The Reversible Process

The development of thennodynamics is facilitated by introduction of a special kind of closed-system proeess eharaeterized as reversible  

A process is reversible when its direction can be reversed at any point by an infinitesimal change in external conditions. 

The nature of reversible processes is illustrated by the example of a simple expansion of gas in a piston/cylinder arrangement. The apparatus shown in Fig. 2.2 is imagined to exist in an evacuated space. The gas trapped inside the cylinder is chosen as the system all else is the surroundings. Expansion processes result when mass is removed from tlie piston. F or simplicity, assume that the piston slides within the cylinder without friction and that the piston and cylinder neither absorb nor transmit heat. Moreover, because the density of the gas in the cylinder is low and because the mass of gas is small, we ignore the effects of gravity on the contents of the 

The oscillations of the piston assembly are damped out because the viscous nature of the gas gradually converts gross directed motion of tlie molecules into chaotic molecular motion. This dissipative process transforms some of tlie work initially done by the gas in accelerating the piston back into internal energy of tlie gas. Once tlie process is initiated, no infinitesimal change in external conditions can reverse its direction the process is irreversible. 

All processes carried out in finite time with real substances are accompanied in some degree by dissipative effects of one kind or anotlier, and all are therefore irreversible. However, one can imagine processes tliat are free of dissipative effects. For the expansion process of Fig. 2.2, such effects have tlieir origin in tlie sudden removal of a finite mass from tlie piston. The resulting imbalance of forces acting on tlie piston causes its acceleration, and leads to its subsequent oscillation. The sudden removal of smaller mass increments reduces but does not eliminate this dissipative effect. Even tlie removal of an infinitesimal mass leads to piston 

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A particular path from a given initial state to a given final state is the reversible process, one in which after each infinitesimal step the system is in equilibrium with its surroundings, and one in which an infinitesimal change in the conditions (constraints) would reverse the direction of the change. 

Obviously die first law is not all there is to the structure of themiodynamics, since some adiabatic changes occur spontaneously while the reverse process never occurs. An aspect of the second law is that a state fimction, the entropy S, is found that increases in a spontaneous adiabatic process and remains unchanged in a reversible adiabatic process it caimot decrease in any adiabatic process. 

The constant-temperature constant-pressure situation yields an analogous result. One can write for the reversible process... 

The hydration shell is formed with the increasing of the water content of the sample and the NA transforms from the unordered to A- and then to B form, in the case of DNA and DNA-like polynucleotides and salt concentrations similar to in vivo conditions. The reverse process, dehydration of NA, results in the reverse conformational transitions but they take place at the values of relative humidity (r.h.) less than the forward direction [12]. Thus, there is a conformational hysteresis over the hydration-dehydration loop. The adsorption isotherms of the NAs, i.e. the plots of the number of the adsorbed water molecules versus the r.h. of the sample at constant temperature, also demonstrate the hysteresis phenomena [13]. The hysteresis is i( producible and its value does not decrease for at least a week. 

Clearly, for symmetry reasons, the reverse process should also be considered. In fact, early versions of our reaction prediction and synthesis design system EROS [21] contained the reaction schemes of Figures 3-13, 3-15, and 3-16 and the reverse of the scheme shown in Figure 3-16. These four reaction schemes and their combined application include the majority of reactions observed in organic chemistry. Figure 3-17 shows a consecutive application of the reaction schemes of Figures 3-16 and 3-13 to model the oxidation of thioethers to sulfoxides. 

A second disadvantage in the use of topological indices is that whereas the process of transformation of connectivity into one number is straightforward, the reverse process of reconstruction of connectivity from the index is not possible. 

The subscript 0 indicates averaging over the ensemble of configurations represejitativs the initial state X. If the averaging is over the ensemble corresponding to the final stat (indicated by the subscript 1) then we are effectively simulating the reverse process, fi which AA can be determined by ... 

Most of the time we are concerned only with whether a particular reaction is an oxidation or reduction rather than with determining the precise change m oxidation num ber In general Oxidation of carbon occurs when a bond between carbon and an atom that IS less electronegative than carbon is replaced by a bond to an atom that is more electronegative than carbon The reverse process is reduction... 

Many biological processes involve oxidation of alcohols to carbonyl compounds or the reverse process reduction of carbonyl compounds to alcohols Ethanol for example is metabolized m the liver to acetaldehyde Such processes are catalyzed by enzymes the enzyme that catalyzes the oxidation of ethanol is called alcohol dehydrogenase... 

These equations tell us that the reverse process proton transfer from acids to bicarbon ate to form carbon dioxide will be favorable when of the acid exceeds 4 3 X 10 (pK, < 6 4) Among compounds containing carbon hydrogen and oxygen only car boxylic acids are acidic enough to meet this requirement They dissolve m aqueous sodium bicarbonate with the evolution of carbon dioxide This behavior is the basis of a qualitative test for carboxylic acids... 

Under acidic conditions, dehydration to an anhydrotetracycline [20154-34-1] (8), C22H22N20y, occurs under basic ones, ring C opens to an isotetracycline [3811-31-2] (9), C22H24N20g. The anhydrotetracyclines, such as (8), appear to exhibit a mode of antibacterial action, but it is unlike that of tetracycline (24). Epimerization (23,25,26) at C-4 occurs in a variety of solvents within the pH range 2—6, particularly in acetic acid (25). A number of anions (27) facihtate this reaction. The reverse process, from 4-epitetracycline [79-85-6] C22H24N20g, to tetracycline, is promoted by chelation with ions such as calcium and magnesium (28). 

Certain nucleophilic sp ies add to carbonyl groups to give tetrahedral intermediates that are unstable and break down to form a new double bond. An important group of such reactions are those with compounds containing primary amino groups. Scheme 8.2 lists some of the more familiar classes of such reactions. In general, these reactions are reversible, and mechanistic information can be obtained by study of either the forward or the reverse process. 

There are several general classes of pericyclic reactions for which orbital symmetry factors determine both the stereochemistry and relative reactivity. The first class that we will consider are electrocyclic reactions. An electrocyclic reaction is defined as the formation of a single bond between the ends of a linear conjugated system of n electrons and the reverse process. An example is the thermal ring opening of cyclobutenes to butadienes ... 

The principle of microscopic reversibility requires that the reverse process, ring closure of a butadiene to a cyclobutene, must also be a coiuotatory process. Usually, this is thermodynamically unfavorable, but a case in which the ring closure is energetically favorable is conversion of tra s,cis-2,4-cyclooctadiene (1) to bicyclo[4.2.0]oct-7-ene (2). The ring closure is favorable in this case because of the strain associated with the trans double bond. The ring closure occurs by a coiuotatory process. 

Evaporation of liquid to form vapour is accompanied by a considerable increase in volume. For example, at atmospheric pressure one volume of water will generate 1600 volumes of steam. Similarly 4.54 litres of gasoline will yield 0.93 m of neat vapour on complete vaporization. The reverse process, condensation, is accompanied by a considerable - and often rapid - decrease in volume. As a result ... 

The formation of cotar none from cotar nine methine methiodide by the action of potash (IX—X) led Roser to represent cotarnine and its salts by the following formulae, the loss of a molecule of water in the formation of cotarnine salts being explained by the production of a partially reduced pyridine ring, which is fully hydrogenated in the reduction of cotarnine to hydrocotarnine. In the reverse process, oxidation of liydrocotarnine to cotarnine, Roser assumed the scission of the ring at the point indicated, with the formation of a hydration product, and oxidation of the latter to cotarnine thus —... 

On boiling with 25 per cent, hydrochloric acid cphedrine is partially converted into -ephedrine. This change is reversible, an equilibrium mixture of the two bases being formed, though according to Mitchell the commercially desirable conversion of 0-ephedrine into Z-ephedrine is effected with more difficulty than the reverse process. Mitchell also states that when ephedrine is heated with acetic anhydride at 70° for ten minutes it is converted into 0-acetylephedrine,. 2H2O,... 

The total energy of condensation from the ideal gas to the liquid state (the reverse process of vaporization) as a consequence of 1-1 contacts (i.e., intermolecular interactions of component 1 with like molecules) is the product of the energy of condensation per unit volume, the volume of liquid, and the volume fraction of component 1 in the liquid, or... 

In his first work on thermodynamics in 1873, Gibbs immediately combined the differential forms of the first and second laws of thermodynamics for the reversible processes of a system to obtain a single Tundamciital equation ... 

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