Stoichiometry stoichiometric concentrations

The model assumes that liquid evaporation is always the rate controlling step. At some point the model must fail, since as droplet size approaches zero the predicted MIE approaches zero rather than the MIE of the vapor in air. In practice, droplets having diameters less than 10-40 /rm completely evaporate ahead of the flame and burn as vapor (5-1.3). The model also predicts that the MIE continuously decreases as equivalence ratio is increased, although as discussed above, combustion around droplets is not restrained by the overall stoichiometry and naturally predominates at the stoichiometric concentration. It is recommended that the model be applied only to droplet diameters above about 20/rm and equivalence ratios less than about one. 

With liquid DGEBA epoxy resins, DETA is normally used at the stoichiometric concentration of 10 to 11 parts per hundred (pph), and TETA is used at a concentration of 14 pph. However, both curing agents can be used at mix ratios as low as 70 to 75 percent of stoichiometry for greater toughness and increased pot life at the sacrifice of heat and chemical resistance. The effect of the mix ratio of DETA and TETA on the heat deflection temperature of castings is shown in Fig. 5.3. 

A first observation is that the volume is different in nature from the other variables. Some questions raised are Should this volume be considered at all Should it be used to compensate for dilution effects These questions are not answered here but the answer depends on the goal of the study. A second observation is that the pH is not a concentration. Should it be made into a H+ concentration or not It is easily done but whether it is appropriate is not always obvious. A third problem is typical for chemistry or rather stoichiometry. The concentrations in ppb are not in stoichiometric form. To get real chemical meaning they may have to be expressed in molarity, molality or normality values. In this way the balance between cations and anions may be studied. Again, the choice is not always easy. For dilute samples, molarity and molality are close to each other, but normality may be determined by the type of reaction under consideration. 

Analysis of products from the reaction of phenol with nitric oxide, ONOO", or both (added simultaneously) provides some insight into possible reaction mechanisms as well as products that might be formed in vivo from phenolics such as tyrosine. Based on the apparent stoichiometry of the ONOO /nitric oxide reaction (see Fig. 2), a series of reactions were carried out in which ONOO was added at three different concentrations (0.2, 0.4, and 0.8 mM) in the absence and presence of a fixed concentration of nitric oxide (0.2 mM) added simultaneously. Ratios were chosen which would allow nitric oxide to remain in excess (0.2 mM ONOO" plus 0.2 mM nitric oxide), at stoichiometric concentrations (0.4 mM ONOO" plus 0.2 mM nitric oxide), and where ONOO" was in excess (0.8 mM ONOO" plus... 

The stoichiometric relationship between chlorine dioxide added and color removed during bleaching is nonlinear, but it is independent of temperature, pH, and pulp concentration under conditions normally used. Models used to explain the kinetics and stoichiometry show a strong dependence on chromophore concentration that probably results from differences in the reaction rates of the various chromophores present in the pulps (80). 

It is not necessary for a compound to depart from stoichiometry in order to contain point defects such as vacant sites on the cation sub-lattice. All compounds contain such iirndirsic defects even at the precisely stoichiometric ratio. The Schottky defects, in which an equal number of vacant sites are present on both cation and anion sub-lattices, may occur at a given tempe-ramre in such a large concentration drat die effects of small departures from stoichiometry are masked. Thus, in MnOi+ it is thought that the intrinsic concentration of defects (Mn + ions) is so large that when there are only small departures from stoichiometry, the additional concentration of Mn + ions which arises from these deparmres is negligibly small. The non-stoichiometry then varies as in this region. When the departure from non-stoichio-... 

P the total pressure, aHj the mole fraction of hydrogen in the gas phase, and vHj the stoichiometric coefficient of hydrogen. It is assumed that the hydrogen concentration at the catalyst surface is in equilibrium with the hydrogen concentration in the liquid and is related to this through a Freundlich isotherm with the exponent a. The quantity Hj is related to co by stoichiometry, and Eg and Ag are related to - co because the reaction is accompanied by reduction of the gas-phase volume. The corresponding relationships are introduced into Eqs. (7)-(9), and these equations are solved by analog computation. 

The numerical methods in this book can be applied to all components in the system, even inerts. When the reaction rates are formulated using Equation (2.8), the solutions automatically account for the stoichiometry of the reaction. We have not always followed this approach. For example, several of the examples have ignored product concentrations when they do not affect reaction rates and when they are easily found from the amount of reactants consumed. Also, some of the analytical solutions have used stoichiometry directly to ease the algebra. This section formalizes the use of stoichiometric constraints. 

The value of the activation energy approaches 50000r near the stoichiometric composition. This diffusion process therefore approximates to the selfdiffusion of metals at stoichiometry where the vacancy concentration on the carbon sub-lattice is small. 

A useful tool for dealing with reaction stoichiometry in chemical kinetics is a stoichiometric table. This is a spreadsheet device to account for changes in the amounts of species reacted for a basis amount of a closed system. It is also a systematic method of expressing the moles, or molar concentrations, or (in some cases) partial pressures of reactants and products, for a given reaction (or set of reactions) at any time or position, in terms of initial concentrations and fractional conversion. Its use is illustrated for a simple system in the following example. 

Fig. 2 Determination of the binding stoichiometry of human serum albumin (HSA) to its mouse monoclonal IgG antibody (anti-HSA). (A) The concentration of anti-HSA was 0.33 /J.M. DNS-E was dansylglutamic acid used as internal standard. The intermediate species is considered to be due to the 1 1 complex. (B) A plot of the concentration of free ligand vs. the ratio of [HSA]/[anti-HSA] gives a sharp break at the stoichiometric point. (Reprinted with permission from Ref. 8. Copyright 1994 American Chemical Society.)...

Consider the polyesterification of Eq. 2-58 under stoichiometric conditions, where k and k2 are the rate constants for the forward and back reactions. The initial carboxyl and hydroxyl group concentrations are [M]0. The values at any time are [M], which is given by (1 — p) [M]0. The concentrations of the products, [COO] and [H20], at any time are equal because of the stoichiometry and are given by p[M]0. The polymerization rate is the difference between the rates of the forward and back reactions... 

This is the first time we have encountered multiple reactions. For these in general, if it is necessary to write N stoichiometric equations to describe what is happening, then it is necessary to follow the decomposition of N reaction components to describe the kinetics. Thus, in this system following C, or Cr, or Q alone will not give both ki and k2. At least two components must be followed. Then, from the stoichiometry, noting that + Cr + Q is constant, we can find the concentration of the third component. 

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.)... 

Using relations (5.14)-(5.16), along with equations (5.3) -(5.8), we can determine the concentrations of various defects in Region II on both sides of the stoichiometric composition. The stoichiometry is rigorously defined by the condition... 

A thorough comparative study of the reactivity of O-, OJ, and Oj toward alkanes and alkenes on MgO has been carried out by Lunsford and co-workers (see Sections V and VI in Ref. 1 and Section VI in this article). In these stoichiometric studies, a known concentration of oxygen species on the surface was reacted with a known amount of hydrocarbon in a recirculation reactor and the products were analyzed. In all cases, a 1 1 stoichiometry was observed. 

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