problems related to chiral CE. As shown in Fig. 4, despite the involvement of different parts of the CL molecule in complex formation, the stoichiometry of CL complexes most likely is the same (1 1) with /3-CD and HDAS-/3-CD (65). 

In Chapter 7 we considered catalytic reactions on solid surfaces and foimd that transport steps are essential in describing these reactions because mass transfer of reactants and products between phases must accompany reaction. In this chapter we consider the reactions of solids in which the solid enters the stoichiometry of the reaction as a reactant or product or both. We remark that the texts of Levenspiel give excellent and thorough descriptions of the reactions of solids, and we will only summarize some of the features of reactions involving solids here. 

Table III summarizes some information on the initial rates of oxidation of fluorene in several solvents. In the alcohol-containing solvents the stoichiometry was nearly one molecule of oxygen per mole of fluorene, an observation that excludes 9-fluorenol as an intermediate. In all solvents, including HMPA, interrupted oxidations yielded only fluorenone (or the DMSO-fluorenone adduct) and fluorene. Apparently Reaction 6 or 7 occurs readily in the presence of hydroxylic solvents. In HMPA the high...

Ferric chloride (0.002M) reduced the rate of oxidation of benzhydrol (0.15M) in the presence of 0.39M potassium ferf-butoxide in tert-butyl alcohol to a rate of 0.001 mole of oxygen per mole of benzhydrol per minute, while arsenic trioxide (0.01M) reduced the rate of oxidation of 0.12M benzhydrol and 0.36M potassium ferf-butoxide to 0.0001 mole of oxygen per mole of benzhydrol per minute for a 4-hour period, after which the oxidation occurred at the uninhibited rate (Figure 3). Table IX summarizes some observed stoichiometries in the oxidation of benzhydrol. 

Interpretations of Structural Modulations The following paragraphs summarize the reported models concerning the origin of the modulations and report some of the recent experiments. The origin of the modulations, the role of anion stoichiometry and of the cation substitution affecting the modulations and Tc are not yet fully resolved and need further experimental clarification. 

---