Equation Helmholtz

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

The partial molar enthalpy for every component i is found from an appropriate form of the Gibbs-Helmholtz equation... 

Gibbs-Helmholtz equation This equation relates the heats and free energy changes which occur during a chemical reaction. For a reaction carried out at constant pressure... 

Helmholtz free energy The maximum amount of energy available to do work resulting from changes in a system at constant volume. See free energy and Gibbs-Helmholtz equation. 

Convert AS° to kJ/K using the relation 1J = 10-3 kj. Finally, calculate AG° from the Gibbs-Helmholtz equation with T = 298 K. 

The Gibbs-Helmholtz equation can be used to calculate the standard free energy of formation of a compound. This quantity, AGf, is analogous to the enthalpy of formation, AH . It is defined as the free energy change per mole when a compound is formed from the elements in their stable states at 1 atm. 

To find AG° at temperatures other than 25°C, use the Gibbs-Helmholtz equation. 

Strategy The first step is to write a balanced equation for the chemical reaction. Then calculate AH° using Table 8.3 (page 209) and AS° using Table 17.1 (page 456). Finally, use the Gibbs-Helmholtz equation to determine AG° at 230°C (3 sig. fig.)... 

As far as the Gibbs-Helmholtz equation is concerned, there is another reason for ignoring the temperature dependence of AH and AS. These two quantities always change in the same direction as the temperature changes (i.e., if AH becomes more positive, so does AS). Hence the two effects tend to cancel each other. 

From Example 17.5 and the preceding discussion, it should be clear that AG°, unlike AH° and AS°, is strongly dependent on temperature. This comes about, of course, because of the T in the Gibbs-Helmholtz equation ... 

A change in reaction conditions can, and often does, change the direction in which a reaction occurs spontaneously. The Gibbs-Helmholtz equation in the form... 

When the temperature of a reaction system is increased, the sign of AG°, and hence the direction in which the reaction proceeds spontaneously, may or may not change. Whether it does or does not depends on the signs of AH° and AS°. The four possible situations, deduced from the Gibbs-Helmholtz equation, are summarized in Table 17.2 (p. 464). 

Strategy This is another application of the Gibbs-Helmholtz equation. Setting AG° = 0 gives AH° = TAS° solving for T gives T = AH°/AS°. Since you know AH° and AS°, T is readily calculated. 

Ghiorso, Albert, 515 Giauque, William, 174 Gibbs, J. Willard, 459 Gibbs-Helmholtz equation The relation AG = AH - TAS, 459,461,474q Gillespie, R. J., 175 Glucose... 

The relation between reaction free energy, temperature, cell voltage, and reversible heat in a galvanic cell is reflected by the Gibbs-Helmholtz equation [Eq. (31)]. 

There is a very important equation relating to the electromotive forces of reversible cells which was deduced independently by J. Willard Gibbs (1875) and H. von Helmholtz (1882), and is usually called the Gibbs-Helmholtz Equation. 

Equations (7), (9), and (10) are different forms of the Gihbs-Helmholtz equation, which is the fundamental equation of electrochemistry. 

Gas, cells, 464, 477, 511 characteristic equation, 131, 239 constant, 133, 134 density, 133 entropy, 149 equilibrium, 324, 353, 355, 497 free energy, 151 ideal, 135, 139, 145 inert, 326 kinetic theory 515 mixtures, 263, 325 molecular weight, 157 potential, 151 temperature, 140 velocity of sound in, 146 Generalised co-ordinates, 107 Gibbs s adsorption formula, 436 criteria of equilibrium and stability, 93, 101 dissociation formula, 340, 499 Helmholtz equation, 456, 460, 476 Kono-walow rule, 384, 416 model, 240 paradox, 274 phase rule, 169, 388 theorem, 220. Graetz vapour-pressure equation, 191... 

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... 

Electropositive adsorbates cause a decrease in the work function, of surfaces while electronegative adsorbates increase O. The variation in with the coverage, 0j, of an adsorbate is described by the Helmholtz equation ... 

Using the Helmholtz equation (2.21) and the initial AO vs 9aik slopes of Fig. 2.4 one computes alkali initial dipole moments P as high as 15 D. 

On the basis of the dipole moment, Paik, values computed from the Helmholtz equation (2.21) and the alkali ion radius one can estimate the effective positive charge, q, on the alkali adatom, provided its coordination on the surface is known. Such calculations give q values between 0.4 and 0.9 e (e.g. 0.86e for K on Pt(lll) at low coverages) which indicate that even at very low coverages the alkali adatoms are not fully ionized.6 This is confirmed by rigorous quantum mechanical calculations.27,28... 

In general Pj is coverage-dependent and also the Helmholtz equation has to be written in its general form ... 

Wagner, 7 Wolkenstein, 279 Work function and absolute potential, 353 and electrochemical promotion, 138 and cell potential, 138, 218 Helmholtz equation, 24 of metals, 139 measurement of, 138 spatial variations, 222 variation with coverage, 24 Working electrode as catalyst, 9 overpotential of, 123... 

Monochromatic Waves (1.14) A monochromatic e.m. wave Vcj r,t) can be decomposed into the product of a time-independent, complex-valued term Ucj r) and a purely time-dependent complex factor expjojt with unity magnitude. The time-independent term is a solution of the Helmholtz equation. Sets of base functions which are solutions of the Helmholtz equation are plane waves (constant wave vector k and spherical waves whose amplitude varies with the inverse of the distance of their centers. 

The surface potential change, besides the surface pressure, is the most important quantity describing the surface state in the presence of an adsorbed substance. However, the significance in molecular terms of this very useful experimental parameter still remains unclear. It is common in the literature to link A% with the properties of the neutral adsorbate by means of the Helmholtz equation" ... 

The EMF values of galvanic cells and the electrode potentials are usually determined isothermally, when all parts of the cell, particularly the two electrode-electrolyte interfaces, are at the same temperature. The EMF values will change when this temperature is varied. According to the well-known thermodynamic Gibbs-Helmholtz equation, which for electrochemical systems can be written as... 

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