Equilibrium constant, high pressure chemical

Some chemical reactions are reversible and, no matter how fast a reaction takes place, it cannot proceed beyond the point of chemical equilibrium in the reaction mixture at the specified temperature and pressure. Thus, for any given conditions, the principle of chemical equilibrium expressed as the equilibrium constant, K, determines how far the reaction can proceed if adequate time is allowed for equilibrium to be attained. Alternatively, the principle of chemical kinetics determines at what rate the reaction will proceed towards attaining the maximum. If the equilibrium constant K is very large, for all practical purposes the reaction is irreversible. In the case where a reaction is irreversible, it is unnecessary to calculate the equilibrium constant and check the position of equilibrium when high conversions are needed. 

Figure 7.5 Variation of equilibrium oxygen partial pressure (a) equilibrium between a metal, Ag, and its oxide, Ag20, generates a fixed partial pressure of oxygen irrespective of the amount of each compound present at a constant temperature (b) the partial pressure increases with temperature (c) a series of oxides will give a succession of constant partial pressures at a fixed temperature and (d) the Mn-O system. [Data from T. B. Reed, Free Energy of Formation of Binary Compounds An Atlas of Charts for High-Temperature Chemical Calculations, M.I.T. Press, Cambridge, MA, 1971.]...

In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2lT"], shows that. 

Only those components which are gases contribute to powers of RT. More fundamentally, the equilibrium constant should be defined only after standard states are specified, the factors in the equilibrium constant should be ratios of concentrations or pressures to those of the standard states, the equilibrium constant should be dimensionless, and all references to pressures or concentrations should really be references to fiigacities or activities. For reactions involving moderately concentrated ionic species (>1 mM) or moderately large molecules at high pressures ( 1—10 MPa), the activity and fiigacity corrections become important in those instances, kineticists do use the proper relations. In some other situations, eg, reactions on a surface, measures of chemical activity must be introduced. Such cases may often be treated by straightforward modifications of the basic approach covered herein. 

The influence of concentration (or pressure if the species are gases) on the position of a chemical equilibrium is conveniently described in quantitative terms by means of an equilibrium-constant expression. Such expressions are derived from thermodynamics. They are important because they permit the chemist to predict the direction and completeness of a chemical reaction. An equilibrium-constant expression, however, yields no information concerning the rate at which equilibrium is approached. In fact, we sometimes encounter reactions that have highly favorable equilibrium constants but are of little analytical use because their rates are low. This limitation can often be overcome by the use of a catalyst, which speeds the attainment of equilibrium without changing its position. 

Sieverts Law c = Ks4p, where c is the subsurface concentration (solubility) of the dissolved atom in the solid metal, P is the partial pressure of the diatomic gas (sometimes replaced by the fugacity, j), and Ks is the solubility constant (temperature dependent), which is the chemical equilibrium constant between the molecular species in the gas phase and the atomic species within the metal lattice. This empirical relation was first demonstrated by Sieverts in 1929 for the solubility of hydrogen in iron. Departures from this law occur at high gas pressures and/or high concentrations of dissolved atoms. 

The standard chemical potential for substances other than gases depends on pressure, and so equilibrium constants for reactions in solution depend on pressure. Often a considerable dependence is found. This is highly relevant to the study of electrolyte solutions. 

Figure 10.3-4 Schematic diagram of a high-pressure vapor-liqud equilibrium cell in which both the vapor and liquid are constantly circulated to ensure that the vapor and liquid phases are in equilibrium. The detachable bombs are used to collect samples for chemical analysis. Items P and T are ports for pressure and temperature measurement, respectively.

When an electric discharge is passed through a cold diatomic gas at low pressure it is partially dissociated into atoms in this way reasonable concentrations of O, H, D, N, halogen or other atoms can be produced in a chemically inert diluent. The recombination of these atoms, and their reaction with other molecules can be observed as the gas flows down a long tube. Many of the reactions produce molecules in excited electronic states the resulting chemiluminescence can be used to measure the concentration of atomic species as a function of distance, and hence time, down the tube. Dr Clyne describes this important technique, which has produced direct measurements of the rates of many exothermic reactions of atoms and free radicals at room temperature and below. The reverse of the recombination steps are, of course, the dissociation reactions whose kinetics at high temperatures were described in the first chapter if the ratio of forward and reverse rate constants is equal to the equilibrium constant, the temperature dependence of these rates can be deduced over very wide ranges of temperature. 

In these two examples, the chemical equilibrium constants are both less than unity and reactor conversions are less than 50% at temperatures high enough to achieve reasonable reaction rates. Because both reactions involve shrinkage in the number of moles (4 to 2 for the ammonia reaction and 3 to 1 for the methanol reaction), the reactor conversion can also be increased by increasing the pressure, but practical considerations limit the operating pressure. However, with the recovery and recycle of unconverted reactants, overall process conversions of 100% are approached. 

Typically, the reactor operation at adiabatic conditions gives an outlet temperature of approximately 800°C, which limits the extent of the reaction to that of chemical equilibrium, with an equilibrium constant of 126.8, with compositions in partial pressures in atm. Reactor pressure is generally set by the available pressure of the methane and may be as high as 30 atm. 

This is known as the Lindemann form, and since the units of kj, k2 are [l/(concentration x time)] and those of are [1/time], k -, has units of [1/time], usually [s] . At very high pressures, when [A] is very large, the first form for k j in (1.4) simplifies to (kj,kjk2), i.e. k times the equilibrium concentration of A, and so it is independent of pressure this limiting value of the high pressure rate constant is usually denoted by the symbol k. At the opposite limit of very low pressure, the denominator in the second form of equation (1.4) goes to unity and ku becomes ki[A] which is, of course, directly proportional to the pressure of the reactant A. At these two extremes we say that the reaction is at its first order limit, or at its second order limit respectively notice, however, that at the second order limit the reaction does not obey the textbook second order rate law for a rather subtle reason. Processes (i) and (ii) are not chemical reactions in the normal sense for example, we could equally well write process (i) as... 

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