Thermodynamic analyses

Electrical studies The electrical analysis on gum Arabica includes a wide range of studies that extract the electroactive nature of gum specimens. Almost each and every electrical technique is based on electrical conductivity measurement. The electrical conductivity of an electrolyte is given in Equation 12.3, 

The electronic conductivity is due to contributions from negative electrons and positive electron holes and is given in Equation 12.5. 

The ionic conductivity is due to both cation and anion species. The cationic transference number = (o / o. ). The anionic transference number x = 1 - x. Different ionic and electronic contributions to the total conductivity can be measured by an electrolysis experiment with the use of selective blocking electrodes which is for blocking all the conducting ion species but the desired one [16, 22].This is a direct current (d.c.) experiment. 

Impedance spectroscopy Impedance spectroscopy describes the response of a circuit to an alternating current or voltage as a function of frequency. In alternative current (a.c.) theory following Ohm s law given in Equation 12.6, 

As in previous examples, we will make use of an energy landscape to analyze the reaction scheme in (6.1)-(6.4) from a thermodynamic perspective and make the connection with the system dynamics. Since there are two possible paths to go from R + X + Y to Rxy, the complete energy landscape is three dimensional and this makes it difficult to visualize. Fortunately, we do not need the complete picture. It is enough to know how the energy changes along the two possible trajectories those corresponding to reactions (6.1) and (6.3), and to reactions (6.2) and (6.4). A schematic representation of such profiles is presented in Fig. 6.2. 

From Kramer s theory (Van Kampen 1992) and following the same argumentation that lead to Eqs. (3.29) and (3.30), the reaction rates in (6.1)-(6.4) can be written in terms of the various energy levels in the energy profiles of Fig. 6.2 as 

Let us save this result for the time being. Later on it will be useful and we shall interpret it. Just have in mind that it comes from the fact that the forward and backward rates of reactions (6.1) and (6.4) are equal. The same result can be 

Observe that both energy profiles look like the ones previously studied in Chap. 4 (see Fig. 4.4). In Sect. 4.4 we saw that when there is a constant number of molecules jumping between the states corresponding to the three minima of the energy landscape, the stationary state corresponds to thermodynamic equilibrium. Moreover, thermodynamic equilibrium is characterized by equal chemical potentials in all three states. In the present case we have a similar situation a constant number of receptors are switching between different binding states. Thus, when the stationary condition is imposed to both reaction pathways we get 

Notice that the term I r l x exponential of the right-hand side of Eq. (6.60) corresponds to the energy difference between states R + X + Y and Rx + Y. Similarly, the term iXry - ijlr- p y in Eq. (6.60) is the energy difference between states R + X + Y MRy + X, while pi rxy IJ r - pi x I y is the energy difference between states Rxy slMR + X + Y. However, if we substitute Eq. (6.58), we obtain 

The kinetic scheme such as the one shown in figure 4 can be used for an analysis of the thermodynamic aspects of photoredox reactions. In the classical approach, the conversion of the precursor complex [S. ..(2] to the successor complex [S. ..Q ] is treated according to the activated complex formalism  

Insertion of this concept into the general expression for the quenching rate constant (equation 13) leads to equation (17)  

The above equation is usually used to calculate the dependence of the experimental bimolecular quenching constant kq, on the overall free energy change provided that a functional relationship between AG 23 AG 23 

Two options are available to relate these two terms. According to Marcus theory [29], AG depends on AG as follows  

If the quenching of the excited state by a homogeneous family of quenchers having a variable redox potential, the values of X, k23, k32 and Z are assumed to be constant. Hence kq is only the function of the free energy change AG . 

The minimum information covers chemical formula, molecular weight, normal boiling point, freezing point, liquid density, water solubility and critical properties. Additional properties are enthalpies of phase transitions, heat capacity of ideal gas, heat capacity of liquid, viscosity and thermal conductivity of liquid. Computer simulation can estimate missing values. The use of graphs and tables of properties offers a wider view and is strongly recommended. 

Plotting residue curves maps (RCM) allows the designer to anticipate problems by the separation of nonideal mixtures, namely when dealing with homogeneous and heterogeneous azeotropes. By reactor selection, it may foresee problems incurred by the recycle of some reactants. 

The main steps involved in the chemical-reaction network determine the number of reactors and consequently, the number of simple plants. The following approach is useful for the synthesis of a complex plant  

Consider individual plants around each chemical reactor. 

If chemical species are produced in different reactors, consider the possibility of handling these components in a common separation system. 

We reported on the design, development and optimization of a compact self-sustained ATR reactor for the production of about 5 m (STP) h ofhydrogen [79,80]. 

The reactor was thermally integrated by two heat exchangers for the preheating of the air and liquid water fed to the reactor at the expense of the hot reactor outlet stream. 

The reactor operated in a stable maimer over a wide range of operating conditions with both pellets and structured catalysts. 

A conceptual design and selection of an ATR biodiesel processor for a vehicle fuel cell auxiliary power unit were reported by Specchia et al. [81]. Three processor options were compared for H2 production with respect to efficiency, complexity, compactness, safety, controllability and emissions. The ATR with both high-temperature shift (HTS) and low-temperature shift (LTS) reactors showed the most promising results. 

Other simulation studies reported on the differences between ATR and SR fuel processors for liquid hydrocarbons [82]. The results showed that a fuel processor based on the SR technology gives a higher power than an ATR-based fuel processor. However, this higher performance is counterbalanced by a much higher plant complexity, resulting in increased cost and an impact on system controllability and start-up time. 

The main tank is filled with liquid hydrogen from a trailer. Despite the sophisticated heat insulation in any container for cryogenic liquids, the small amount of remaining heat input vfill trigger off a warming process in the tank which causes the liquid in the container to evaporate and the pressure to rise. After a certain pressure build-up time the maximum operating pressure of the tank is reached. The pressure relief valve has to be opened. From this point onwards, gas must be released (boil-off). The container now acts as an open system with gas usually being lost to the environment. 

The first law of thermodynamics for open systems applies the transport of work dl heat dQ mass dm, with its enthalpy h and external energy (kinetic and potential energy) across the system boundaries equals the change in internal energy dtJ and external energy d a in the system. 

There is no work transferred. Neglecting kinetic and potential energy yields  

The conservation of mass states that added mass minus relieved mass equals the 

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Koopal and co-workers [186] have extended this thermodynamic analysis to investigate the competitive wetting of a solid by two relatively immiscible liquids. They illustrate the tendency of silica to be preferentially wet by water over octane, a phenomenon of importance in oil reservoirs. 

Stem layer adsorption was involved in the discussion of the effect of ions on f potentials (Section V-6), electrocapillary behavior (Section V-7), and electrode potentials (Section V-8) and enters into the effect of electrolytes on charged monolayers (Section XV-6). More speciflcally, this type of behavior occurs in the adsorption of electrolytes by ionic crystals. A large amount of wotk of this type has been done, partly because of the importance of such effects on the purity of precipitates of analytical interest and partly because of the role of such adsorption in coagulation and other colloid chemical processes. Early studies include those by Weiser [157], by Paneth, Hahn, and Fajans [158], and by Kolthoff and co-workers [159], A recent calorimetric study of proton adsorption by Lyklema and co-workers [160] supports a new thermodynamic analysis of double-layer formation. A recent example of this is found in a study... 

Schwarz G, Stankowski S and Rizzo V 1986 Thermodynamic analysis of incorporation and aggregation in a membrane Blochim. Blophys. Acta 141-51... 

Yu H-A and M Karplus 1988. A Thermodynamic Analysis of Solvation. ]ouniul of Chemical Physics 89 2366-2379. 

Unfortunately, the number of mechanistic studies in this field stands in no proportion to its versatility" . Thermodynamic analysis revealed that the beneficial effect of Lewis-acids on the rate of the Diels-Alder reaction can be primarily ascribed to a reduction of the enthalpy of activation ( AAH = 30-50 kJ/mole) leaving the activation entropy essentially unchanged (TAAS = 0-10 kJ/mol)" . Solvent effects on Lewis-acid catalysed Diels-Alder reactions have received very little attention. A change in solvent affects mainly the coordination step rather than the actual Diels-Alder reaction. Donating solvents severely impede catalysis . This observation justifies the widespread use of inert solvents such as dichloromethane and chloroform for synthetic applications of Lewis-acid catalysed Diels-Alder reactions. 

The theory predicts high stabilities for hard acid - hard base complexes, mainly resulting from electrostatic interactions and for soft acid - soft base complexes, where covalent bonding is also important Hard acid - soft base and hard base - soft acid complexes usually have low stability. Unfortunately, in a quantitative sense, the predictive value of the HSAB theory is limited. Thermodynamic analysis clearly shows a difference between hard-hard interactions and soft-soft interactions. In water hard-hard interactions are usually endothermic and occur only as a result of a gain in entropy, originating from a liberation of water molecules from the hydration shells of the... 

It has long been known that the adsorption of a gas on a solid surface is always accompanied by the evolution of heat. Various attempts have been made to arrive at a satisfactory thermodynamic analysis of heat of adsorption data, and within the past few years broad agreement has been achieved in setting up a general system of adsorption thermodynamics. Here we are not concerned with the derivation of the various thermodynamic functions but only with the more relevant definitions and the principles involved in the thermodynamic analysis of adsorption data. For more detailed treatments, appropriate texts should be consulted. " ... 

The attitude we adopt in this discussion is that only those chain segments in the middle of the chain possess sufficient regularity to crystallize. Hence we picture crystallization occurring from a mixture in which the concentration of crystallizable units is Xj and the concentration of solute or diluent is Xg. The effect of solute on the freezing (melting) point of a solvent is a well-known result T j, is lowered. Standard thermodynamic analysis yields the relationship... 

B. Linnhoff, Thermodynamic Analysis in the Design of Process Networks, Ph.D. dissertation. University of Leeds, Leeds, U.K., 1979. 

Thermodynamic analysis of this reaction shows favorable energy relations (18). The standard free energy of formation of DPA is 310.5 kj /mol (74.2 kcal/mol) (19). 

Kelvin showed the interdependence of these phenomena by thermodynamic analysis, assuming that the irreversible processes were independent of the reversible ones. This approach was later proved theoretically sound using Onsager s concepts of irreversible thermodynamics (9). 

Each reactant and product appears in the Nemst equation raised to its stoichiometric power. Thermodynamic data for cell potentials have been compiled and graphed (3) as a function of pH. Such graphs are known as Pourbaix diagrams, and are valuable for the study of corrosion, electro deposition, and other phenomena in aqueous solutions.Erom the above thermodynamic analysis, the cell potential can be related to the Gibbs energy change... 

Because some substances may preferentially adsorb onto the surface of the electrode, the composition near the iaterface differs from that ia the bulk solution. If the cell current is 2ero, there is no potential drop from ohmic resistance ia the electrolyte or the electrodes. Yet from the thermodynamic analysis it is seen that there is a measurable cell potential. The question from where this potential arises can be answered by considering the iaterface. 

Real irreversible processes can be subjected to thermodynamic analysis. The goal is to calciilate 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. 

Although the T-s diagram is veiy useful for thermodynamic analysis, the pressure enthalpy diagram is used much more in refrigeration practice due to the fact that both evaporation and condensation are isobaric processes so that heat exchanged is equal to enthalpy difference A( = Ah. For the ideal, isentropic compression, the work could be also presented as enthalpy difference AW = Ah. The vapor compression cycle (Ranldne) is presented in Fig. H-73 in p-h coordinates. 

The protonation equilibria for nine hydroxamic acids in solutions have been studied pH-potentiometrically via a modified Irving and Rossotti technique. The dissociation constants (p/fa values) of hydroxamic acids and the thermodynamic functions (AG°, AH°, AS°, and 5) for the successive and overall protonation processes of hydroxamic acids have been derived at different temperatures in water and in three different mixtures of water and dioxane (the mole fractions of dioxane were 0.083, 0.174, and 0.33). Titrations were also carried out in water ionic strengths of (0.15, 0.20, and 0.25) mol dm NaNOg, and the resulting dissociation constants are reported. A detailed thermodynamic analysis of the effects of organic solvent (dioxane), temperature, and ionic strength on the protonation processes of hydroxamic acids is presented and discussed to determine the factors which control these processes. 

The thermodynamic analysis presented here is an outline of the air-standard Bray ton cycle and its various modifications. These modifications are evaluated to examine the effects they have on the basic cycle. One of the most important is the augmentation of power in a gas turbine, this is treated in a special section in this chapter. 

An interesting and practical example of the use of thermodynamic analysis is to explain and predict certain features that arise in the application of chromatography to chiral separations. The separation of enantiomers is achieved by making one or both phases chirally active so that different enantiomers will interact slightly differently with the one or both phases. In practice, it is usual to make the stationary phase comprise one specific isomer so that it offers specific selectivity to one enantiomer of the chiral solute pair. The basis of the selectivity is thought to be spatial, in that one enantiomer can approach the stationary phase closer than the other. If there is no chiral selectivity in the stationary phase, both enantiomers (being chemically identical) will coelute and will provide identical log(Vr ) against 1/T curve. If, however, one... 

Lee, I. and Wool, R.P, Thermodynamic analysis of polymer adhesion sticker and receptor group effects. J. Polym. Sci. Phys Ed., submitted. 

The heat capacity of a substance is extremely important in thermodynamic analysis involving both the first and second laws. 

The combination of properties U - TS occurs so frequently in thermodynamic analysis that it is given a special name and symbol, namely A, the work fimction or maximum luork (because it represents the maximum work per unit mass, obtainable during any isothermal reversible change in any given system). Therefore, it is seen that... 

A thermodynamic analysis regarding the relation between enthalpy and entropy values on the one hand and non-bulk electrostatic contributions on the other leads to the same result144). 

The synthesis of tantalum and niobium fluoride compounds is, above all, related to the fluorination of metals or oxides. Table 3 presents a thermodynamic analysis of fluorination processes at ambient temperature as performed by Rakov [51, 52]. It is obvious that the fluorination of both metals and oxides of niobium and tantalum can take place even at low temperatures, whereas fluorination using ammonium fluoride and ammonium hydrofluoride can be performed only at higher temperatures. 

The results of a thermodynamic analysis of the interactions in Equations (127) and (128), as presented in [452], show that a coherent shell of tantalum and niobium hydroxides is formed on the surface of the columbite or tantalite during the interaction with sulfuric acid. The formation of the shell drives the process towards a forced thermodynamic equilibrium between the initial components and the products of the interaction, making any further interaction thermodynamically disadvantageous. It was also shown that, from a thermodynamic standpoint, the formation of a pseudomorphic structure on the surface of columbite or tantalite components is preferable to the formation of tantalum and niobium oxysulfates. Hence, the formation of the pseudomorphic phases catalyzes the interaction described by Equation (127) while halting that described by Equation (128). 

The decomposition process can be significantly intensified by the mechanical activation of the material prior to chemical decomposition. Based on a thermodynamic analysis of the system, Akimov and Chernyak [452] showed that the mechanical activation initiates dislocations mostly on the surface of the grains, and that heterogeneities in the surface cause the predominant migration of iron and manganese to the grain boundaries. It is noted that this phenomenon is more pronounced for manganese than it is for iron. 

The thermodynamic analysis of the selectivity of ion exchange with the participation of ions of quaternary ammonium bases [56--58] has shown that an increase in bonding selectivity, when metal ions are replaced by organic ions, which is usually accompanied by an increase in entropy of the system (Table 5). It follows from Table 5 that a drastic increase in bonding selectivity upon passing to a triethylbenzylammonium counterion (the most complex ion) is due to a considerable increase in the entropy of the system. 

Table 5. Thermodynamic analysis of the substitution of ions of quaternary ammonium bases by sodium ions...

The thermodynamic analysis of these systems played an important role in the interpretation of these data and of the high selectivity. It was found that selective sorption of complex organic ions is accompanied by an increase in the entropy of the system (Table 6). 

As a result of thermodynamic analysis it is shown that protein bonding to carboxylic CP exhibiting a local internal chain structure is determined by the entropy factor, whereas, if the arrangement of flexible chain parts on the protein globule is possible, the energetic component predominates. 

The thermodynamic analysis of conformational and structural transformations in the melt at high pressures34 showed that the free volume and free energy minimum required for hydrostatic compression is attained as a result of the transition of the molecules in the melt into a more extended conformation (gauche —> trans transitions) since the extended molecules ensure a more compact packing of the chains at compression. Chain uncoiling leads to a decrease in their flexibility parameter f with increasing pressure p ... 

This model of the structure of orientationally crystallized samples based on experimental data is in good agreement with the results of the foregoing thermodynamic analysis which resulted in relationships describing the formation of two structures, FCC and ECC, during the crystallization of strongly oriented melts of flexible-chain polymers. 

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