Gibbs free energy, hypothetical

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]... 

Coupling-in-series Reactions are said to be coupled-inseries when the product of one reaction is the substrate for the next reaction the principle underlying this coupling is explained by reference to the Gibbs free energy equation. In the reaction A B, in the hypothetical pathway S —> P, reaction A to B is catalysed by enzyme E2 as follows ... 

Figure 3. Hypothetical surface of Gibbs free energy shows G ntLl, n. Additional axes cannot be shown for n/JI and n/Ji in multicomponent mixtures.

The thermodynamic characteristics of solutions are often expressed by means of excess functions. These are the amounts by which the free energy, entropy, enthalpy, etc. exceed those of a hypothetical ideal solution of the same composition (Denbigh, 1981). The excess free energy is closely related to the activity coefficients. The total free enthalpy (Gibbs free energy) of a system is ... 

It is customary to work with the equilibrium constants Kx,KLc, and Km, so that one always refers to free energy changes for the reaction Yi,i ViAi = 0 under the hypothetical constraint of standard conditions. The same applies to the quantities H and V for the chemical reaction under the same conditions. Values of the equilibrium constants can be deduced from tabulations of the Gibbs free energies for all the species engaged in the chemical reactions, which are generally provided in terms of standard conditions. 

Given sufficient time, chemical substances in contact with each other tend to come to chemical equilibrium. Chemical equilibrium is the time-invariant, most stable state of a closed system (the. state of minimum Gibbs free energy). We study chemical equilibrium concepts so as to learn the direction of spontaneous change of chemical reactions in any system, especially for conditions of constant temperature and pressure. We want to be able to compute the hypothetical equilibrium stale of a system. We would like to predict the conditions for equilibrium in different systems and at different temperatures and pressures without having to measure them. 

Figure 2. Gibbs free energy curves for a hypothetical system of polymorphs A, B, and C. The systems are classified as monotropic (forms A and C, forms B and C) or enantiotropic (forms A and B) with a transition temperature, T,. Melting points, T , for the polymorphs are shown by the intersection of the curves for the crystalline and liquid states. Adapted from Rodriguez-Spong et al., (2004) according to the relationships developed by Shalaev and Zografi (2002).

Figure 7.4 A hypothetical Gibbs free energy curve as a function of the number of moles of acetone added to the water.

To put this in other terms, if you have the fugacity of some substance i in some system, then RT In is the difference in Gibbs free energy per mole of i in the system at T and i as an ideal gas at T. Whether i could ever come close to existing as an ideal gas is irrelevant. Other examples of hypothetical standard states are discussed below. 

The thermodynamic relationship between standard state chemical potential differences and the position of chemical equihbrium can be shown graphically. Figure 3.2 illustrates what happens to the Gibbs free energy G when the solute is partitioned between an aqueous phase in contact with an immiscible organic phase, diethyl ether in this example. The hypothetical plots of G versus the mole fraction, denoted by X, of solute i dissolved in the ether phase are superimposed for comparison. When there is no solute in the ether phase, a standard state chemical potential, can be realized. In the other extreme, when 100% of all of the mass of solute is in the ether phase... 

The standard states correspond to a hypothetical ideal gas at atmospheric pressure (101,325 Pa) and a hypothetical ideal 1 M aqueous solution. The standard molar Gibbs free energy, enthalpy, and entropy changes for the above reaction are donated by symbols AG°, AH°. and AS°, respectively. 

Since the short range contribution was developed as a symmetric model, the reference states were pure solvent and completely ionized pure electrolyte, which may be hypothetical. The reference state Gibbs free energies per mole are thus expressed as ... 

AGk, AH, AH thus obtained represent the stoichiometric variations of the Gibbs free energy, enthalpy and entropy, respectively, on the transfer of one mole of solute between the two phases in standard state. AG is the same for the hypothetical ideal state and the real state pro wded that the activity equals unity in both. However AHJ is different in the two cases and reference should be made to the hypothetical ideal state. Because the intermolecular attractions which determine AH are identical in the hypothetical (standard) and reference states, AH refers also to the modification of partial molar enthalpy between the reference states. The same conclusion holds true for the modification of molar heat capacities. A/Sk, like AGk, does not apply to the modification of partial molar entropy between reference states but refers to the hypothetical standard state described above. 

Figure 4.7 Calculated Gibbs free energies (in kcal/mol relative to free (PCP)Ir and ester) for the reaction of (PCP)lr with methyl acetate occurring via a cis methylene hydride intermediate (a hypothetical pathway, not proposed).

Cells metabolize in an aqueous environment and, except for those of the cells, the thermodynamic properties of the reactants and products of growth-processes are those of these substances in aqueous solution. Values for the free energy, enthalpy, and entropy of formation of all substances from the elements at 298.15 K and 1 atm are referred to as thermodynamic properties. These can be found in several compendia [32-34] listed for quantities of one mol in a given standard state. In aqueous solution, all substances are taken to be at a concentration of one mol at unit activity for values of A , and of a hypothetical one mol at infinite dilution for Af//°. Values for Af5" can be calculated using the following form of the Gibbs free energy equation, where the superscript refers to the aqueous standard state. 

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