Some Thermodynamic Terms

The thermodynamic state of a system is defined by a set of conditions that completely specifies all the properties of the system. This set commonly includes the temperature, pressure, composition (identity and number of moles of each component), and physical state (gas, liquid, or solid) of each part of the system. Once the state has been specified, all other properties—both physical and chemical—are fixed. 

The properties of a system—such 2ls P,V, T—are called state functions. The value of a state function depends only on the state of the system and not on the way in which the system came to be in that state. A change in a state function describes a dijference between the two states. It is independent of the process or pathway by which the change occurs. 

For instance, consider a sample of one mole of pure liquid water at 30°C and 1 atm pressure. If at some later time the temperature of the sample is 22°C at the same pressure, then it is in a different thermodynamic state. We can tell that the net temperature change is — 8°C. It does not matter whether (1) the cooling took place directly (either slowly or rapidly) from 30°C to 22°C, or (2) the sample was first heated to 36°C, then cooled to 10°C, and finally warmed to 22°C, or (3) any other conceivable path was followed from the initial state to the final state. The change in other properties (e.g., the pressure) of the sample is likewise independent of path. 

The most important use of state functions in thermodynamics is to describe changes. We describe the difference in any quantity, X, as 

When X increases, the final value is greater than the initial value, so AX is positive-, a decrease in X makes AX a negative value. 

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Some Thermodynamic Terms 15-3 Enthalpy Changes 15-4 Calorimetry 15-5 Thermochemical Equations 15-6 Standard States and Standard Enthalpy Changes Standard Molar Enthalpies of... 

Chemical reaction equilibrium calculations are structured around another thermodynamic term called tlie free energy. Tliis so-callcd free energy G is a property that also cannot be defined easily without sonic basic grounding in tlicmiodynamics. However, no such attempt is made here, and the interested reader is directed to tlie literature. " Note that free energy has the same units as entlialpy and internal energy and may be on a mole or total mass basis. Some key equations and information is provided below. 

It is seen in Eqs. (11) and (12) that the diffusion coefficients are superficially comprised of two factors a frictional term as represented by f12 or f21 and a thermodynamic term 0 /01 or 0p2/0m2. However, some caution should be levelled at this description because the two terms are closely connected as seen by Eqs. (8) and (9) which describe the direct relationship between the gradient of the chemical potential and the frictional term. 

A new approach to the application of group theory in the study of the physical properties of crystals, which is more powerful than the direct method described in Section 15.2, has been developed by Nowick and is described fully in his book Crystal Properties via Group Theory (Nowick (1995)). A brief outline of Nowick s method will be given here. The equilibrium physical properties of crystals are described by constitutive relations which are Taylor expansions of some thermodynamic quantity Yt in terms of a set of thermodynamic variables Xj. Usually, only the first term is retained giving the linear relations... 

For some reactions, especially those involving large molecules, it might be difficult to determine the precise structure and energy levels of the activated complex. In such cases, it can be useful to phrase the transition-state theory result for the rate constant in thermodynamic terms. It does not bring any new information but an alternative way of interpreting the result. This formulation leads to an expression where the preexponential factor is related to an entropy of activation that, at least qualitatively, can be related to the structure of the activated complex. We will encounter the thermodynamic formulation again in Chapter 10, in connection with chemical reactions in solution, where this formulation is particularly useful. 

The above equations, although highly approximate, are uniquely useful because they relate the thermodynamic terms that arise from interactions of solute and solvent molecules (e.g., solute i and solvent p in Eq. 2.33) to the properties (i.e., the S values) of the pure solutes and solvents. Remarkably, the equations provide some guidance on solvent selection applicable not only to the small nonpolar molecules intended by theory but also to species of moderate polarity and size [14]. 

To understand the concepts of thermodynamics we must agree on the meaning of some basic terms discussed below ... 

There are some multifunctional biometals like Mg and Mn(II) the complexes of which are rather labile in both kinetic and thermodynamic terms (Taube 1952 Riedel 2004 Jordan 1994), in spite of their high AC orders. This situation goes beyond the description by Sabatier s principle every (bio-)autocatalytic process promoted by such metal ions is going to have an exit order near 1 at least, summing up to an exit order 1 for snch metals. This also holds for photosynthe-... 

The chapter will assume an understanding of Hess law and the thermodynamic terms enthalpy of formation and free energy, together with some prior knowledge of the structures of ionic solids in terms of the close packing of spheres. 

The importance of thermodynamics in the pharmaceutical sciences is apparent when it is realised that such processes as the partitioning of solutes between immiscible solvents, the solubility of dmgs, micellisation and dmg-receptor interaction can all be treated in thermodynamic terms. This brief section merely introduces some of the concepts of thermodynamics which are referred to throughout the book. Readers requiring a greater depth of treatment should consult standard texts on this subject. ... 

The reliance on experimental H+ values is a significant challenge in producing accurate pKa calculations using some thermodynamic cycles. Relative pKa calculations, which solve for the pKa of one acid in terms of another, are often used [5,20,27-32] to cancel out this error. The calculation is based on the two species in equilibria, where AH+ and BH+ are two acids ... 

With emulsions, nanoemulsions and microemulsions, the surfactant adsorbs at the oil/water (O/W) interface, with the hydrophilic head group immersed in the aqueous phase and leaving the hydrocarbon chain in the oil phase. Again, the mechanism of stabilisation of emulsions, nanoemulsions and microemulsions depends on the adsorption and orientation of the surfactant molecules at the Uquid/liquid (L/L) interface. Surfactants consist of a small number of units and are mostly reversibly adsorbed, which in turn allows some thermodynamic treatments to be applied. In this case, it is possible to describe adsorption in terms of various interaction parameters such as chain/surface, chain solvent and surface solvent. Moreover, the configuration of the surfactant molecule can be simply described in terms of these possible interactions. 

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