Equilibrium conditions for reaction

We then note that the equilibrium condition for reaction (3.7) now taking place not only at the tpb (three phase boundaries), but over the entire gas exposed Pt electrode surface is very similar to Eq. (3.28), i.e. 

This criterion is very popular in chemistry to examine the equilibrium condition for reactions and it can easily be derived... 

The equilibrium constant describes only equilibrium conditions. For reactions not at equilibrium, a similar equation gives information about the reaction ... 

Equilibrium conditions for reactions between the catalyst and hydrogen, water vapor, hydrogen sulfide, and sulfur trioxide were determined. In these calculations interactions between the molybdena and the alumina support were not considered. 

Equilibrium conditions for reactions 7-2 and 7-3 (sulfite/bisulfite distribution) and for reactions 7-14 and 7-15 (carbonate/bicarbonate distribution) are defined by die curves of Figure 7-7 (Head, 1977). Equations for calculating equilibrium constants for reactions 7-1 through 7-5 and 7-8 as a function of temperature, at zero imi stmgth, have been compiled by Pasiuk-Bronikowska and Rudzinski (1991). 

The concentrations are contained in separate terms, and the equation (17) for the whole reaction can be divided into a number of separate equations expressing the equilibrium conditions for various possible partial reactions. 

While these calculations provide information about the ultimate equilibrium conditions, redox reactions are often slow on human time scales, and sometimes even on geological time scales. Furthermore, the reactions in natural systems are complex and may be catalyzed or inhibited by the solids or trace constituents present. There is a dearth of information on the kinetics of redox reactions in such systems, but it is clear that many chemical species commonly found in environmental samples would not be present if equilibrium were attained. Furthermore, the conditions at equilibrium depend on the concentration of other species in the system, many of which are difficult or impossible to determine analytically. Morgan and Stone (1985) reviewed the kinetics of many environmentally important reactions and pointed out that determination of whether an equilibrium model is appropriate in a given situation depends on the relative time constants of the chemical reactions of interest and the physical processes governing the movement of material through the system. This point is discussed in some detail in Section 15.3.8. In the absence of detailed information with which to evaluate these time constants, chemical analysis for metals in each of their oxidation states, rather than equilibrium calculations, must be conducted to evaluate the current state of a system and the biological or geochemical importance of the metals it contains. 

The reaction of Pt(C03)(dppp)] with a modest excess of vicinal diols in CH2C12 solution affords the corresponding [Pt(a,/3-diolato)(dppp)] species under equilibrium conditions, a reaction that is readily reversed by the addition of dry ice to the product. The reaction with triols such as glycerol and alditol carbohydrates also affords the corresponding diolato species, with the reaction exhibiting excellent equilibrium regioselectivities for a number of isomers, of which the 7, 6-threo diols are the most favored. 

From changes in free energy in standard reference conditions it is possible to calculate equilibrium constants for reactions involving several reactants and products. Consider, for example, the chemical reaction aA + bB = cC + dD at equilibrium in solution. For this reaction we can define a stoichiometric equilibrium constant in terms of the concentrations of the reactants and products as... 

However, if reaction 3 is rate limiting we can deduce something useful and we will illustrate the quasi-equilibrium method by using it to derive the kinetic equation under these conditions. This method assumes that all reactions prior to the rate limiting step are in equilibrium. Thus, for reaction 1 ... 

Allowing an open system to close and come to equilibrium implies an extent of reaction - a measure of how close the system has come towards the equilibrium condition. For a single species the extent of the reaction towards an equilibrium concentration is given by ... 

The reaction between cellulose and acrylamide was studied by quantitative, chromatographic separation of the substituted D-glucoses obtained on acid hydrolysis of the reaction product,320 followed by an analysis by Spurlin s method.249 Although, apparently, no check was made on the stability of the ethers to the conditions of hydrolysis, it might be expected that the ethers would isomerize only under basic conditions. The ratios of the relative equilibrium-constants for reaction at 0-2, 0-3, and 0-6 were 9 1 19, and these are attributable to the high, relative stability of the primary ether, together with the low reactivity of 0-3, also observed in rate-controlled reactions. 

For a metal, the negative of the work function gives the position of the Fermi level with respect to the vacuum outside the metal. Similarly, the negative of the work function of an electrochemical reaction is referred to as the Fermi level Ep (redox) of this reaction, measured with respect to the vacuum in this context Fermi level is used as a synonym for electrochemical potential. If the same reference point is used for the metal s,nd the redox couple, the equilibrium condition for the redox reaction is simply Ep (metal)= Ep(redox). So the notion of a Fermi level for a redox couple is a convenient concept however, this terminology does not imply that there are free electrons in the solution which obey Fermi-Dirac statistics, a misconception sometimes found in the literature. 

In the study of the reaction of 2,4,6-trinitrotoluene with base (NaOMe, under first-order conditions), kinetic and equilibrium data for reaction in methanol-DMSO have been obtained. Since it has been found that plots of logarithms of rate and equilibrium constants versus the mole fraction of DMSO are linear, the value in pure methanol have been extrapolated (Kp = 12.4 lmol-1)213. 

The equilibrium condition for the distribution of one solute between two liquid phases is conveniently considered in terms of the distribution law. Thus, at equilibrium, the ratio of the concentrations of the solute in the two phases is given by CE/CR = K, where K1 is the distribution constant. This relation will apply accurately only if both solvents are immiscible, and if there is no association or dissociation of the solute. If the solute forms molecules of different molecular weights, then the distribution law holds for each molecular species. Where the concentrations are small, the distribution law usually holds provided no chemical reaction occurs. 

Equilibrium conditions for the chain length distribution are set up in these reactions, the mean chain length n of the anion being greater the higher the temperature used in the preparation and the lower the water... 

From the data in Appendix C, calculate (a) the enthalpy of reaction and (b) the equilibrium constant for reaction 12.1 (the Deacon process) at standard conditions, (c) Above what temperature does the reaction cease to be thermodynamically favored (i.e., AG° becomes positive), if ACp can be ignored ... 

The Phillips Steam Active Reforming (STAR) process catalytically converts isobutane to isobutylene. The reaction is carried out with steam in tubes that are packed with catalyst and located in a furnace. The catalyst is a solid, particulate noble metal. The presence of steam diluent reduces the partial pressure of the hydrocarbons and hydrogen present, thus shifting the equilibrium conditions for this system toward greater conversions. 

The number of independent components, c, in a given system of interest can generally be evaluated as the total number of chemical species minus the number of relationships between concentrations. The latter may consist of initial conditions (defined by conditions of preparation of the system) or by chemical equilibrium conditions (for chemical reactions that are active in the actual system). Sidebar 7.1 provides illustrative examples of how c is determined in representative cases. 

Similarly, the equilibrium condition for the cell reaction (dGcen = 0) must be modified from the earlier cell-free form (electrical work term ... 

Consider the reaction C2H4(e)+ HzO(w) - C2HsOH(a) at 200 °C and 34.5 bar. At these conditions the liquid phase is mixture of alcohol and water in which almost no ethene is dissolved and the vapour phase is a mixture of the three reactants. The equilibrium composition can be calculated from the equilibrium condition for the reaction in the gas phase together with the vapour liquid equilibrium conditions ... 

Equation (2.57) can be compared with Eqn. (2.50). Noting that the standard value of the vacancy chemical potential of a crystal is only slightly dependent on T, Nv is in essence exponentially dependent on 0/T). This Arrhenius-type of temperature dependence is also found for the interstitials, since in view of the site-preserving formation reaction Aa+V) = Af +VA, the equilibrium condition for this defect formation reaction shows that... 

Defect clustering is the result of defect interactions. Pair formation is the most common mode of clustering. Let us distinguish the following situations a) two point defects of the same sort form a defect pair (B + B = B2 = [B, B] V+V = V2 = [V, V]) and b) two different point defects form a defect pair (electronic defects can be included here). The main question concerns the (relative) concentration of pairs as a function of the independent thermodynamic variables (P, T, pk). Under isothermal, isobaric conditions and given a dilute solution of B impurities, the equilibrium condition for the pair formation reaction B + B = B2 is 2-pB = The mass balance reads NB + 2-NBi = NB, where NB denotes the overall B content in the matrix crystal. It follows, considering Eqns. (2.39) and (2.40), that... 

---