Gibbs free energy constant

G = the Gibbs free energy (constant pressure and volume)... 

Gibbs free energy or Gibbs molar free energy molar flow of gas phase acceleration of gravity enthalpy, molar enthalpy, weight enthalpy Henry s constant Planck s constant height horsepower radiation intensity molar flux... 

For spontaneous processes at constant temperature and pressure it is the Gibbs free energy G that decreases, while at equilibrium under such conditions dG = 0. 

We have seen that equilibrium in an isolated system (dt/= 0, dF= 0) requires that the entropy Sbe a maximum, i.e. tliat dS di )jjy = 0. Examination of the first equation above shows that this can only be true if. p. vanishes. Exactly the same conclusion applies for equilibrium under the other constraints. Thus, for constant teinperamre and pressure, minimization of the Gibbs free energy requires that dGId Qj, =. p. =... 

Figure A2.5.2 shows schematically the behaviour of several thennodynamic fiinctions along a constant-pressure line (shown as a dotted line in Figure A2.5.1 )—the molar Gibbs free energy G(for a one-component system the same as...

Figure A2.5.2. Schematic representation of the behaviour of several thennodynamic fiinctions as a fiinction of temperature T at constant pressure for the one-component substance shown in figure A2.5.1. (The constant-pressure path is shown as a dotted line in figure A2.5.1.) (a) The molar Gibbs free energy Ci, (b) the molar enthalpy n, and (c) the molar heat capacity at constant pressure The fimctions shown are dimensionless...

Within the framework of the same dielectric continuum model for the solvent, the Gibbs free energy of solvation of an ion of radius and charge may be estimated by calculating the electrostatic work done when hypothetically charging a sphere at constant radius from q = 0 q = This yields the Bom equation [13]... 

Finally, exchange is a kinetic process and governed by absolute rate theory. Therefore, study of the rate as a fiinction of temperature can provide thennodynamic data on the transition state, according to equation (B2.4.1)). This equation, in which Ids Boltzmaim s constant and h is Planck s constant, relates tlie observed rate to the Gibbs free energy of activation, AG. ... 

Thermodynamics shows that equilibrium constants can be related to Gibbs free energies, AG, by Eq. (3). 

Our discussion so far has considered the calculation of Helmholtz free energies, which a obtained by performing simulations at constant NVT. For proper comparison with expe inental values we usually require the Gibbs free energy, G. Gibbs free energies are obtaini trorn a simulation at constant NPT. 

Having calculated the standai d values AyW and S" foi the participants in a chemical reaction, the obvious next step is to calculate the standard Gibbs free energy change of reaction A G and the equilibrium constant from... 

Figure 4.3a shows schematically how the Gibbs free energy of liquid (subscript 1) and crystalline (subscript c) samples of the same material vary with temperature. For constant temperature-constant pressure processes the criterion for spontaneity is a negative value for AG, where the A signifies the difference final minus initial for the property under consideration. Applying this criterion to Fig. 4.3, we conclude immediately that above T , AGf = Gj - G. is negative... 

The relationship between the chemical equihbrium constant K and the Gibbs free energy is... 

A solution is a single-phase mixture of more than one compound, and the driving force for its spontaneous formation from the pure compounds at constant T and p is the negative Gibbs free energy change of the mixing process, —AG, as... 

As noted above, it is very difficult to calculate entropic quantities with any reasonable accmacy within a finite simulation time. It is, however, possible to calculate differences in such quantities. Of special importance is the Gibbs free energy, as it is the natoal thermodynamical quantity under normal experimental conditions (constant temperature and pressme. Table 16.1), but we will illustrate the principle with the Helmholtz free energy instead. As indicated in eq. (16.1) the fundamental problem is the same. There are two commonly used methods for calculating differences in free energy Thermodynamic Perturbation and Thermodynamic Integration. 

A = work function (Helmholtz free energy), Btu/lb or Btu C = heat capacity, Btu/lb °R Cp = heat capacity at constant pressure = heat capacity at constant volume F= (Gibbs) free energy, Btu/lb or Btu g = acceleration due to gravity = 32.174 ft/s ... 

This expression shows that the maximum possible useful work (i.e., reversible work) that can be obtained from any process occurring at constant temperature and pressure is a function of the initial and final states only and is independent of the path. The combination of properties U + PV - TS or H - TS occurs so frequently in thermodynamic analysis that it is given a special name and symbol, F, the free energy (sometimes called the Gibbs Free Energy). Using this definition, Equation 2-143 is written... 

Integration of this requires a limit to be defined. The limit is taken simply as follows. We define a standard pressure p at which the Gibbs free energy has a standard value G. We have thereby defined a standard state for this component of the system a standard temperature too, is implicit in this since the above equations are treated for constant temperature. 

Fig. 16. A. Plot of log iNa as a function of T 1 (°K) using the experimental values of the rate constants and the location of the binding sites in Eq. 4. The Gibbs free energy of activation is calculated from Eq. 3 the AS are taken to be zero, and the current is calculated by means of Eq. 4. The purpose is to demonstrate that multibarrier channel transport can be seen as single rate process with average values for the enthalpies of activation. Non-linearity of such a plot is then taken to arise form the dynamic nature of the channel.

The equilibrium constant of a reaction can be related to the changes in Gibbs Free Energy (AG), enthalpy (AH) and entropy (AS) which occur during the reaction by the mathematical expressions ... 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

Since these mixing processes occur at constant pressure, // is the heat evolved or absorbed upon mixing. It is usually measured in a mixing calorimeter. The excess Gibbs free energy, is usually obtained from phase equilibria measurements that yield the activity of each component in the mixtureb and S is then obtained from equation (7.17). The excess volumes are usually obtained... 

These techniques are known as linear free energy relations, LFER. Imagine that one has determined the rate constants, or the Gibbs free energies of activation, for a series of reactions. The reactions are all the same, save for (for example) a different substituent on each reactant. The substituent is not a direct participant in the reaction. In an LFER, the values of log k or AG are correlated with some characteristic of the substituent as manifested in another reaction series. If the correlation is successful, then the two series of reactions have a common denominator. This technique has proved to be a powerful one for systematizing reactivity. We shall see a number of such correlations. 

FIGURE 7.24 At constant temperature and pressure, the direction of spontaneous change is toward lower Gibbs free energy. The equilibrium state of a system corresponds to the lowest point on the curve. 

FIGURE 7.26 For some substances and at certain pressures, the molar Gibbs free energy of the liquid phase might never lie lower than those of the other two phases. For such substances, the liquid is never the stable phase and, at constant pressure, the solid sublimes when the temperature is raised to the point of intersection of the solid and vapor lines. 

The change in Gibbs free energy for a process is a measure of the change in the total entropy of a system and its surroundings at constant temperature and pressure. Spontaneous processes at constant temperature and pressure are accompanied by a decrease in Gibbs free energy. 

The decrease in Gibbs free energy as a signpost of spontaneous change and AG = 0 as a criterion of equilibrium are applicable to any kind of process, provided that it is occurring at constant temperature and pressure. Because chemical reactions are our principal interest in chemistry, we now concentrate on them and look for a way to calculate AG for a reaction. 

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