Reversibility conditions for

The inequality accounts for irreversibilities that occur in practical systems. The theoretical, maximum attainable work must be extracted under reversible conditions for which equality holds ... 

Entropy change for the system is q/T under reversible conditions. Therefore, A y = q/T = 24,050/298.15 = -1-80.67 J K" mol". Maximum work, w is obtained under reversible conditions for the entire system (e.g., chemical reaction and an external circuit for electric work), when the internal entropy change is zero. Then, w = -AG = -(A - TA5sys) = 79.88 kJ mol... 

Since the enzyme reaction is reversible, conditions for the synthesis of Neu5Ac and natural or synthetic derivatives in high yield as well as of Kdn with the aid of bacterial lyase were elaborated (see section 6.1). The recombinant and overexpressed sialate-pyruvate lyase from E. coli is now in wide use as a speeific chiral catalyst which mediates highly enantioselective aldol condensation reactions leading to a variety of sialic acids. 

Unfortunately, most candidate distributions don t satisfy the reversibility condition. For some 0 and 0 ... 

Figure 13.16 shows two possible thermal profiles for endothermic plug-fiow reactors. This time the temperature falls for low rates of heat addition and/or high heat of reaction. The temperature rises for the reverse conditions. Under conditions between the profiles shown in Fig. 13.16, a minimum can occur in the temperature profile at an intermediate point between the inlet and exit. 

Direct property prediction is a standard technique in drug discovery. "Reverse property prediction can be exemplified with chromatography application databases that contain separations, including method details and assigned chemical structures for each chromatogram. Retrieving compounds present in the database that are similar to the query allows the retrieval of suitable separation conditions for use with the query (method selection). 

Attack on the electrophilic C-2 may occur as in the 2-aminothiazoles series, which probably explains the rearrangements observed in acidic medium (121, 711, 712, 723, 724), in aqueous medium with NaOAc (725), or with aqueous NaHCOj (725) (Scheme 232). That the initial attack probably involves the C-2 atom is substantiated by the fact that this rearrangement occurs under extremely mild conditions for 2-iinino-3-substituted-5-nitro-4-thiazolines (725). As the whole mechanism proposed (see p. 92) is reversible, when imino derivatives are submitted to such rearrangement conditions the rearrangement is expected to occur faster if steric interaction between 3- and 4-substituents exists in the 2-imino isomer. Another reaction may occur in acidic medium phenylimino-2-bipheny]-3,4-4-thiazoline hydrolyzed with hydrochloric acid gives the corresponding 4-thiazoline-2-one and aniline (717). 

Many of these reactions are reversible, and for the stronger nucleophiles they usually proceed the fastest. Typical examples are the addition of ammonia, amines, phosphines, and bisulfite. Alkaline conditions permit the addition of mercaptans, sulfides, ketones, nitroalkanes, and alcohols to acrylamide. Good examples of alcohol reactions are those involving polymeric alcohols such as poly(vinyl alcohol), cellulose, and starch. The alkaline conditions employed with these reactions result in partial hydrolysis of the amide, yielding mixed carbamojdethyl and carboxyethyl products. 

If all the components have the same elastic constants,the condition for reversed yielding is the same as that given by equation 20. 

Once the mass flux G has been determined. Fig. 6-21r or Q>-2 h can be used to determine the pressure at any point along the pipe, simply by reducing 4fL/D and computing p From the Figures, given G, instead of the reverse. Charts for calculation between two points in a pipe with known flow and known pressure at either upstream or downstream locations have been presented by Loeb (Chem. Eng., 76[5], 179-184 [1969]) and for known downstream conditions By Powley (Can. J. Chem. Eng., 36, 241-245 [1958]). 

Although experimental results could be fitted well with irreversible rate models, ignoring thermodynamic facts could be disastrous. Although reversibility moderated the maximum temperature at runaway, it was not the most important qualitative result. In fact, the one dimensional (directional, or irreversible, correctly) model was not realistic at these conditions. For the prediction of incipient runaway and the AT ax permissible before runaway, the reversibility was obviously important. 

The relative stability of the intermediates determines the position of substitution under kinetically controlled conditions. For naphthalene, the preferred site for electrophilic attack is the 1-position. Two factors can result in substitution at the 2-position. If the electrophile is very bulky, the hydrogen on the adjacent ring may cause a steric preference for attack at C-2. Under conditions of reversible substitution, where relative thermodynamic stability is the controlling factor, 2-substitution is frequently preferred. An example of this behavior is in sulfonation, where low-temperature reaction gives the 1-isomer but at elevated temperatures the 2-isomer is formed. ... 

The turbine exit condition (for reversible cooled cycles)... 

As an illustration of the biased sampling method in application to the problems of polymer chain adsorption on a hard wall we shall recall here briefly the procedure used on a diamond lattice [35]. Starting the chain at the origin, the first bond is fixed at the plane and all the following bonds are determined at random apart from the non-reversal condition. Suppose, after a certain number i of steps, that the (/+l)st monomer reaches the plane at z = 0 again. With = 4 on the diamond lattice one has the probability p = /3 for each new possible choice of a bond. Thus in... 

The efficiency of these inhibitors may depend on reaction conditions. For example the reaction of radicals with stable radicals (e.g. nitroxides) may be reversible at elevated temperatures (Section 7.5.3) triphenylmethyl may initiate polymerizations (Section 7.5.2). A further complication is that the products may be capable of undergoing further radical chemistry. In the case of DPPH (22) this is attributed to the fact that the product is an aromatic nitro-compound (Section 5.3.7). Certain adducts may undergo induced decomposition to form a stable radical which can then scavenge further. 

As we have seen before, exact differentials correspond to the total differential of a state function, while inexact differentials are associated with quantities that are not state functions, but are path-dependent. Caratheodory proved a purely mathematical theorem, with no reference to physical systems, that establishes the condition for the existence of an integrating denominator for differential expressions of the form of equation (2.44). Called the Caratheodory theorem, it asserts that an integrating denominator exists for Pfaffian differentials, Sq, when there exist final states specified by ( V, ... x )j that are inaccessible from some initial state (.vj,.... v )in by a path for which Sq = 0. Such paths are called solution curves of the differential expression The connection from the purely mathematical realm to thermodynamic systems is established by recognizing that we can express the differential expressions for heat transfer during a reversible thermodynamic process, 6qrey as Pfaffian differentials of the form given by equation (2.44). Then, solution curves (for which Sqrev = 0) correspond to reversible adiabatic processes in which no heat is absorbed or released. 

E2.16 For an ideal gas under reversible conditions, a differential element of heat can be expressed in the form... 

We have noted previously that the forward and reverse rates are equal at equilibrium. It seems, then, that one could use this equality to deduce the form of the rate law for the reverse reactions (by which is meant the concentration dependences), seeing that the form of the equilibrium constant is defined by the condition for thermodynamic equilibrium. By and large, this method works, but it is not rigorously correct, since the coefficients in the equilibrium condition are only relative, whereas those in the rate law are absolute.19 Thus, if we have this net reaction and rate law for the forward direction,... 

The work done in a reversible compression will be considered first because this refers to the ideal condition for which the work of compression is a minimum a reversible compression would have to be carried out at an infinitesimal rate and therefore is not relevant in practice. The actual work done will be greater than that calculated, not only because of irreversibility, but also because of frictional loss and leakage in the compressor. These two factors are difficult to separate and will therefore be allowed for in the overall efficiency of the machine. 

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