Gibbs-Helmholtz expression

Since thermal analyses are usually run under conditions of constant pressure, the underlying thermodynamic equation is the Gibbs-Helmholtz expression ... 

Expressed in this form, the Gibbs-Helmholtz equation is widely used in experimental thermodynamics to determine AH, the enthalpy of a reaction, from the experimentally de-... 

It follows from Eq. (3.1.50) that the product nFE can be expressed by the Gibbs-Helmholtz equation ... 

Gibbs-Helmholtz equation phys chem An expression for the influence of tern perature... 

Applying the well-known Gibbs-Helmholtz equation (Atkins, 1998), we may express the right-hand term of Eq. 3-48 as ... 

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)... 

Another important equation, the Gibbs-Helmholtz equation, is derived from the Maxwell relations. A chemist may use this equation to determine the enthalpy change in a reaction, and a pharmaceutical scientist may use it to calculate colligative properties (i.e., freezing point depression and boiling point elevation). The expression for free energy with respect to temperature at constant pressure is given by Equation (1.105) ... 

These two expressions are forms of the equation derived by J. W. Gibbs (1875) and H. von Helmholtz (1882), and usually referred to as the Gibbs-Helmholtz equation. Upon dividing equation (25.26) by 7, and rear rang-... 

This equation represents the variation of AF, or rather of AF/T, with temperature at constant pressure. If is expressed as a function of the temperature ( 12k), it is thus possible, upon integration, to derive an expression for AF in terms of the temperature. This matter, as well as other applications of the various forms of the Gibbs-Helmholtz equation, will be taken up in later sections. 

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.,... 

One typically starts with an internal energy of a macroscopic system, expressed as the internal energy of the periodically repeated unit cell. This state function is part of another state function H, the enthalpy, which is a very useful energetic measure for conditions of constant pressure p. For a complete picture, one also needs to know the value of the state function T, the temperature, and that of the state function S, the entropy, a measure of chaos and also probability. These functions may be combined to yield the Gibbs energy (or free enthalpy) G, the true and final measure of stability. In its difference form, the so-called Gibbs-Helmholtz formula reads... 

Temperature is flie second parameter that influences the electromotive force. The correlation between and temperature is expressed thermodynamically by the Gibbs—Helmholtz equation ... 

This equation can be arranged to give the Gibbs-Helmholtz equation, an expression which will be very useful in calculating the effect of temperature on equilibrium constants and is given by ... 

Assume that AH changes little with temperature, integrate the Gibbs-Helmholtz equation (5.2.14) and express AGf at temperature Tf in terms of AH, AGi and the corresponding temperature T-,. 

In this form the temperature dependence of the solubility is not explicit because AGfus is itself a function of T. This expression can also be written in terms of the enthalpy of fusion, Afffus, by differentiating it with respect to T and using the Gibbs-Helmholtz equation d AG/T)/dT — —AH/T (5.2.14) ... 

Derive relations for the physical properties of materials whose magnetization follows the Curie-Weiss law M = AxM-ol T + ), where is a parameter, called the Weiss constant. Check on the expression (5.8.14) by basing your derivation on the Gibbs-Helmholtz relation and solving the first-order differential equation. 

Gibbs-Helmholtz equation (physchem) An expression for the influence of temperature upon the equilibrium constant of a chemical reaction, d In K /iJT)p = AfTVRT, where K is the equilibrium constant, AH the standard heat of the reaction at the absolute temperature T, and R the gas constant. gibz helm,holts i,kw5-zh3n )... 

Things are more complicated for equilibria involving gas phases, whose experimental handling sometimes poses severe problems. Using equation 7.53, together with the dependence of AG° from temperature (the Gibbs-Helmholtz equation), the following expressions are obtained for chemical equilibria ... 

The partial molar entoalpy,, for real solution can be expressed in terms of the Gibbs— Helmholtz equation as... 

The relations which permit us to express equilibria utilize the Gibbs free energy, to which we will give the symbol G and which will be called simply free energy for the rest of this chapter. This thermodynamic quantity is expressed as a function of enthalpy and entropy. This is not to be confused with the Helmholtz free energy which we will note sF (L" j (j, > )... 

The excess energy associated with an interface is formally defined in terms of a surface energy. This may be expressed in terms either of Gibbs, G, or Helmholtz, A, free energies. In order to circumvent difficulties associated with the unavoidably arbitrary position of the surface plane, the surface energy is defined as the surface excess [7,8], i.e the excess (per unit area) of the property concerned consequent upon the presence of the surface. Thus Gibbs surface free energy is defined by... 

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