Irreversible reaction, defined

Usually when reaction paths are simulated, the irreversible reactant is an unstable mineral or a suite of unstable minerals that is, the stoichiometry of the irreversible reaction is fixed. Evaporation poses a special problem in reaction path simulation because the stoichiometry of the irreversible reaction (defined by the aqueous solution composition) continually changes as other minerals precipitate (or dissolve). In the second problem (above) evaporation of seawater was simulated by irreversible addition of "sea salt", that is, a hypothetical solid containing calcium, magnesium, sodium, potassium, chloride, sulfate and carbon in stoichiometric proportion to seawater. The approach used was valid as long as intermediate details of the reaction path are not required. The reaction path during evaporation could be solved in PHRQPITZ by changing the stoichiometry of the irreversible reactant (altered "sea salt") incrementally between phase boundaries, but this method would be extremely laborious. 

For an irreversible reaction Pj - 0 at the center of the pellet when the size of the pellet becomes very large. Thus p — YT p at the center of large pellets. Clearly, from (11.45), the pressure rises towards this value on moving into the pellet when n > 1 and falls to it when n < 1. Thus we can define the following bounds for the pressure... 

In the case of an irreversible reaction, therefore, two parameters are now defined with respect to the number of electrons transferred in the reaction n now refers to the electrons transferred overall, while na indicates the number of electrons participating in the rds. Thus, for example, we can rewrite equations (2,144) and (2.146) as ... 

The effectiveness factor rj, defined in equation 8.5-5, is a measure of the effectiveness of the interior surface of the particle, since it compares the observed rate through the particle as a whole with the intrinsic rate at the exterior surface conditions the latter would occur if there were no diffusional resistance, so that all parts of the interior surface were equally effective (at cA = cAs). To obtain T], since all A entering the particle reacts (irreversible reaction), the observed rate is given by the rate of diffusion across the permeable face at z = 0 ... 

The concentration and temperature Tg will, for example, be conditions of reactant concentration and temperature in the bulk gas at some point within a catalytic reactor. Because both c g and Tg will vary with position in a reactor in which there is significant conversion, eqns. (1) and (15) have to be coupled with equations describing the reactor environment (see Sect. 6) for the purpose of commerical reactor design. Because of the nonlinearity of the equations, the problem can only be solved in this form by numerical techniques [5, 6]. However, an approximation may be made which gives an asymptotically exact solution [7] or, alternatively, the exponential function of temperature may be expanded to give equations which can be solved analytically [8, 9]. A convenient solution to the problem may be presented in the form of families of curves for the effectiveness factor as a function of the Thiele modulus. Figure 3 shows these curves for the case of a first-order irreversible reaction occurring in spherical catalyst particles. Two additional independent dimensionless paramters are introduced into the problem and these are defined as... 

The above discussion is based on the reversible reactions that produce the most thermodynamically stable products. In contrast, irreversible reactions produce kinetically-controlled products. In such cases, the self-correction mechanism is not operative. Well-defined building blocks with appropriate geometrical features are even more important for the synthesis of kinetically-controlled macrocycles. It is possible to obtain larger cycles because different sizes of linear species form in the reaction, which will cyclize to give a mixture ofdifferent sizes of cycles. Smaller cycles will still be favored over larger cycles in such kinetically-controlled reactions owing to kinetic factors. 

Calculating x this way is somewhat advantageous since the rate of charging of the double layer is minimal (not zero) at (dE/dt)min. Derivative chronopoten-tiometry has not been widely used, probably because the improvement over the ordinary E versus t response is insufficient to justify the more complex instrumentation required. A more serious criticism is that the minimum dE/dt occurs at a time that is dependent on the kinetics of the heterogeneous reaction. For fast (reversible) reactions, = 4i/9, and for very slow (irreversible) reactions, tmin = t/4. Unfortunately, a great many reactions fall somewhere in between, and the relation of to i is not likely to be clearly defined. 

Let us consider that the rate of reaction r is that of a simple first-order irreversible reaction, namely r = ko- ttt Ca- We define dimensionless temperature and concentration by introducing y = T/Tf for the dimensionless temperature and xa = Ca/Cas for the dimensionless concentration. With these settings, equation (5.18) becomes... 

As the Hatta number increases, the effective liquid-phase mass-transfer coefficient increases. Figure 14-13, which was first developed by Van Krevelen and Hoftyzer [Rec. Trav. Chim., 67, 563 (1948)] and later refined by Perry and Pigford and by Brian et al. [AlChE J., 7,226 (1961)], shows how the enhancement (defined as the ratio of the effective liquid-phase mass-transfer coefficient to its physical equivalent q = ki/kl) increases with NHa for a second-order, irreversible reaction of the kind defined by Eqs. (14-60) and (14-61). The various curves in Fig. 14-13 were developed based upon penetration theory and... 

In words when a system undergoes a change, the increase in entropy of the system is equal to or greater than the heat absorbed in the process divided by the temperature. On the other hand, the equality, which provides a definition of entropy increment, applies to any reversible process, whereas the inequality refers to a spontaneous (or irreversible) process, defined as one which proceeds without intervention from the outside. Example 1 illustrates the reversible and irreversible reactions. 

Most textbooks in chemical thermodynamics place the main focus on the equilibrium of chemical reactions. In this textbook, however, the affinity of irreversible processes, defined by the second law of thermodynamics, has been treated as the main subject. The concept of affinity is applicable in general not only to the processes of chemical reactions but also to all kinds of irreversible processes. 

Equation 56 can be used only for spherical catalyst pellets and first order, irreversible reactions. However, for convenience, and in analogy to the Thiele modulus, a generalized modulus ij/pn can be defined as well which applies to arbitrary pellet shape and arbitrary reaction order. This is defined as... 

The conservation equations for mass and enthalpy for this special situation have already been given with eqs 76 and 62. As there is no diffusional mass transport inside the pellet, the overall catalyst effectiveness factor is identical to the film effectiveness factor i/cxl which is defined as the ratio of the effective reaction rate under surface conditions divided by the intrinsic chemical rate under bulk fluid phase conditions (see eq 61). For an nth order, irreversible reaction we have the following expression ... 

Irreversible reactions of carbohydrates include the formation of glycosides and 1-deoxy-l-thioglycosides from acylglycosyl halides and thio-acetals, " respectively, esterifications by acyl and sulfonyl halides or anhydrides in pyridine, displacements of sulfonyloxy groups by various reagents, and most examples of formation and scission of anhydro rings, It is more difficult to define the influence of stereo effects on the course of these reactions and some of the results obtained await explanation. 

Current/Voltage Relationships for Irreversible Reactions Many voltammetric electrode processes, particularly those associated with organic systems, are partially or totally irreversible, which leads to drawn-out and less well defined waves. The quantitative description of such waves requires an additional term (involving the activation energy of the reaction) in Equation 23-11 to account for the kinetics of the electrode process. Although half-wave potentials for irreversible reactions ordinarily show some dependence on concentration, diffusion currents are usually still linearly related to concentration many irreversible processes can, therefore, be adapted to quantitative analysis. 

A measure of the absence of internal (pore diffusion) mass transfer limitations is provided by the internal effectiveness factor, t, which is defined as the ratio of the actual overall rate of reaction to the rate that would be observed if the entire interior surface were exposed to the reactant concentration and temperature existing at the exterior of the catalyst pellet. A value of 1 for rj implies that all of the sites are being utilized to their potential, while a value below, say, 0.5, signals that mass transfer is limiting performance. The value of rj can be related to that of the Thiele modulus, 4>, which is an important dimensionless parameter that roughly expresses a ratio of surface reaction rate to diffusion rate. For the specific case of an nth order irreversible reaction occurring in a porous sphere,... 

In Eq. 10.30, the first term corresponds to accumulation in the fluid and the surfaces, the second term describes convective transport, and the third term indicates the loss by the kinetic dissolution reaction defined by Eq. 10.28. Equation 10.30 applies to any chemical transport process that includes fast and reversible ion-exchange, and slow and irreversible dissolution of the mth-order kinetics. In reservoir sands, both fine silica and clay minerals dissolve under attack by the alkali, yielding a complex distribution of soluble solution products... 

Consider a molecule diffusing in free space or a solute molecule diffusing in solution. Upon colliding with a surface, assume that the molecule is sufficiently entrained by surface forces that there results a reduction in dimensionality of its diffusion space from d = 3 to d — 2, and that in its subsequent motion the molecule is sterically constrained to follow the pathways defined by the lattice structure of the surface (or, perhaps, the boundary lines separating adjacent domains). If at some point in its trajectory the molecule becomes permanently immobilized, either because of physical binding at a site or because an irreversible reaction has occurred at that site, then, qualitatively, this sequence of events is descriptive of many diffusion-reaction processes in biology, chemistry and physics. 

In step one, the free RNA polymerase (R) interacts reversibly with the promoter (P) as defined by the equilibrium constant XB. In the second step, DNA-bound RNA polymerase (RPc) translocates to the -10 region, which initiates an isomerization reaction (defined by the rate constant kf) that results in the irreversible formation of the open complex (RPO). As will be discussed in Chapters 28 and 29, a prevailing model to explain the mechanism of the transcriptional regulation is that regulatory factors alter either XB or ki and thereby influence RNA synthesis-initiation rates. 

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