Gibbs-Helmholtz relationship

We use the Gibbs-Helmholtz relationship to obtain the derivatives on the left... 

When an adsorbing surface is exposed to a gas or vapour adsorption will take place, being accompanied by the absorption or evolution of heat. Such thermal changes have already been noted in the extension and contraction of surface films of liquids. Although the direct determination of the surface energy of solid surfaces presents many experimental difficulties yet of its existence there is no doubt. On the adsorption of a gas or vapour a diminution in the free surface energy of the system likewise occurs. From the Gibbs-Helmholtz relationship dcr... 

According to Gibbs-Helmholtz relationship, the Helmholtz energy of mixing of system can be obtained by integrating the internal energy... 

By analogy with free energy, the solvation enthalpy can be represented by the addition of the corresponding enthalpy components, as noted in Eq. 4-9, where each term might be determined a priori by using the Gibbs-Helmholtz relationship (Eq. 4-3) ... 

For the HPLC separation of low molecular weight organic compounds and various biomacromolecules, the near-equilibrium criterion has generally been assumed for the binding and desorption behaviour. Changes in thermodynamic parameters due to polypeptide- or protein-ligate interaction can thus be depicted in terms of the Gibbs-Helmholtz relationship, namely,... 

Finally, once G° (0) is aveiUable as a function of temperature, and S° can be immediately obtained using the appropriate Gibbs-Helmholtz relationships S =... 

If the standard potential of an electrode is known at two or more temperatures, the entropy of the reversible ion can be determined by using a form of the Gibbs-Helmholtz relationship. As seen in 331 the standard entropy change may be expressed in terms of the standard electrode potential, viz.,... 

In the RPC and HlC of peptides and proteins, the near-equilibrium eondition has generally been assumed for binding and desorption. Changes in the thermo-dynamie parameters of the ligand-1 igate interaetion ean thus be depleted in terms of eriteria speeified by the Gibbs-Helmholtz relationship ... 

Equation (3.42) is called the Gibbs-Helmholtz equation. We will find it to be a very useful relationship. A similar derivation would show that... 

The Van t Hoff isotherm establishes the relationship between the standard free energy change and the equilibrium constant. It is of interest to know how the equilibrium constant of a reaction varies with temperature. The Varft Hoff isochore allows one to calculate the effect of temperature on the equilibrium constant. It can be readily obtained by combining the Gibbs-Helmholtz equation with the Varft Hoffisotherm. The relationship that is obtained is... 

The Gibbs-Helmholtz equation (Eq. (3.25) below) can be conveniently used to calculate the enthalpy if the rate of change of Gibbs energy with temperature is known. AS is obtained from Eq. (3.24a) by differentiating it with respect to temperature, so dAG/dT = AS. Substituting back into Eq. (3.24a) gives the relationship... 

Extensive theoretical analyses of the compensatory enthalpy-entropy relationship were first carried out by Leffler and later by Leffler and Grunwald, Exner, and Li. The empirical linear relationship between the thermodynamic or activation parameters AH and AS) directly leads to Eq. 11, where the proportional coefficient p, or the slope of the straight line in Figure 9, has a dimension of temperature. Merging Eq. 11 into the differential form of the Gibbs-Helmholtz Eq. 12 gives Eq. 13 ... 

The Gibbs-Helmholtz equation provides another familiar thermodynamic relationship that is useful in the present context ... 

Starting with the above equations (principally the four fundamental equations of Gibbs), the variables U, S, H, A, and G can be related to p, T, V, and the heat capacity at constant volume (Cy) and at constant pressure (Cp) by the differential relationships summarized in Table 11.1. We note that in some instances, such as the temperature derivative of the Gibbs free energy, S is also an independent variable. An alternate equation that expresses G as a function of H (instead of S) is known as the Gibbs-Helmholtz equation. It is given by equation (11.14)... 

Both K and AGq depend on temperature. The relationship between the equilibrium constant K and temperature is given by the Gibbs-Helmholtz equation, the integrated version of which is... 

Relationships between the thermodynamic functions. The Gibbs-Helmholtz equations. 

Basic Relationships Between the Defect Equilibria and Charge Transfer in Solids 67 The Gibbs-Helmholtz equation states that... 

A similar linear logarithmic relationship, known as a van t Hoff plot, usually exists between adjusted retention data and the reciprocal of column temperature in gas, liquid (constant composition) and supercritical fluid (constant density) chromatography. The effect of temperature on retention is based on the Gibbs-Helmholtz equation and has a sound thermodynamic basis, Eq. (1.9)... 

---