Reversible transformation free energy change

The equality is valid if the control parameter is changed reversibly, i.e., if the system is in equilibrium at all times during the transformation. Equivalently, this result can be stated as the maximum work theorem [34] the amount of work delivered by a system during a transformation from a specific initial to a specific final state is always smaller than the free energy difference between the initial and final states. The work is maximum and equal to the free energy difference for a reversible process, hence the term reversible work for the equilibrium free energy. 

The transformation of Hg (1) to Hg (g) at temperature 433 K and at the corresponding equilibrium pressure 4.19 mm Hg will be reversible in nature. Thus DG for this process will be equal to zero. But there will occur a change of free energy when the pressure of Hg (g) is changed from 4.19 mm Hg to 760 mm Hg which can be calculated using the expression... 

The free energy functions are defined by explicit equations in which the variables are functions of the state of the system. The change of a state function depends only on the initial and final states. It follows that the change of the Gibbs free energy (AG) at fixed temperature and pressure gives the limiting value of the electrical work that could be obtained from chemical transformations. AG is the same for either the reversible or the explosively spontaneous path (e.g. H2 -I- CI2 reaction) however, the amount of (electrical) work is different. Under reversible conditions... 

The conditions and kinetic equations for phase transformations are treated in Chapters 17 and 20 and involve local changes in free-energy density. The quantification of thermodynamic sources for kinetically active interface motion is approximate for at least two reasons. First, the system is out of equilibrium (the transformations are not reversible). Second, because differences in normal component of mechanical stresses (pressures, in the hydrostatic case) can exist and because the thermal con-... 

Figure 4.20 shows the correlation of experimental data of Hammerschmidt (1939) with five inhibitors with the pressure and temperature axes reversed from their normal position. The striking feature of Figure 4.20 is the parallel nature of all experimental lines, for the inhibition effect of both alcohols and salts relative to pure water. The parallel solid lines provide some indication of the molecular nature of the inhibition. Normally a phase transformation is considered relative to the change in Gibbs free energy defined as ... 

Calculate the change in Gibbs free energy for reversible and spontaneous phase transformations (Section 13.7, Problems 31-34). 

There are several important aspects about which Figures 1 and 2 tell little or nothing (1) the reversibility of the reactions (2) the probability of metastable, rather than the stable (free energy-wise), mineral species formation (3) the rate at which the mineral transformations will occur in response to pH-Eh changes (4) the eflFect of solid solution (both anions and cations) and (5) the eflFect of complex ion formation. All of these aspects are important for a quantitative description of the solution concentration of heavy metals in dynamic systems. The particle size of the hydrous oxides aflFects several of the above items, particularly (2) and (3). Microbiological activity is undoubtedly important with regard to the occurrence of metastable oxide species. 

The thermodynamic changes for reversible, free, and intermediate expansions are compared in the first column of Table 5.1. This table emphasizes the difference between an exact differential and an inexact differential. Thus, U and H, which are state functions whose differentials are exact, undergo the same change in each of the three different paths used for the transformation. They are thermodynamic properties. However, the work and heat quantities depend on the particular path chosen, even though the initial and final values of the temperature, pressure, and volume, respectively, are the same in all these cases. Thus, heat and work are not thermodynamic properties rather, they are energies in transfer between system and surroundings. 

For a scientist, the primary interest in thermodynamics is in predicting the spontaneous direction of natural processes, chemical or physical, in which by spontaneous we mean those changes that occur irreversibly in the absence of restraining forces—for example, the free expansion of a gas or the vaporization of a hquid above its boiling point. The first law of thermodynamics, which is useful in keeping account of heat and energy balances, makes no distinction between reversible and irreversible processes and makes no statement about the natural direction of a chemical or physical transformation. 

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