Stability and equilibrium

The final tenu applies to the system, for wlrich the heat transfer d Q has a sign opposite to tlrat of d Q, and the temperature of the system T replaces Tsurr, because both must Irave the same value for reversible heat transfer. The second law requires  

Since this relation involves properties only, it must be satisfied for changes in state of any closed system of uniform T and P, without restriction to the conditions of mechanical and tliemial reversibility assumed in its derivation. The inequality applies to every incremental change of the system between nonequilibrium states, and it dictates the direction of change tliat 

Equation (14.62) is so general drat application to practical problems is difficult restricted versions are much more useful. For example, by inspection  

Air isolated system is necessarily constrairredto coirstairt irrtenral energy aird vohurre, aird for such a system it follows directly from dre second law that dre last equation is valid. 

If a process is restricted to occur at constant T aird P, dren Eq. (14.62) nray be wriden  

Composition dependence of free energy, with examples of systems that are (a) unstable and (b) locally stable. Local stability is determined by the sign of the second derivative of free energy with respect to composition. 

This equation can be solved for the fractions of the material that will have each composition (since f = —fa)  

The free energy of the demixed state is the weighted average of the free energies of the material in each of the two states and Tp), neglecting the 

This linear composition dependence of the free energy of the demixed state Tap(0o) results in the straight lines in Fig. 4.5 that connect the free energies and Fp of the two compositions 0a and 0p- The local curvature of 

Ideal mixtures with AUmix = 0 have their free energy of mixing [Eq. (4.13)] convex over the entire composition range, as can be seen in Fig. 4.3. To understand why it is convex, we differentiate Eq. (4.13) with respect to composition 

We are now ready, having concluded the general discussion of Ihe thermophysical properties of mixtures, to consider the third objective of Chemical Engineering Thermodynamics Phase and Chemical Reaction Equilibrium. 

These two areas are of paramount importance in practice design of distillation and extraction columns, gas absorbers, evaporators, reactors, etc. is based on the analytical description of phase or chemical reaction equilibrium and, sometimes, of both. And one rarely finds a chemical plant or refinery where several of these units are not present. 

But what is Ae reason for the existence of two phases in equilibrium with each other Why do two species react to form an equilibrium mixture of products and reactants What is the force that drives these systems into equilibrium  

From the more practical point of view, what is the basis for developing the analytical description of these equilibrium states In previous Chapters, for example, we accepted that when two phases are in equilibrium at a given temperature and pressure, the fugacity of any component in the one phase is equal to that in the other phase. [We used this equality to arrive at a physical interpretation of fugacity in Chapters 9 and 11 to determine vapor pressures of pure fluids in Chapter 10 using equations of state and to calculate gas solubilities in liquids, or solid and liquid solubilities in compressed gases, in Chapter 11.] Where does this equality of fugacities come from  

We will answer these questions and develop the basic equations required for the analytical description of phase and of chemical reaction equilibrium in this Chapter and proceed to apply them in these areas in the ensuing Chapters 13, 14 and IS. 

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Gas, cells, 464, 477, 511 characteristic equation, 131, 239 constant, 133, 134 density, 133 entropy, 149 equilibrium, 324, 353, 355, 497 free energy, 151 ideal, 135, 139, 145 inert, 326 kinetic theory 515 mixtures, 263, 325 molecular weight, 157 potential, 151 temperature, 140 velocity of sound in, 146 Generalised co-ordinates, 107 Gibbs s adsorption formula, 436 criteria of equilibrium and stability, 93, 101 dissociation formula, 340, 499 Helmholtz equation, 456, 460, 476 Kono-walow rule, 384, 416 model, 240 paradox, 274 phase rule, 169, 388 theorem, 220. Graetz vapour-pressure equation, 191... 

The ionization state of the coenzyme is also important. During reduction a charged pyridinium species is created while during oxidation the charge is lost. Thus, more polar environments favor reduction while more hydrophobic conditions favor oxidation [69]. Therefore the apoenzyme environment and model system scaffolds must not only enhance the reactivity of the coenzyme, but must also address these issues of equilibrium and stability. 

It is proposed that in mixed organic base-alkali systems, the presence of the organic base changes the solid-liquid equilibrium and stabilizes larger sol-like aluminosilicate species ( 25 m/ ). The alkali ion affects agglomeration of the sol particles to larger amorphous precipitate particles from 100 to 500 min size which subsequently crystallize to zeolite. 

Conditions of equilibrium and stability the phase rule be determined. The energy of each phase is given in differential form by... 

In general, any substance that is above the temperature and pressure of its thermodynamic critical point is called a supercritical fluid. A critical point represents a limit of both equilibrium and stability conditions, and is formally delincd as a point where the first, second, and third derivatives of the energy basis function for a system equal zero (or, more precisely, where 9P/9V r = d P/dV T = 0 for a pure compound). In practical terms, a critical point is identifled as a point where two or more coexisting fluid phases become indistinguishable. For a pure compound, the critical point occurs at the limit of vapor-Uquid equilibrium where the densities of the two phases approach each other (Figures la and lb). Above this critical point, no phase transformation is possible and the substance is considered neither a Uquid nor a gas, but a homogeneous, supercritical fluid. The particular conditions (such as pressure and temperature) at which the critical point of a substance is achieved are unique for every substance and are referred to as its critical constants (Table 1). 

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