Chemical reaction equilibrium state

Isotope Effects on Equilibrium Constants of Chemical Reactions Transition State Theory of Isotope Effects... 

Solubility equihbrium is the final state to be reached by a chemical and the subsurface aqueous phase under specific environmental conditions. Equihbrium provides a valuable reference point for characterizing chemical reactions. Equilibrium constants can be expressed on a concentration basis (/ ), on an activity basis (K ), or as mixed constants (K" ) in which all parameters are given in terms of concentration, except for H, OH", and e" (electron) which are given as activities. 

For a PVT system of uniform T and P containing N species and 71 phases at thermodynamic equilibrium, the intensive state of the system is hilly determined by the values of T, P, and the (N — 1) independent mole fractions for each of the equilibrium phases. The total number of these variables is then 2 + tt(N — 1). The independent equations defining or constraining the equilibrium state are of three types equations 218 or 219 of phase-equilibrium, N(77 — 1) in number equation 245 of chemical reaction equilibrium, r in number and equations of special constraint, s in number. The total number of these equations is Ar(7r — 1) + r + s. The number of equations of reaction equilibrium r is the number of independent chemical reactions, and may be determined by a systematic procedure (6). Special constraints arise when conditions are imposed, such as forming the system from particular species, which allow one or more additional equations to be written connecting the phase-rule variables (6). 

The situation becomes much less problematic if the reaction in Eq. 3.1 is considered only at equilibrium. Equilibrium states are steady states in which the net reaction fluxes to produce products or reactants, regardless of the reaction pathway, are equal and opposite. From the perspective of chemical thermodynamics, equilibrium states are unique and independent of thermodynamic path. Thus these states can be described by a unique set of chemical species irrespective of the intermediate steps of their formation. Dissolution- precipitation reactions and the chemical species that affect them at equilibrium can be described by an extension of the methodology discussed in Section 2.4 (cf. Fig. 

This criterion of equilibrium provides a general method for determination of equilibrium states. One writes an expression for G as a function of the numbers of moles (mole numbers) of the species in the several phases, and then finds the set of values for the mole numbers that minimizes G subject to the constraints of mass conservation. This procedure can be applied to problems of phase, chemical-reaction, or combined phase and chemical-reaction equilibrium it is most useful for complex equilibrium problems, and is illustrated for chemical-reaction equilibrium in Sec. 15.9. 

Thus the quantity Vtfi, represents, in general, the rate of change of the total Gibbs energy of the system with the reaction coordinate at constant T and P. Figure 15.1 shows that this quantity is zero at the equilibrium state. Therefore a criterion of chemical-reaction equilibrium is... 

Use has here been made in steps 2 through 4 of the fact that there is no change in the Gibbs energy for processes carried out under conditions of membrane and chemical-reaction equilibrium. This explains why the value of AG° is related directly to the ratios of the equilibrium-state and standard-state fugacities (ft = 1). 

When liquid and gas phases are both present in an equilibrium mixture of reacting species, Eq. (11.30), a criterion of vapor/liquid equilibrium, must be satisfied along with the equation of chemical-reaction equilibrium. There is considerable choice in the method of treatment of such cases. For example, consider a reaction of gas A and water B to form an aqueous solution C. The reaction may be assumed to occur entirely in the gas phase with simultaneous transfer of material between phases to maintain phase equilibrium. In this case, the equilibrium constant is evaluated from AG° data based on standard states for the species as gases, i.e., the ideal-gas states at 1 bar and the reaction temperature. On the other hand, the reaction may be assumed to occur in the liquid phase, in which case AG° is based on standard states for the species as liquids. Alternatively, the reaction may be written... 

If chemical reactions occur, then we must introduce a new variable, the i coordinate e for each independent reaction, in order to formulate the mate balance equations. Furthermore, we are able to write a new equilibrium rela [Eq. (15.8)] for each independent reaction. Therefore, when chemical-rea equilibrium is superimposed on phase equilibrium, r new variables appear r new equations can be written. The difference between the number of va and number of equations therefore is unchanged, and Duhem s theorem originally stated holds for reacting systems as well as for nonreacting syste Most chemical-reaction equilibrium problems are so posed that it is 1 theorem that makes them determinate. The usual problem is to find the corn-tion of a system that reaches equilibrium from an initial state of fixed an of reacting species when the two variables T and P are specified. 

Most chemical-reaction equilibrium problems are so posed that it is Duhem s theorem that makes them determinate. The usual problem is to find the composition of a system that reaches equilibrium from an initial state of fixed amounts of of reacting species when the fu o variables T and P are specified. 

Chapters 2-5 deal with chemical engineering problems that are expressed as algebraic equations - usually sets of nonlinear equations, perhaps thousands of them to be solved together. In Chapter 2 you can study equations of state that are more complicated than the perfect gas law. This is especially important because the equation of state provides the thermodynamic basis for not only volume, but also fugacity (phase equilibrium) and enthalpy (departure from ideal gas enthalpy). Chapter 3 covers vapor-liquid equilibrium, and Chapter 4 covers chemical reaction equilibrium. All these topics are combined in simple process simulation in Chapter 5. This means that you must solve many equations together. These four chapters make extensive use of programming languages in Excel and MATE AB. 

To solve equations of state, you must solve algebraic equations as described in this chapter. Later chapters cover other topics governed by algebraic equations, such as phase equilibrium, chemical reaction equilibrium, and processes with recycle streams. This chapter introduces the ideal gas equation of state, then describes how computer programs such as Excel , MATLAB , and Aspen Plus use modified equations of state to easily and accurately solve problems involving gaseous mixtures. 

Certain equilibrium states of thermodynamic systems are stable to small fluctuations others are not. For example, the equilibrium state of a simple gas is stable to all fluctuations, as are most of the equilibrium states we will be concerned with. It is possible, however, to carefully prepare a subcooled liquid, that is, a liquid below its normal solidiflcation temperature, that satisfies the equilibrium criteria. This is an tin-.stable equilibrium. state because the slightest disturbance, such as tapping on the. side of the containing ve.s.sel, will cause the liquid to freeze. One sometimes encounters mixtures that, by the chemical reaction equilibrium criterion (see Chapter 13). should react however, the chemical reaction rate is so small as to be immeasurable at the temperature of interest. Such a mixture can achieve a state of thermal equilibrium that is stable with respect to small fluctuations of temperature and pressure. If, however, there is a sufficiently large, but temporary, increase in temperature. so that die rate of the chemical reaction is appreciable for some period of time) and then the system... 

Any mixture apart from the chemical reaction equilibrium reacts along these lines to the corresponding equilibrium state (Frey and Stichlmair, 1999a). Thus, a family of stoichiometric lines results from the variation of initial components concentration, which intercept at the pole tt (figure 2.2), whose concentration is defined as x. ... 

As indicated by the pK value, only the first dissociation stage is of concern when it comes to HT-PEM fuel cell application. Besides the dissociation equilibria, the chemical reaction equilibrium of the polycondensation reaction of orthophosphoric acid to polyphosphoric acid is of vital importance. By changing the concentration of the solution, the chemical equilibrium composition shifts as well. The polycondensation reaction, shown by Fig. 18.2, is a dehydration reaction, hence the equilibrium state shifts towards a composition containing more polymeric species when water is removed and the solution gets more concentrated. 

Intertwined with these two topics is equilibrium. If a chemical reaction is conducted in which reactants are converted to fMxxlucts, the products will be formed at a rate governed (in part) by the concentration of the reactants and conditions such as temperature and pressure. Eventually, as the reactants form products and the products react to form reactants, the net rate of reaction must equal zero. At this point, equilibrium will have been achieved, How does this relate to chemical reactor analysis The chemical industry is usually concerned with the attainment of a product or jwo-ducts. [It should also be noted that the environmental industry centers on the destruction (or removal) of a reactant, often referred to as a waste—see Chapter 16.J Chemical reaction equilibrium principles allow the engineer/scientist to determine the end-products of a chemical reaction for a given set of operation conditions and initial reac-tant(s) if the final state is at equilibrium. However, from the standpoint of obtaining sufficient product(s) of economic value, a final state of equilibrium is almost always undesirable. 

Similarly, chemical reaction equilibrium represents a dynamic process on the molecular scale. Macroscopically, a reaction can proceed in the forward direction from reactants to products or in the reverse direction from products to reactants. A given reaction is said to be at chemical reaction equilibrium when there is no net reaction in either direction. However, again there is a dynamic process on a molecular scale. Reactant molecules will react to form products at the same rate that the product molecules form reactants. If we followed an individual molecule, it might indeed react. However, for each molecule that reacts in the forward direction, another molecule will be reacting in the reverse direction. On the other hand, if an excess of reactants is present, there will be a net macroscopic reaction in ihe forward direction, since more individual molecules will react in this direction than in the reverse direction. Reaction will occur until equilibrium is reached and there is no more tendency to react on a macroscopic scale. Conversely, if an excess of products is present, macroscopic reaction will occur in the reverse direction until the same equilibrium state is reached. 

Consider how the change of a system from a thennodynamic state a to a thennodynamic state (3 could decrease the temperature. (The change in state a —> f3 could be a chemical reaction, a phase transition, or just a change of volume, pressure, magnetic field, etc). Initially assume that a and (3 are always in complete internal equilibrium, i.e. neither has been cooled so rapidly that any disorder is frozen in. Then the Nemst heat... 

For non-zero and the problem of defining the thennodynamic state fiinctions under non-equilibrium conditions arises (see chapter A3,2). The definition of rate of change implied by equation (A3,4,1) and equation (A3.4.2) includes changes that are not due to chemical reactions. 

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. 

General first-order kinetics also play an important role for the so-called local eigenvalue analysis of more complicated reaction mechanisms, which are usually described by nonlinear systems of differential equations. Linearization leads to effective general first-order kinetics whose analysis reveals infomiation on the time scales of chemical reactions, species in steady states (quasi-stationarity), or partial equilibria (quasi-equilibrium) [M, and ]. 

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