Gibbs free energy conditions

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. 

Physical Equilibria and Solvent Selection. In order for two separate Hquid phases to exist in equiHbrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy, G, of a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in two phases. Eor the binary system containing only components A and B, the condition (22) for the formation of two phases is... 

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. 

Under certain p, V, T conditions we can relate the Helmholtz free energy and the Gibbs free energy to work done in the process. To find the relationship between dA and 6u, we write... 

Use the standard Gibbs free energies of formation in Appendix 2A to calculate AG° for each of the following reactions at 25°C. Comment on the spontaneity of each reaction under standard conditions at 25°C. 

The reaction Gibbs free energies are for pH = 7 but otherwise standard conditions.) What amount (in moles) of ATP could be formed if all the Gibbs free energy released in the oxidation of... 

The emf of the Daniell cell for certain concentrations of copper and zinc ions is 1.04 V. What is the reaction Gibbs free energy under those conditions ... 

Because 1 C-V = l J, we can conclude that the Gibbs free energy of reaction A under these conditions is —201 kj because this value is negative, the reaction is spontaneous in the forward direction for this composition of the cell. 

AG° = the molar standard state Gibbs free energy (the change in free energy of a reaction when the products and reactants are maintained at standard conditions)... 

The quantity of primary interest in our thermodynamic construction is the partial molar Gibbs free energy or chemical potential of the solute in solution. This chemical potential reflects the conformational degrees of freedom of the solute and the solution conditions (temperature, pressure, and solvent composition) and provides the driving force for solute conformational transitions in solution. For a simple solute with no internal structure (i.e., no intramolecular degrees of freedom), this chemical potential can be expressed as... 

In order to have a consistent basis for comparing different reactions and to permit the tabulation of thermochemical data for various reaction systems, it is convenient to define enthalpy and Gibbs free energy changes for standard reaction conditions. These conditions involve the use of stoichiometric amounts of the various reactants (each in its standard state at some temperature T). The reaction proceeds by some unspecified path to end up with complete conversion of reactants to the various products (each in its standard state at the same temperature T). 

Whether a reaction is spontaneous or not depends on thermodynamics. The cocktail of chemicals and the variety of chemical reactions possible depend on the local environmental conditions temperature, pressure, phase, composition and electrochemical potential. A unified description of all of these conditions of state is provided by thermodynamics and a property called the Gibbs free energy, G. Allowing for the influx of chemicals into the reaction system defines an open system with a change in the internal energy dt/ given by ... 

The condition for a spontaneous reaction is that the change in the Gibbs free energy must be negative (dG < 0) - a so-called exoergic reaction. 

The local conditions of temperature and pressure, as well as the new energy source in the form of the electrochemical gradient, can all be incorporated into the Gibbs free energy by adding new terms to the chemical potential. Variation of AG and AH with temperature are all standard thermodynamics, although we will resist the temptation to explore them here. 

The stable equilibrium thermodynamic state of a system at constant pressure and temperature is the one with the minimum Gibbs free energy, G. This thermodynamic condition is defined as ... 

The equilibrium state is generated by minimizing the Gibbs free energy of the system at a given temperature and pressure. In [57], the method is described as the modified equilibrium constant approach. The reaction products are obtained from a data base that contains information on the enthalpy of formation, the heat capacity, the specific enthalpy, the specific entropy, and the specific volume of substances. The desired gaseous equation of state can be chosen. The conditions of the decomposition reaction are chosen by defining the value of a pair of variables (e.g., p and T, V and T). The requirements for input are ... 

Thermodynamics predicts under which conditions a catalyst can be reduced. As with every reaction, the reduction will proceed when the change in Gibbs free energy, AG, has a negative value. Equation (2-2) shows how AG depends on pressures and temperature ... 

The computation of chemical equilibria can be posed as an optimization problem with linear side conditions. For any infinitesimal process in which the amounts of species present may be changed by either the transfer of species to or from a phase or by chemical reaction, the change in the Gibbs free energy is... 

Monte Carlo simulations were carried out to determine the free energy curve for the reaction in solution. The simulations were executed for the solute surrounded by 250 water molecules (or 180 DMF molecules) in the isothermal-isobaric ensemble at 25 °C and 1 atm, including periodic boundary conditions. As a consequence, the Gibbs free energy is obtained in this case. There is sufficient solvent to adequately represent the bulk participation in the chemical reaction. 

G is the total Gibbs free energy of the crystal. The condition for equilibrium is that the Gibbs free energy is a minimum,... 

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