Thermodynamic data reduction

Depending on technical details of the equipment, on the sensitivity of the temperature detector, on measuring temperature, solvent vapor pressure and polymer concentration in the solution drop, a steady state for AT can be obtained after some minutes. The value of AT is the basis for thermodynamic data reduction (see below). If measuring conditions do not allow a steady state, an extrapolation method to AT at zero measuring time can be employed for data reduction. Sometimes a value is used that is obtained after a predetermined time however, this may lead to some problems with knowing the exact polymer concentration in the solution. The extrapolation method is somewhat more complicated and needs experience of the experimentator but gives an exact value of polymer concentration. Both methods are used within solvent activity measurements when polymer concentrations are higher and condensation is faster than in common polymer characterization experiments. A way to avoid these problems is discussed below. 

For a maximum value for the scaled pressure p = 0.1, a reduction in Vj of 10% was calculated when the co-volume parameter was applied to a sphere breaking in half. In general, fragment velocity is lower than that calculated in the ideal-gas case. Baum (1987) recommends that energy E be determined from thermodynamic data (see Section 6.3.2.3) for the gas in question. 

Aluminothermic reduction is one among the few pyrometallurgical processes where the actual process closely follows the route theoretically predicted from thermodynamic data. This characteristic, coupled with the simplicity associated with the whole process, makes it well suited for demonstration experiments. The reduction of magnetite by aluminum is a suitable example in this context. 

There are also voices critical of the rTCA cycle Davis S. Ross has studied kinetic and thermodynamic data and concludes that the reductive, enzyme-free Krebs cycle (in this case the sequence acetate-pyruvate-oxalacetate-malate) was not suitable as an important, basic reaction in the life evolution process. Data on the Pt-catalysed reduction of carbonyl groups by phosphinate show that the rate of the reaction from pyruvate to malate is much too low to be of importance for the rTCA cycle. In addition, the energy barrier for the formation of pyruvate from acetate is much too high (Ross, 2007). 

A detailed theoretical study of the properties of the redox system FeS/FeS2 was carried out in the Department of Geosciences of SUNY Stony Brook (Schoonen et al., 1999). The authors conclude that the hypothetical reduction of CO2 (by the FeS/FeS2 redox pair) formulated in Wachtershauser s early work, and the carbon fixation cycle on the primeval Earth associated with it, probably could not have occurred. This judgement is made on the basis of a theoretical analysis of thermodynamic data other conditions would naturally have been involved if CO had reacted rather than C02. It is not known whether free CO existed in the hydrosphere, or if so, at what concentrations. 

Table 2.1 Thermodynamic data for the reduction of metal oxides in hydrogen at 400 °C [4].

Based upon thermodynamic data given in Table I, oxidant strength decreases in the order NijO > Mn02 > MnOOH > CoOOH > FeOOH. Rates of reductive dissolution in natural waters and sediments appear to follow a similar trend. When the reductant flux is increased and conditions turn anoxic, manganese oxides are reduced and dissolved earlier and more quickly than iron oxides (12, 13). No comparable information is available on release of dissolved cobalt and nickel. 

Reaction (9) generates methyl iodide for the oxidative addition, and reaction (10) converts the reductive elimination product acetyl iodide into the product and it regenerates hydrogen iodide. There are, however, a few distinct differences [2,9] between the two processes. The thermodynamics of the acetic anhydride formation are less favourable and the process is operated much closer to equilibrium. (Thus, before studying the catalysis of carbonylations and carboxylations it is always worthwhile to look up the thermodynamic data ) Under standard conditions the AG values are approximately ... 

The mixed-potential model demonstrated the importance of electrode potential in flotation systems. The mixed potential or rest potential of an electrode provides information to determine the identity of the reactions that take place at the mineral surface and the rates of these processes. One approach is to compare the measured rest potential with equilibrium potential for various processes derived from thermodynamic data. Allison et al. (1971,1972) considered that a necessary condition for the electrochemical formation of dithiolate at the mineral surface is that the measmed mixed potential arising from the reduction of oxygen and the oxidation of this collector at the surface must be anodic to the equilibrium potential for the thio ion/dithiolate couple. They correlated the rest potential of a range of sulphide minerals in different thio-collector solutions with the products extracted from the surface as shown in Table 1.2 and 1.3. It can be seen from these Tables that only those minerals exhibiting rest potential in excess of the thio ion/disulphide couple formed dithiolate as a major reaction product. Those minerals which had a rest potential below this value formed the metal collector compoimds, except covellite on which dixanthogen was formed even though the measured rest potential was below the reversible potential. Allison et al. (1972) attributed the behavior to the decomposition of cupric xanthate. 

The thermodynamic data shown in Figure 21 indicate, post factum, how magnesia and alumina fit the requirements for the UltraCat process. The figure shows values for standard AG for reduction of the sulfate with hydrogen at 980°F to make SO2 for... 

The two-electron reduction of O2 leads to the peroxide ion, 02 , which is stable in basic aqueous solutions as H02 and as hydrogen peroxide, H2O2, in acidic media. Hydrogen peroxide is a very weak acid (pATi = 11.6), which does not lose its second proton in aqueous alkaline solutions (16 < p r2 < 18) [19, 24, 28]. The potential of the two-electron reduction reaction, in acidic and basic aqueous media, has been calculated from thermodynamic data (Scheme 2) ... 

In aqueous solution, thorium exists as Th(IV), and no definitive data have been presented for the presence of lower-valent thorium ions in this medium. The standard potential for the Th(IV)/Th(0) couple has not been determined from experimental electrochemical data. The values presented thus far for the standard reduction potential have been calculated from thermodynamic data or estimated from spectroscopic measurements. The standard potential for the four-electron reduction of Th(IV) ions has been estimated as —1.9 V in two separate references 12. The reduction of Th(OH)4 to Th metal was estimated at —2.48 V in the same two publications. Nugent et al. calculated the standard potential for the oxidation ofTh(III) to Th(IV) as +3.7 V versus SHE, while Miles provides a value of +2.4 V [13]. The standard potential measurements from studies in molten-salt media have been the subject of some controversy. The interested reader is encouraged to look at the summary from Martinot [10] and the original references for additional information [14]. 

The metals of Group 11 all form + l states that vary in their stability with respect to the metallic state. The standard reduction potentials for the couples Cu+/Cu and Ag + /Ag are +0.52 V and +0.8 V, respectively. That for Au + /Au has an estimated value of + 1.62 V. The thermodynamic data for the calculation of the reduction potentials are given in Table 7.18, which also contains the calculated potentials for Cu and Ag. 

S. , J. Manczinger, S. Skold-Jorgensen and K. T6th, Reduction of thermodynamic data by means of the multiresponse maximum likelihood principle, AIChE J. 28 (1982) 21-30. 

Most nitroreductases found in bacteria to date fall into this type I category. Type I nitroreductive transformations may be limited by the first of two electron transfers in a tight sequence of one-electron transfers since the enzymatic rates correlate with the corresponding (ArN02) (see Eq. 14-32) values (Riefler and Smets, 2000). However, it has also been noted that the free energies of the one-electron and two-electron reductions correlate with one another, and therefore this thermodynamic data may not distinguish between the one- vs. two-electron possibilties (Nivinskas et al., 2001). 

Although the entire discussion of electrochemistry thus far has been in terms of aqueous solutions, the same principles apply equaly well to nonaqueous solvents. As a result of differences in solvation energies, electrode potentials may vary considerably from those found in aqueous solution. In addition the oxidation and reduction potentials characteristic of the solvent vary with the chemical behavior of the solvent. as a result of these two effects, it is often possible to carry out reactions in a nonaqueous solvent that would be impossible in water. For example, both sodium and beryllium are too reactive to be electroplated from aqueous solution, but beryllium can be electroplated from liquid ammonia and sodium from solutions in pyridine. 0 Unfortunately, the thermodynamic data necessary to construct complete tables of standard potential values are lacking for most solvents other than water. Jolly 1 has compiled such a table for liquid ammonia. The hydrogen electrode is used as the reference point to establish the scale as in water ... 

Arsenic. The inorganic species arsenate [As(V)] and arsenite [As(III)] were measured in the depth profile of the lake over the seasonal cycle (Figure 6) (32). The relevant reduction and oxidation processes will be briefly considered. The equilibrium constants for the various reactions are calculated on the basis of the thermodynamic data given in refs. 66 and 67. According to the thermodynamic sequence, the reduction of As(V) to As(III) occurs in a p range similar to that of the reduction of Fe(OH)3(s) to Fe(II) (Figure 2). 

Physical chemical studies of dilute alkali metal-ammonia solutions indicate the principal solution species as the ammoniated metal cation M+, the ammoniated electron e , the "monomer M, the "dimer" M2 and the "metal anion" M. Most data suggest that M, M2, and M are simple electrostatic assemblies of ammoniated cations and ammoniated electrons The reaction, e + NH3 - lf 2 H2 + NH2 is reversible, and the directly measured equilibrium constant agrees fairly well with that estimated from other thermodynamic data. Kinetic data for the reaction of ethanol with sodium and for various metal-ammonia-alcohol reductions of aromatic compounds suggest that steady-state concentrations of ammonium ion are established. Ethanol-sodium reaction data allow estimation of an upper limit for the rate constant of e + NH4+ 7, H2 + NH3. 

A modified version of the free-volume theory is used to calculate the viscoelastic scaling factor or the Newtonian viscosity reduction where the fractional free volumes of pure polymer and polymer-SCF mixtures are determined from thermodynamic data and equation-of-state models. The significance of the combined EOS and free-volume theory is that the viscoelastic scaling factor can be predicted accurately without requiring any mixture rheological data. 

We now look at some examples of redox reactions involving simple cations in aqueous solution. Electrochemical terminology will often be encountered, since e.m.f. measurements on electrochemical cells are important sources of thermodynamic data in this area. For example, the reduction potential ° for the half-reaction ... 

Under natural conditions, these organisms derive little energy from nitrate reduction so the total biomass increase is small and slow in comparison to the turnover of reactants. Equilibrium models from thermodynamic calculations can often provide a useful first approximation for a real system. These models are limited by the accuracy and availability of thermodynamic data including temperature, pressure and activity dependencies, knowledge of all pertinent chemical species and related equilibria. 

The various thermodynamic approximations made in the data reductions seem internally consistent, and hopefully valid. The standard entropy of EuCl2(s) estimated as 34.5 eu is in close agreement with the second-law derived value of 32.9+2.4eu. The second-law and third-law enthalpies of sublimation and vaporization also correspond very well. Brewer s estimates (4, 5) of 2300 K 55 kcal/gfw and 24 eu for the boiling point, enthalpy and entropy of vaporization are in good agreement with the values we obtained. 

---