Gibbs free-energy function

Thus, values for C°p m T, S°m T, (H°m T - H°m 0) and (G°mT H°m0) can be obtained as a function of temperature and tabulated. Figure 4.16 summarizes values for these four quantities as a function of temperature for glucose, obtained from the low-temperature heat capacity data described earlier. Note that the enthalpy and Gibbs free energy functions are graphed as (// , T - H°m 0)/T and (G T — H q)/T. This allows all four functions to be plotted on the same scale. Figure 4.16 demonstrates the almost linear nature of the (G°m T H°m 0)/T function. This linearity allows one to easily interpolate between tabulated values of this function to obtain the value at the temperature of choice. 

Table 4.3 summarizes values taken from the JANAF tables for the Gibbs free energy functions and standard enthalpies of formation for a few common substances. The JANAF tables provide a more complete tabulation. 

Example 4.1 Use the Gibbs free energy functions from Table 4.3 to calculate ArG° at 1000 K for the reaction... 

The tools for calculating the equilibrium point of a chemical reaction arise from the definition of the chemical potential. If temperature and pressure are fixed, the equilibrium point of a reaction is the point at which the Gibbs free energy function G is at its minimum (Fig. 3.1). As with any convex-upward function, finding the minimum G is a matter of determining the point at which its derivative vanishes. 

Application to Macromolecular Interactions. Chun describes how one can analyze the thermodynamics of a particular biological system as well as the thermal transition taking place. Briefly, it is necessary to extrapolate thermodynamic parameters over a broad temperature range. Enthalpy, entropy, and heat capacity terms are evaluated as partial derivatives of the Gibbs free energy function defined by Helmholtz-Kelvin s expression, assuming that the heat capacities integral is a continuous function. 

Cells are isothermal systems—they function at essentially constant temperature (they also function at constant pressure). Heat flow is not a source of energy for cells, because heat can do work only as it passes to a zone or object at a lower temperature. The energy that cells can and must use is free energy, described by the Gibbs free-energy function G, which allows prediction of the direction of chemical reactions, their exact equilibrium position, and the amount of work they can in theory perform at constant temperature and pressure. Heterotrophic cells acquire free energy from nutrient molecules, and photosynthetic cells acquire it from absorbed solar radiation. Both kinds of cells transform this... 

In a recent paper Shapiro Shapley [4] have considered the problem of the uniqueness of equilibrium of systems of reactions in several phases in great detail. The computation of equilibrium compositions by direct minimization of the Gibbs free energy function has proved a valuable tool in the discussion of very complex systems and it is important to show that this minimum is unique and achieved under the same conditions that satisfy the mass action laws. This is what Shapiro Shapley have done Sellers has suggested some improvements [5]. 

For Landau free energy (m = 0, - the order parameter), Zt is a partition function of an extended system with additional variable . The integral denoted in square brackets in Eq. (3-12) is simply the configurational partition function of the system with a fixed value of -Z. The statistical definition of the Gibbs free energy function combined with Eq (12) results in the following expression ... 

This chapter has presented the basics of how thermodynamics are treated for biochemical systems, with an emphasis on the impact of pH and ion binding on apparent equilibria and Gibbs free energy functions. This field owes much to the work of Robert Alberty an extensive study of the field is presented in Alberty s text, Thermodynamics of Biochemical Systems [4], In our study of the theory and simulation of biochemical systems, we will usually be concerned with biochemical reactants such as ATP and ADP, although the detailed breakdown of these reactants into individual species will be important for many applications. 

To avoid explicit reference to the system s entropy we make use of the differentiated form of the Gibbs free energy function. We thus obtain... 

Important as the Gibbs free energy function is in equilibrium thermodynamics. it is of somewhat limited use for our purposes since most practical processes don t have the same pressure and temperature in all streams and vessels. We therefore need an alternative way to express the work equivalent in a fluid system. Not too surprisingly, the first and second law s will again be our workhorses. Our system will contain a fluid mixture but is otherwise closed. The environment will be the conditions on the earth s surface, that is, the same as what we typically refer to as the environment. 

This section briefly reviews some elementary aspects of the thermodynamics of chemical reactions, (e.g. Atkins (1978)) which are used to analyze a-Si H. The thermodynamic equilibrium state of a system is described by a minimum of the Gibbs free energy function... 

For the third law evaluations of the reaction enthalpies from mass spectrometric equilibrium measurements the Gibbs free energy functions of the reactants are needed. Likewise the enthalpy functions are needed in order to correct the second law reaction enthalpies obtained at the average temperature of measurement to the desired reference temperature. These thermal functions can be calculated according to standard statistical... 

Scientists of a retiring disposition who make important discoveries, but pubHsh them in journals of limited circulation, tend to be overlooked in their own day and receive appreciation only after they have died, when their innovations have been rediscovered. The work of Willard Gibbs (1839-1903) at Yale University on chemical thermodynamics and statistical mechanics, published in the Transactions of the Connecticut Academy of Sciences, was approved by Clerk Maxwell in 1875, but little known to others in Europe at the time. Yet the Gibbs Free Energy function and the Gibbs equations became standard in chemical thermodynamics student courses from the 1920s onwards. Chemists who work on non-standard topics receive... 

Finally, we introduce the Gibbs (free) energy function via... 

When T and P are held fixed it is appropriate to return to the Gibbs free energy function analogous to Eq. (5.7.3),... 

Fig. 46. Stationary points in the modified Gibbs free energy function over the composition space for multispecies mixtures. Diagram is approximate.

Figure 2.5. Variation of the Gibbs free energy function G and the Gibbs free energy change of the reaction AG for a single reaction in a system of variable composition, for example, reactions in solution.

Define the Gibbs free energy function and state the criterion it provides for the spontaneity of a process (Section 13.7). 

To show this, recall the definition of the Gibbs free energy function G ... 

It was the work of Josiah Willard Gibbs that introduced the concept of the thermodynamics of multi-component systems and applied the ideas to the behavior of chemical systems. A homogenous system is one in which the system properties are uniform throughout. An open system is one in which mass may be transferred between phases. We can then write the fundamental equation defining the Gibbs free energy function, G, for this system. 

The chemical potential provides the fundamental criteria for determining phase equilibria. Like many thermodynamic functions, there is no absolute value for chemical potential. The Gibbs free energy function is related to both the enthalpy and entropy for which there is no absolute value. Moreover, there are some other undesirable properties of the chemical potential that make it less than suitable for practical calculations of phase equilibria. Thus, G.N. Lewis introduced the concept of fugacity, which can be related to the chemical potential and has a relationship closer to real world intensive properties. With Lewis s definition, there still remains the problem of absolute value for the function. Thus,... 

We may then re-define the Gibbs free energy function in terms of instead of n. Hence, the modified state function definition yields ... 

On the other hand, the Gibbs free energy function is defined as G = U+ PV - TS from Equations (104) and (124), which may be expressed as, dG = dU + PdV + VdP - TdS -SdT, and the excess Gibbs free energy, Gs, of the interfacial region in a reversible process, for a completely plane interface can be expressed as... 

This chapter introduces the second law of thermodynamics and THE Gibbs free-energy function. It also discusses the relationship BETWEEN Gibbs free energy and chemical equilibrium. 

---