Gibbs energy difference

Plotting Oq xct vs then leads to a straight line with an intercept equal to the Gibbs energy difference between the f.c.c. and b.c.c. forms of Cr, at the temperature where measurements were made (Fig. 6.5), while the slope of the line yields the associated regular solution interaction parameter. The lattice stability and the interaction parameter are conjugate quantities and, therefore, if a different magnitude... 

As has been shown by a calculation of the temperature evolution of the Gibbs energy differences in the isomeric Si6H6 (g), at a temperature above 340 K hexasilabenzene (Did structure) becomes relatively more stable than (288) [89CPL(161)175 90JST143]. 

This equilibrium was first studied by Cope et a .54 in 1952. The Gibbs energy difference is small and the rate of interconversion slow at room temperature. Huisgen et al.55 examined the influence of variations of the ethane fragment on the position of the equilibrium. Attachment of a tricarbonyliron moiety apparently causes stabilization of the bicyclo[4.2.0]octadiene system,56 whereas with tricarbonylmolybdenum the monocyclic isomer is isolated as its metal complex.57... 

The Calvin-Benson cycle and the pentose phosphate pathway (Eq. 17-12) have many features in common but run in opposite directions. Since the synthesis of glucose from C02 requires energy, the energy expenditure for the two processes will obviously differ. Describe the points in each pathway where a Gibbs energy difference is used to drive the reaction in the desired direction. 

A fundamental postulate of the chemiosmotic theory is the presence of an oriented ATP synthase that utilizes the Gibbs energy difference of the proton gradient to drive the synthesis of ATP (Fig. 18-9). 

The molar Gibbs energy of micelle formation is the Gibbs energy difference between a mole of monomers in micelles and the standard chemical potential in dilute solution ... 

The Gibbs energy difference of the denatured and native states corresponds to the work required for the transition of a system from the native to the denatured state, i.e., the work of disruption of the native cooperative structure. Therefore, this quantity is usually considered as a measure of the stability of the cooperative structure, i.e., the stability of a small globular protein or cooperative domain. As for the large proteins, their stability cannot be expressed by a single value, but only by a set of values specifying the stability for each domain within these molecules and the interaction between the domains. 

Thus the Gibbs energy difference between the native and denatured protein states is given as... 

The Gibbs energy difference between the native and denatured states is represented by Eq. (8), a function with an extremum (Fig. 6). Its maximum value is reached at the temperature Tm, which can be determined from the condition... 

Since the Gibbs energy difference of the native and denatured states determines the stability of a cooperative unit, it follows from Eq. (11) that the stability of a small globular protein (or a single domain) is maximal at the temperature at which the entropies of the native and denatured states are equal. At this temperature, the structure is stabilized only by the... 

Fio. 6. The Gibbs energy difference of the native and denatured states of myoglobin and ribonuclease A calculated per mole of amino acid residues under the same conditions as indicated in Fig. 4. The dot-and-dash lines represent functions obtained in the assumption that the denaturation heat capacity increment is temperature independent. 

The bracketed difference is the Gibbs energy of the reaction that would occur on direct contact. As the Gibbs energy differs from the reaction enthalpy by TAS (T thermodynamic temperature, AS reaction entropy), a positive AS would result in theoretical efficiencies greater than 100% (then the environment would cool). Usually, those efficiencies are approximately 100%, as AS is negligible. This high theoretical efficiency is another asset of electrochemical conversion devices. 

Gibbs energy of activation A G (standard free energy of activation A G ) (Id mol-1) — The standard Gibbs energy difference between the -> transition state of a reaction (either an elementary reaction or a stepwise reaction) and the ground state of the reactants. It is calculated from the experimental rate constant k via the conventional form of the absolute reaction rate equation ... 

Thus, the Gibbs energy difference AAG for the ionization of a mol of HA in solvent 1 and solvent 2 with relative permittivities er(i) and r(2), respectively, provided that the radii of the reactants are the same in both solvents, is given by Eq. (4-9). 

Table 4-7. Solvent dependence of the relative rotamer population (mole fraction of (30b)) and the standard molar Gibbs energy differences between rotamers of chloroacetaldehyde at 36 °C [87],...

Table 4-9. Solvent dependence of standard molar Gibbs energy differences between cu/fmn -isomers of 2-isopropyl-5-methoxy-l,3-dioxane at 25 °C [89],...

Unlike those for cis/trans isomers, the activation barriers separating s-cis and s-trans isomers are usually small ca. 40... 50 kJ/mol) the Gibbs energy differences for s-cis and s-trans isomers are also small [ca. 4... 20 kJ/mol). For example, a more easily measurable cisitrans isomerization reaction can be carried out with 3-tert-butylaminopropenal (36) [203]. 

Is the calculated temperature at which the Gibbs energy difference is zero for the reaction Cu(t) AjH between gas and liquid at "... 

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