Gibbs free energy composition dependence

For an open system of variable snrface area, the Gibbs free energy must depend on composition, temperatnre, T, pressure, p, and the total snrface area. A ... 

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... 

What Are the Key Ideas Instead of going tu cumpletiun, reactions proceed until the composition of a reaction mixture corresponds to minimum Gibbs free energy. This composition is described by an equilibrium constant that is characteristic of the reaction and depends on the temperature. 

Gibbs free energy of reaction depends on the composition of the reaction mixture and how it changes as the reaction approaches equilibrium. 

The effect of temperature on the equilibrium composition arises from the dependence of the equilibrium constant on the temperature. The relation between the equilibrium constant and the standard Gibbs free energy of reaction in Eq. 8 applies to any temperature. Therefore, we ought to be able to use it to relate the equilibrium constant at one temperature to its value at another temperature. 

To establish how the emf of a cell depends on concentration, we first note that the emf is proportional to the reaction Gibbs free energy (Eq. 2). We already know how AGr varies with composition ... 

As equation 2.4.8 indicates, the equilibrium constant for a reaction is determined by the temperature and the standard Gibbs free energy change (AG°) for the process. The latter quantity in turn depends on temperature, the definitions of the standard states of the various components, and the stoichiometric coefficients of these species. Consequently, in assigning a numerical value to an equilibrium constant, one must be careful to specify the three parameters mentioned above in order to give meaning to this value. Once one has thus specified the point of reference, this value may be used to calculate the equilibrium composition of the mixture in the manner described in Sections 2.6 to 2.9. 

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 ... 

Once the standard Gibbs free energy is known for a reaction, then the effect of composition can also be considered by adding in the concentration-dependent... 

Before discussing all these biopolymer applications, we first take this opportunity to remind the reader that, in general, any thermodynamic variable can be expressed as the sum of two functions, one of which depends only on the temperature and pressure, and another which depends on the system composition (expressed as the mole fraction xt of the /-component). Therefore, for example, the chemical potential fM of the /-component of the system at constant temperature T and pressure p (the general experimental conditions), /. e., partial molar Gibbs free energy (dG/dn TtP may be expressed as (Prigogine and Defay, 1954) ... 

Chemical equilibrium state corresponds to the minimum value of the Gibbs free energy. Hence, the chemical equilibrium composition and the reaction direction can be predicted from the dependence of the Gibbs free energy on the reaction extend. For the reaction... 

Expression (2-58) contains only the Gibbs free energies of the analyte interactions in the column and no eluent-related terms. This means that in ideal systems (in the absence of secondary equilibria effects) the eluent type or the eluent composition should not significantly influence the chromatographic selectivity. This effect could be illustrated from the retention dependencies of alkylbenzenes on a Phenoemenex Luna-C18 column analyzed at various ace-tonitrile/water eluent compositions (Figure 2-13, Table 2-2). 

Consider a physical property (such as the total Gibbs free energy G) of a continuous mixture, the value of which depends on the composition of the mixture. Because the latter is a function of, say, the mole distribution n(x), one has a mapping from a function to (in this case) a scalar quantity G, which is expressed by saying that G is given by afunctional of n(x). [One could equally well consider the mass distribution function m(x), and consequently one would have partial mass properties rather than partial molar ones.] We use z for the label x when in-... 

The activity concept arises from the dependence of the Gibbs free energy on the pressure of a pure substance or on the composition of a solution, regardless of the phase of the system. The discussion just before Equation 14.3 shows that the change in Gibbs free energy when a gas is taken from a reference state to any pressure P is given by... 

The change in Gibbs free energy (AG), which occurs as a system proceeds toward equilibrium, can be expressed as the sum of two terms. The first term is the standard free energy change (A G°), which is fixed for any given reaction. AG° can be calculated from the stoichiometry of the reaction (i.e., how many moles of one compound react with how many moles of another compound) and the standard free energies of the chemicals involved. The second term contains the reaction quotient (Q), which depends on the concentrations of chemicals present. The fact that AG can be expressed in terms of the concentrations of all chemicals present in a system makes it possible to determine in which direction a chemical reaction will proceed and to predict its final composition when it reaches equilibrium. 

The UNIQUAC method of Abrams and Prausnitz divides the excess Gibbs free energy into two parts, the combinatorial part and a part describing the inter-molecular forces. The sizes and shapes of the molecule determine the combinatorial part and are thus dependent on the compositions and require only pure component data. As the residual part depends on the intermolecular forces, two adjustable binary parameters are used to better describe the intermolecular forces. The UNIQUAC equations are about as simple for multicomponent solutions as for binary solutions. Parameters for the UNIQUAC equations can be found by Gmehling, Onken, and Arlt. ... 

The equilibrium constant and the Gibbs free energy of reaction are independent of the composition and pressure of the system but are dependent on the temperature of the system and the choice of the reference pressure. The greater the value of the equilibrium constant (which corresponds to more negative values of the Gibbs free energy of reaction), the further the reaction proceeds to completion. Given a value for the equilibrium constant and the pressure of the system, Eq. (12.10) can be solved to determine the equilibrium composition of the system. In the next section, we discuss how to determine the value of the equilibrimn constant. 

Gibbs free energy as given in the far right-hand side of Equation (146). The chemical potential, jUj, is also an intensive property and its value depends on T, P and the composition of the system. 

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