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Irreversible process calculation

The entropy, Spontaneous vs non-spontaneous, Reversible and irreversible processes, Calculation of entropy changes (Isothermal, isobaric, isochoric, adiabatic), Phase changes at equilibrium, Trouton s rule, Calculation for irreversible processes... [Pg.297]

At the instant a pressure vessel ruptures, pressure at the contact surface is given by Eq. (6.3.22). The further development of pressure at the contact surface can only be evaluated numerically. However, the actual p-V process can be adequately approximated by the dashed curve in Figure 6.12. In this process, the constant-pressure segment represents irreversible expansion against an equilibrium counterpressure P3 until the gas reaches a volume V3. This is followed by an isentropic expansion to the end-state pressure Pq. For this process, the point (p, V3) is not on the isentrope which emanates from point (p, V,), since the first phase of the expansion process is irreversible. Adamczyk calculates point (p, V3) from the conservation of energy law and finds... [Pg.191]

Equation (2.66) indicates that the entropy for a multipart system is the sum of the entropies of its constituent parts, a result that is almost intuitively obvious. While it has been derived from a calculation involving only reversible processes, entropy is a state function, so that the property of additivity must be completely general, and it must apply to irreversible processes as well. [Pg.77]

Denaturing albumen is an irreversible process, yet the derivations below assume thermodynamic reversibility. In fact, complete reversibility is rarely essential try to avoid making calculations if a significant extent of irreversibility is apparent. [Pg.167]

Diagnostic Criteria to Identify an Irreversible Process. In order to characterize an irreversible process it would be necessary to be able to calculate either the thermodynamic parameter E° or the kinetic parameters a. and k°. Unfortunately, we will see below that k° can only be calculated if E0/ is known, and E0 cannot be calculated by voltammetric techniques. Thus, either one knows Eel (for example, by using potentiometric techniques in solutions containing both Ox and Red), or one is limited to give simply the peak potential of the electrode process at a certain rate (usually at 0.1 V s-1 or at 0.2 V s-1). [Pg.60]

The definition of entropy requires that information about a reversible path be available to calculate an entropy change. To obtain the change of entropy in an irreversible process, it is necessary to discover a reversible path between the same initial and final states. As S is a state function, AS is the same for the irreversible as for the reversible process. [Pg.133]

Values of ke = 2.5 x 1010, 1.4 x 1010, and 1.2 x 1010 M-1s-1 are calculated using eqs. 7-9, respectively, and data from Table 1. These values are similar to the calculated rate of diffusion in benzene solution (2 x 1C)10 M ls-1), thus indicating that excimer formation (eq. 5) is essentially an irreversible process. [Pg.173]

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. [Pg.26]

The hepatic disposition parameters of a drag, representing reversible and irreversible processes, are calculated using the following equations ... [Pg.385]

Fig. 3.4 Comparison of the voltammograms corresponding to a reversible process (calculated from Eq. (2.36)) and to a totally irreversible one (calculated from Eq. (3.26)) with (4/4) = 0, a = 0.5, and... Fig. 3.4 Comparison of the voltammograms corresponding to a reversible process (calculated from Eq. (2.36)) and to a totally irreversible one (calculated from Eq. (3.26)) with (4/4) = 0, a = 0.5, and...
The criterion discussed above is based on the dependence of the surface concentration of the oxidized species with the reversibility degree of the electrode process. So, for a totally irreversible process, the rate of depletion of the surface concentration Cq is much smaller than the mass transport rate process, and therefore, at the formal potential its value should be coincident with the bulk concentration (co(2,°)/coi — l)- In contrast- for reversible electrode reactions, cb(x°)/co = 0.5 (see Eq. (2.20) of Sect. 2.2 for = 0 and y = 1). In order to verify this behavior, the variation of the surface concentration of species O at the formal potential calculated as a function of has been plotted in Fig. 3.5b. From this figure, it can be deduced that at the irreversible limit (i.e., = 0.17),... [Pg.148]

The effect of the reversibility of electrochemical reaction on the theoretical Qp —t curves calculated from Eq. (6.131) is shown in Fig. 6.22. For reversible processes (k°t > 10), the charge-time curves present a stepped sigmoid feature and are located around the formal potential of the electro-active couple. Under these conditions, the charge becomes time independent (see Eq. (6.132)). As the process becomes less reversible, both the shape and location of the Qp — t curves change in such a way that the successive plateaus tend to disappear and a practically continuous quasi-sigmoid, located at more negative potentials as k°r decreases, is obtained. For k°r < 0.1, general Eq. (6.131) simplifies to Eq. (6.134), valid for irreversible processes and leads to a practically continuous Qp — t curve. [Pg.427]

Since entropy is a state function, we can use a reversible process with the same initial and final states to calculate the entropy change that occurs in an irreversible process. [Pg.126]

Calculation of the entropy produced in systems undergoing different flow processes (called irreversible processes) is key for considering steady-state systems. In order to measure the entropy produced in the system, we think of it as transported to the surroundings in a reversible manner and measure the entropy changes in the surroundings. From Eqs. (5) and (7),... [Pg.359]

The properties of nanocomposite systems, whose microstructures aim at reproducing real systems, have been examined in various numerical modelling studies [127, 128], In general, the essential features of the hysteresis cycles may be satisfactory reproduced. In particular, soft layer reversal is quantitatively accounted for, which is expected for reversible phenomena. By contrast, the calculated high-field irreversible reversal of the hard phase magnetization is not reproduced in general. Such discrepancy illustrates the already mentioned difficulty to describe irreversible processes. [Pg.351]

The work of an irreversible process is calculated by a two-step procedure. First, W is determined for a mechanically reversible process that accomplishes the same change of state. Second, this result is multiplied or divided by an efficiency to give the actual work. If the process produces work, the reversible value is too large and must be multiplied by an efficiency. If the process requires work, the reversible value is too smalt and must be divided by an efficiency. [Pg.42]

If the same changes of state are carried out by irreversible processes, the property changes for the steps are identical with those already calculated. However, the values of Q and W are different. [Pg.403]

RCH2X/RCH2X- self-exchange (60-80 kcal mol-1) and an E° pertaining to (100), and not (101). Thus, calculated E° values of methyl halides (Hush, 1957) are around —0.75 V, far above experimental Ein around or below —1.8 V. This behavior would of course be expected for an electrochemically irreversible process, as alkyl halide reduction indeed is found to be experimentally (Mann and Barnes, 1970), and hence the above assumptions are self-consistent. In the following discussion, we shall use E° values for reaction (100) for alkyl and aralkyl halides, with suitable corrections for the formation of resonance-stabilized radicals like benzyl and 4-nitrobenzyl. [Pg.171]

With an E° value of —0.75 V, entry no. 19 of Table 17, reaction between alkyl halides and alkyllithium compounds, represents a strongly exergonic electron-transfer reaction which is expected to proceed at a diffusion-controlled tate. Experimental rate constants are not available, but such reactions are qualitatively known to be very fast. As we proceed to entry no. 21, two model cases of the nucleophilic displacement mechanism, it can first be noted that the nosylate/[nosylate]- couple is electrochemically reversible the radical anion can be generated cathodically and is easily detected by esr spectroscopy (Maki and Geske, 1961). Hence its E° = —0.61 V is a reasonably accurate value. E° (PhS /PhS-) is known with considerably less accuracy since it refers to an electrochemically irreversible process (Dessy et al., 1966). The calculated rate constant is therefore subject to considerable uncertainty and it cannot at present be decided whether the Marcus theory is compatible with this type of electron-transfer step. In the absence of quantitative experimental data, the same applies to entry no. 22 of Table 17. For the PhS-/BuBr reaction we again suffer from the inaccuracy of E° (PhS /PhS-) what can be concluded is that for an electron-transfer step to be feasible the higher E° value (—0.74 V) should be the preferred one. The reality of an electron-transfer mechanism has certainly been strongly disputed, however (Kornblum, 1975). [Pg.171]

Just remember two things. First, when considering molecular properties, we will find that energy is distributed according to this exponential form. Second, thermodynamic quantities can be calculated from these equations they are the essential link between the microscopic molecular world and the macroscopic world of thermodynamic quantities. But let s consider this in a simpler form, Boltzmann s original discovery and formulation of his holy grail —a mathematical description of entropy. We will start by reminding you of the character of spontaneous or irreversible processes. [Pg.292]

Real irreversible processes can be subjected to thermodynamic analysis. The goal is to calculate the efficiency of energy use or production and to show how energy loss is apportioned among the steps of a process. The treatment here is limited to steady-state, steady-flow processes, because of their predominance in chemical technology. [Pg.370]

Kinetic resolution of racemic compounds is by far the most common transformation catalyzed by lipases, in which the enzyme discriminates between the two enantiomeric constituents of a racemic mixture. It is important to note that the maximum yield of a kinetic resolution is restricted to 50% for each enantiomer based on the starting material. The prochiral route and transformations involving meso compounds, the meso-trkk, have the advantage of potentially obtaining a 100% yield of pure enantiomer. A theoretical quantitative analysis of the kinetics involved in the biocatalytic processes described above has been developed. - The enantiomeric ratio ( ), an index of enantioselectivity, can be calculated from the extent of conversion and the corresponding enantiomeric excess (ee) values of either the product or the remaining substrate. The results reveal that for an irreversible process. [Pg.377]


See other pages where Irreversible process calculation is mentioned: [Pg.1126]    [Pg.78]    [Pg.341]    [Pg.392]    [Pg.467]    [Pg.332]    [Pg.139]    [Pg.102]    [Pg.355]    [Pg.355]    [Pg.8]    [Pg.973]    [Pg.143]    [Pg.351]    [Pg.309]    [Pg.366]    [Pg.44]    [Pg.54]    [Pg.107]    [Pg.103]    [Pg.86]    [Pg.84]    [Pg.99]    [Pg.133]    [Pg.137]    [Pg.299]    [Pg.58]    [Pg.191]   
See also in sourсe #XX -- [ Pg.126 , Pg.127 ]




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