Equilibria stoichiometry

In chemistry, stoichiometry is conventionally understood to mean the relationship between elements or fundamental particles and components in their mutual conversions. In the field of chemical equilibria, stoichiometry permits investigation of concentration changes as well as an accurate determination of the maximum number of reactions which may take place in a system, and allows the optimum combinations of these reactions to be selected. For this reason, equilibrium considerations proper must be preceded by a detailed stoichiometrical analysis of the system involved. This puprpose may well be achieved by utilization of linear algebra, and a closed system may be described formally as a system of linear algebraic equations. 

In designing adsorption equipment, the factors to consider are equilibrium, stoichiometry capacity, physical state (size, shape, and manner of packing) of the solid adsorbent, and rates controlling the separation. These subjects will be treated here only from the applica-tional viewpoint. 

Gibbs Reactor Multiphase chemical equilibrium (stoichiometry not required)... 

Molecular absorption, particularly in the UV/Vis range, has been used for a variety of different characterization studies, including determining the stoichiometry of metal-ligand complexes and determining equilibrium constants. Both of these examples are examined in this section. 

In this experiment the method of continuous variations is used to determine the stoichiometry and equilibrium constant for the organic complex of 3-aminopyridine with picric acid in CHCI3, and the inorganic complex of Fe +with salicylic acid. 

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 ... 

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

Compared with XPS and AES sputter depth profiling After achieving sputter equilibrium, and until a layer with different sputtering behavior is reached [3.59], the SN flux represents stoichiometry and not altered layer concentrations evolving because of preferential sputtering effects. 

The efficiencies which may be obtained can consequently be calculated by simple stoichiometry from the equilibrium data. In the ease of countercurrent-packed columns, the solute can theoretically be completely extracted, but equilibrium is not always reached because of the poorer contact between the phases. The rate of solute transfer between phases governs the operation, and the analytical treatment of the performance of such equipment follows closely the methods employed for gas absorption. In the ease of two immiscible liquids, the equilibrium concentrations of a third component in each of the two phases are ordinarily related as follows ... 

PH3. Tetraphosphane(6), P4H6, exists as an equilibrium mixture of the two structural isomers H2PPHPHPH2 in) and P(PH2)3(i), and itself reacts with P3H5 at —20° according to the idealized stoichiometry P4H6 4- P3H5 ---> 2PH3 4-... 

Finally, the total preexponential factor includes the stoichimetry deviation represented by c°(, or c° so an extrapolated Arrhenius plot will show an intercept which is very sensitive to composition. Experimental data will be hard to reproduce both because of stoichiometry variations and because of the slow approach to thermal equilibrium. 

When the oxidation product is an /i-type oxide like ZnO, the conditions are reversed (Fig. 1.78). If a monovalent ion like Li enters the oxide layer in place of Zn one free electron (eo) is destroyed. But the product n(Zn 0)n(eo) is fixed by the reaction governing the non-stoichiometry of ZnO. Hence n(Zn O), the concentration of interstitial Zn ions, increases, and the oxidation rate, which depends upon the concentration of these ions in the oxide in equilibrium with metallic Zn, increases. 

To work this problem, you have to combine principles of stoichiometry and equilibrium. 

The discussion of acid-base titrations in Chapter 4 focused on stoichiometry. Here, the emphasis is on the equilibrium principles that apply to the acid-base reactions involved. It is convenient to distinguish between titrations involving—... 

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. 

Vapor pressures and vapor compositions in equilibrium with a hypostoichiometric plutonium dioxide condensed phase have been calculated for the temperature range 1500 I H 4000 K. Thermodynamic functions for the condensed phase and for each of the gaseous species were combined with an oxygen-potential model, which we extended from the solid into the liquid region to obtain the partial pressures of O2, 0, Pu, PuO and Pu02 as functions of temperature and of condensed phase composition. The calculated oxygen pressures increase rapidly as stoichiometry is approached. At least part of this increase is a consequence of the exclusion of Pu +... 

From the foregoing discussion it will be clear that the stoichiometry of the oxidation [n in Eq. (1)] has no thermodynamic significance. It should not be used in the Nemst equation to describe the potential dependence of the equilibrium shown in Eq. (1). It is therefore better to describe n as the degree of oxidation of the polymer (i.e., the average number of holes per monomer unit), n is a potential-dependent parameter,... 

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 stoichiometry of the reaction implies that, if the partial pressure of 02 decreases by x, then the partial pressure of N2 decreases by 2x and that of N2G increases by 2x. Because there is no N20 present initially, the equilibrium table, with all partial pressures in bar, is... 

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. 

Intercalation from solutions in nonaqueous solvents (S21). This method may suffer from the drawback that final stoichiometries may not correspond to equilibrium conditions, because of partial leaching out of metal halide. For this reason, some chlorides can be intercalated only from solvents in which they have limited solubility iLS). It has often been the practice to wash intercalates with solvents to remove the excess of intercalant this may lead to stoichiometries lower than the original ones. The two-ampoule method may, therefore, be preferable (H24). 

These chemically reactive phases are prepared by slow cooling of melts with the appropriate composition under an inert atmosphere or vacuum. Equilibrium is slow to be attained at the low temperatures necessary to prevent dissociation at 6.9°C Na2K dissociates into a (solid solution of K in Na) and liquid (60/40 Na/K). The KjCs and K7CSJ phases are even less stable and result from cooling mixtures of the elements of the desired stoichiometry to — 100°C in a metal beaker under argon. ... 

It is possible to carry out this type of kinetic analysis whether a mechanism is simple or elaborate. That is, we can always derive the equilibrium expression for a reaction by applying reversibility and setting forward and reverse rates equal to one another at equilibrium. It is unnecessary to go through this procedure for every chemical equilibrium. As our two examples suggest, inspection of the overall stoichiometry always gives the correct expression for the equilibrium constant. That is, a reaction of the form tjA + iBf ofD + eE has an... 

---