Enthalpy and Entropy of Formation

The formation of quadruplex structures, whatever their type, is clearly enthalpy driven, with an enthalpy per quartet of —15 to —25 kcal moD For example, concerning intramolecular quadruplexes, the van t Hoff analysis of the melting process of unmodified DNA samples reveals a AH° of 19.8 and 

Bi- and tetramolecular structures also give quite comparable enthalpies. However, the validity of the van t Hoff analysis for some of these quadruplexes is questionable, as the melting curve used to determine thermodynamic parameters rarely corresponds to a true equilibrium curve. We will address this point later in the manuscript. An enthalpy of formation of —21 to —26 kcal mol per quartet is found for the G2T2NT2G2 sequence in comparison to —22.5 kcal mol per quartet measured for the G4T4G4 sequence. Concerning parallel quadruplexes, analysis of the calorimetric or thermokinetic data gives a value of —72 kcal moD (ref. 27) and —76.5 kcal moD (ref. 28) for the TG4T sample 

Despite the negative contribution of entropy to stability, most quadruplex structures are stable under physiological conditions. For example, most intramolecular quadruplexes have a AG° 0 at 37°C in a buffer that mimics intracellular conditions (near neutral pH, high concentration, with or without Mg ). This simply reflects the fact that at physiological temperature the predominant, and sometimes only, species will be the quadruplex structure rather than the single-stranded form. This observation has been well documented for the human telomeric motif. 

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Standard Free Energies, Enthalpies, and Entropies of Formation of Palladium and Nickel Hydrides ... 

Carell and Olin (58) were the first to derive thermodynamic functions relating to beryllium hydrolysis. They determined the enthalpy and entropy of formation of the species Be2(OH)3+ and Be3(OH)3+. Subsequently, Mesmer and Baes determined the enthalpies for these two species from the temperature variation of the respective equilibrium constants. They also determined a value for the species Be5(OH) + (66). Ishiguro and Ohtaki measured the enthalpies of formation of Be2(OH)3+ and Be3(OH)3+ calorimetrically in solution in water and water/dioxan mixtures (99). The agreement between the values is satisfactory considering the fact that they were obtained with different chemical models and ionic media. 

In contrast to stability constants, there are very few data for enthalpies and entropies of complex formation for hydroxypyranonate and hydroxypyridinonate complexes. Early studies on zinc-maltolate (190) and first-row transition metal(II) complexes of kojate (191) gave estimates of enthalpies and entropies of formation from temperature variation of stability constants, though as accurate stability constant measurements are only possible over a rather short temperature range the Aff and AS values obtained cannot be of high precision. 

The enthalpies and entropies of formation of mono-mandelato-complexes have been determined and, in comparison with other hydroxycarboxylic acid complexes, the enthalpy order of stabilization is lactate > a-hydroxyiso-butyrate mandelate > glycolate, whereas the entropy order of stabilization is glycolate > a-hydroxyisobutyrate > mandelate > lactate. The stability constants and enthalpy of formation of mono- and di-malonate complexes have also been measured.The mono-1,1-cyclopentanedicarboxylato-complexes are less stable than the corresponding malonate species. 

Tab. 8.1 Standard free energies, enthalpies and entropies of formation of the iron oxides at 0.1 MPa and 298 K...

The enthalpy and entropy of formation at the melting point are calculated from Eq. (127) using standard thermodynamic formulas. 

Other features of this behavior are illustrated concretely using the Hg-Te system. The calculations were made using values for the thermodynamic properties that are slightly different than those shown in Table VII and used in the calculations described in the main text. Thus the calculations are not quite correct for Hg-Te but are still valid for illustrative purposes. The enthalpy of fusion is taken as 8,680 cal/mol and the enthalpy and entropy of formation of HgTe(s) at 943. as -13,933 cal/mol and —9.538 cal/°K mol, respectively. After applying the constraints of Eqs. (109)—(111) and setting / 13 = / 14 = / 34 = 0, the independent model parameters are z, SlR, and SlA. The former... 

The data required for method II are the measurable quantities AGf°[ij] and, if Kn is not 0, AHmn, Tmn, and Cps[n] and an extrapolated quantity Cp[n], To make use of available data, the standard Gibbs energy of formation can be expressed in terms of the standard enthalpy and entropy of formation. The advantage of this formulation is that thermodynamic information for unstable or metastable systems is required only for the elements (i.e., Cp[n]), for which a better estimate can usually be made. This data base contains no explicit liquid-solution properties. 

Table 3.1.2 Values of the standard enthalpies and entropies of formation for the products and reactants of the chemical reaction proceeding in the electrochemical cell of Figure 3.1.5, see Equation (8). Note that the listed values for H+soin are zero because by convention the hydrogen electrode under standard condition is the reference system.

Enthalpy and entropy of formation of rare earth complexes. ... 

Defining enthalpy and entropy of formation according to the definition of Gibbs free energy, we have... 

Table 2.7. Decomposition temperature, enthalpy and entropy of formation for some hydroxides and hydrated oxides [30-32].

Many other examples of steric effects are compiled in recent equilibrium data (17) j and many of the observed effects are apparently due to enthalpies and entropies of formation of the free ligand in solution. For this reason, more reliable data on heats and entropies of chelate formation and on heats and entropies of formation of metal ions and ligands in solution should be accumulated for developing further understanding of the chelate effect. 

Measurements of the temperature dependence of the hydrogen pressure in equilibrium with the two hydrides 296,297) and heat capacity measurements at low temperatures 296) have yielded standard enthalpies and entropies of formation for the two compounds at 298 K. 

The standard enthalpy and entropy of formation of GaP were derived from composition and vapour-pressure measurements along the Ga-rich liquidus of the Ga-P system.515... 

What are the equations for computing the Gibbs free energy, enthalpy, and entropy of formation of a binary symmetrical regular solution How are the rational activity coefficients (/I values for the solid components) related to their mole fractions in such a solid solution ... 

An attempt to determine the enthalpy and entropy of formation of InSe(cr) was made by Mustafaev, Azizov, Aliev, and Abbasov [74MUS/AZ1] from electrochemical cell measurements in the temperature range 510 to 710 K. However, the reported values were obtained using thermochemical data of the non-existent phase ln5Se6(s) and are... 

Table V-65 Enthalpy and entropy of formation of CO vSe(s). All values except that in [74M1L], which is a re-assessment of the experimental work in [69LAF/CER], were recalculated by the review from high temperature measurements as discussed in Appendix A.

The Gibbs energy of formation is calculated from the selected enthalpy and entropy of formation to be ... 

The reported values of the enthalpy and entropy of formation were only tabulated at a temperature of 700 K and a recalculation to 298.15 K has been made by the review. 

Table A-91 Enthalpy and entropy of formation of Coi jSe(cr). The last column gives the estimated value of the mean heat capacity in the temperature interval 298.15 to 700 K.

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